From 83bfc1073bb7926bb7ca402b5c3a3b51f2a3b2d9 Mon Sep 17 00:00:00 2001 From: Francesco Radica <51544149+Francyrad@users.noreply.github.com> Date: Tue, 11 Jun 2024 17:42:31 +0200 Subject: [PATCH 1/7] Add files via upload --- .../ascii_perturbation/ascii_perturbation.prm | 179 + .../documentation/ascii_temperature.png | Bin 0 -> 334131 bytes .../ascii_temperature_aspect.png | Bin 0 -> 243837 bytes .../documentation/perturbation.txt | 36004 ++++++++++++++++ .../documentation/temperature.png | Bin 0 -> 190985 bytes .../documentation/tutorial_a.docx | Bin 0 -> 27089 bytes .../documentation/tutorial_ascii.md | 329 + .../documentation/tutorial_ascii.tex | 328 + cookbooks/ascii_perturbation/perturbation.py | 114 + .../ascii_perturbation/perturbation_ascii.txt | 36004 ++++++++++++++++ cookbooks/ascii_perturbation/~$torial_a.docx | Bin 0 -> 162 bytes .../~$torial_ascii_MERGE.docx | Bin 0 -> 162 bytes 12 files changed, 72958 insertions(+) create mode 100644 cookbooks/ascii_perturbation/ascii_perturbation.prm create mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature.png create mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature_aspect.png create mode 100644 cookbooks/ascii_perturbation/documentation/perturbation.txt create mode 100644 cookbooks/ascii_perturbation/documentation/temperature.png create mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_a.docx create mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.md create mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex create mode 100644 cookbooks/ascii_perturbation/perturbation.py create mode 100644 cookbooks/ascii_perturbation/perturbation_ascii.txt create mode 100644 cookbooks/ascii_perturbation/~$torial_a.docx create mode 100644 cookbooks/ascii_perturbation/~$torial_ascii_MERGE.docx diff --git a/cookbooks/ascii_perturbation/ascii_perturbation.prm b/cookbooks/ascii_perturbation/ascii_perturbation.prm new file mode 100644 index 00000000000..618deb32f05 --- /dev/null +++ b/cookbooks/ascii_perturbation/ascii_perturbation.prm @@ -0,0 +1,179 @@ + +set Dimension = 2 +#set Resume computation = auto +set Start time = 0 +set End time = 5e8 +set Use years in output instead of seconds = true +set Adiabatic surface temperature = 1623 +set Use conduction timestep = true +set Output directory = ascii_perturbation + + +set CFL number = 1 +set Nonlinear solver scheme = single Advection, single Stokes +subsection Solver parameters + subsection Stokes solver parameters + set Linear solver tolerance = 1e-5 + set Number of cheap Stokes solver steps = 2000 # 200 + end +end + +subsection Formulation + set Mass conservation = projected density field + set Temperature equation = real density +end + +subsection Checkpointing + set Steps between checkpoint = 100 +end + + +subsection Geometry model + set Model name = spherical shell + + subsection Spherical shell + set Inner radius = 3481000 + set Outer radius = 6371000 + end +end + + +subsection Boundary temperature model + set Fixed temperature boundary indicators = top, bottom + set List of model names = spherical constant + subsection Spherical constant + set Inner temperature = 3700 + set Outer temperature = 273 + end +end + + +subsection Boundary velocity model + set Tangential velocity boundary indicators = bottom, top +end + + +subsection Gravity model + set Model name = ascii data +end + + +# Here we initialize the temeprature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. + +subsection Initial temperature model + set List of model names = adiabatic, ascii data + subsection Adiabatic + set Age bottom boundary layer = 1e9 + set Age top boundary layer = 1e9 + + subsection Function + set Function expression = 0 + end + + end + +# Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. + + subsection Ascii data model + set Data directory = $ASPECT_SOURCE_DIR/data/cookbooks/ascii_perturbation + set Data file name = perturbation_ascii.txt + end +end + + +subsection Material model + set Model name = Steinberger + set Material averaging = harmonic average + + subsection Steinberger model + + set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ + set Lateral viscosity file name = temp-viscosity-prefactor.txt + set Material file names = pyr-ringwood88.txt + set Radial viscosity file name = radial-visc-simple.txt + set Latent heat = false + + # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". + + set Maximum lateral viscosity variation = 1e2 + set Maximum viscosity = 5e23 + set Minimum viscosity = 1e19 + + + set Use lateral average temperature for viscosity = false + set Thermal conductivity formulation = p-T-dependent + + set Composition viscosity prefactors = 1 + + end +end + + +subsection Heating model + set List of model names = adiabatic heating, shear heating +end + + +# We refine the mesh near the boundaries, and where temperature variations are +# large. In addition, we make sure that in the transition zone, where both the +# viscosity and the density change a lot, we use the highest refinement level. +subsection Mesh refinement + set Initial adaptive refinement = 1 + set Initial global refinement = 5 + set Refinement fraction = 0.95 + set Coarsening fraction = 0.05 + set Strategy = temperature, boundary, minimum refinement function + set Time steps between mesh refinement = 5 + + subsection Boundary + set Boundary refinement indicators = top, bottom + end + + subsection Minimum refinement function + set Coordinate system = depth + set Variable names = depth, phi + set Function expression = if(depth<700000, 6, 5) + end +end + +subsection Boundary temperature model + set Fixed temperature boundary indicators = 0,1 +end + + +subsection Nullspace removal + set Remove nullspace = net rotation +end + +subsection Compositional fields + set Number of fields = 1 + set Names of fields = density_field + set Types of fields = density + set Compositional field methods = prescribed field +end + + + +subsection Initial composition model + set Model name = function + subsection Function + set Variable names = x,y + set Function constants = r_inner=3481000, r_outer=6371000 + set Function expression = if(sqrt(x^2+y^2)NnjvAa1S9saCZ+7+}&+(cZcBa4g&-Y5Fki!cXxLgU~qTYlk2{( z_j&hP&xid3_SBlG9#(hLl$_@wRfH?ZNdVpvyn}&(0Z4xPsssZAZvX=WSA~oS{mIKR zks!2!byAWLfvFfHfP-IOrRC^?z&lT-g7)V=mmkXTuxh!vA{=SM~R@{-6r!yEBAsET8!Yb~tN7+cZreg6gkHLeiJ5g^i6lBWC!r-Ks z%1cU0${OB%0e;n;RDG}8TUB*%@TFqks3&N#w;XQ{HO$`tM)CbC99#lbyW8vfY1xU> zxX-D;?kLkH%QXMx38bQ;w4%aE&TSrYa*!7zQkrL(`@a^0Xe$Hv=u`!i5`zD|R3Vna zs*whj2K;ZOt{}kD{}-j$yiqCQ|5{+xa{ku~O9TG@OaHG1`~Tida}od@-+M4bLhwPc z>3%oUtJG~$47V`n<*L|XFoBZ)tS-IbypM1?*6(Tis#x&(XYqnGL*u9CBQrti;S~DA zfXc`oM!)-E=P~ZRg5SS?yC{0o*Zg;67!aH15*Qo`LFxud16+Ov+_s+jSRDSU2i>gq z5!z)5T*SwgOUKVgR`X_$c`C++C*R%HKYMvDbd#iv@t(GT%J=y8xGmbBZ=}`reO%DJ zZ9X%>pmS~bU!AzMH`Am%+8_PyFA5d7%7dKxy?VjxtH*bv3-a+FD8@?FuevTbVdkZ1 zvn%{ls#4gQno@?#dQ|}`fO2EN2#BB8rtN;0Ux`k)>65PSJ?ZqozIoH$Npta^-&OAC zTW@3mw3PwDD7Zx)m%EyNkvQ~P9*AxT5i|nZif&zZcXwarjm*udN7I-o=yjW%lilg` z+g6;h%r-+pL$O-sof~eJtfo1ZtrK16d9Rz-pDXOr@${bR)*IRB)xrAzK9w!I0-(yJ z>{ZKiwnJ;aV^V@N`_3v<@M#mBlsKUcn<=(!!)6H0rKR|+&_AW);b#C%n{Gu;@~^s5 z=%n1Q45)rBNSqrtb$qs34X*gP7|QLm+Yo0I<|3U%q>YWQ77TP8EF-Pv0e6LID(+uP?V$$$cP#i&K|Mufk=!cK&Sdi^1?kQUka4$JJ@h z_WRKgL@H!-zq{^iPCk|_y{9eQ%pzfhAmIZ&uVYgpcfV7wb$KtrePOv8w&TTdU)QGH z46CJ2{O8h)&ptdC1Nl=e_m{G)cKHYp{THzQl>Y0(JPF?p@5|kG^yMbH&p?fTtk=r+ z)WATPVf+2DU6kJk>B@2B!D09NtLMQbf%nC{hFgR`Z#ARM0N}*)JFj!=kVq6 z)J_LTDEZng_!L;lkD7FM7Ak0cH%OH;Ws;Xz9fY>@cOF0j(7pZ7|E&8yBFYa*ufL4B z5fBG94>L3uplADfY9)i?1n&o9r`H~jwjF_ES?Mu62PMwOb$*AmoTk5zVh%}P@A@lb zBA%f`Twa36;cEt~Tg+u=V?X~%yxz}8r4)LQeb-yrwe=SqQ~&<;OVBOfrLhGaWO5R} z?PbrejaAXlK;Gv-@IJ!!Tl)qA<9>YJC#ERhvp~`kJukvovk1@Y<@y`YZA(8F>GQq> ziicBS)bS~f=_{DgkNL@z(W^04e(lHJ)}G*NqebWT>7cxCL?v0u?RHV7t>sJLUiS0ta%CR(WsRAuz%xXiyLI`b*$wox)6ILiH}2+{<8uSq zEPfUx#*Z#2so~tzTBSj zfobF+M@@$nAr_Jv67XP>jIP&`{FqvXKP#4HV~Hv;L@Ca`&xiViw{fCq9MAmF(Hn!< zm)%YB>V6o^QW6NnBm|jdU$-+Pws6;&xy0~Y42)rnyNA5Q>}NR+(ezET@Lw*!`oj}6 zx$Z=O`rk(els!_#fj z*E9zce{R3#<3FcFrDjo{=jD9RAYEG_{BWS&Zh1GX|Kd1(7Wjh3z4LzfwU4uP@*Wze zYp$H!%@QwUMlADxHf<5Hdj8es^-ao%c!NIarf}c&Sw}r zEabAfJC=EPyA$9g&|!~%oK5<27Rt}YuK0h#DO(5bF2UbC$YBro057Az;Kks5J`u6)SOJx3D86{W zRSoME8kE-JjYB`{ek^W%ecrv#G7~KJ&!Bz!1I!LD={L-#K2`BlHRl+JBj1Sq~~g?+_mp^hZN zx_rPlkWYn$d%xbAVc28~=B!|4m}~w_2979YPklIj}d0IZr+M8#%8} zd$-Bg4~Lbvsjk2tDd;oR;Mi=!|{s{&RLpU_dJfA0n5Qo`Dx9A$`undsHPVAq}7c^0rRP@h;(sw_ziovJdfG zXpUzD4bjE(S@QVtAg1ZG6V{Jl${KOO3N?;YU!&N-N14^>QzL4$<1@LlCeAaOH`1kS|0N(jC{W*Ri+Not0}c=r`KO%WLOpz6AJ?VZn>N0)xs9z9Fh-P(vfmI6we2d+HD&wpsI|Tl>lPKe2TR}0DEvmJE=bX9RPJ}C z9l$yJcGRv{k99PtaQ*4?jUD#K8~JFHezd)Vqc8N@w3=;lGPfpQ@)kR;8pnOc9<3Lo zgJX~zh|C1X-Oc!-_t%GlQkK+1=!o4`91_nKrN3%-@e7T8)E73e+QaazW%bUTaBA0THz z>b`73ae}UXHI*Qk24Z99WA*S0l#OJyzI@fS^B@;lfsXG3cZ#J)^cb8<

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z1Tlch$8r;~`e!w6PcnE_MM)kYy8O?@EcBec(GZC1%?X5x331ecc;_fO*xEU=8rnMi zq2!Pt>i_SZ1Lw|%$d_q`jVJ)@?F-S?1i5UCCuDRFjW^G#m_ZA$1PxI(FyMxC#P^G$HE1} zKw^$Kj8*(qvk*{+zNfGePcF>TOgq}HpJf(NWoAIK&6r}j2;F2Z}aa_0&Q$GA!H!Y6-lFpJlKP@pIKxLgb0u&`Z7*{8IjhV|9IWgNA zoIxI=_3%Kl#GivM+xuOdHm9{8Xt zWgBR1c*Zusq6{x_ff1~*5a@Nrkj0xcD)&`9HNUVK=oC~u9v+ByjQ`CbR!p8|NhSvv z?!8_y0fm1rSM7;m-uEIW?(@q^&zQ;Yl*J!-xB2MX!vQ6pL{rFBL19KHM3GRIc)7cE z@71&Y{*v;m$66G4l3=kY`*$A-H6Ck2&>2AT&aWiqs74g{D3-jfQ&1 zZvE)Jpz2-3xB%#Q^Iu!oS;&+FSpDZvX{=?!|_mAJghL+Z`%{9yEoAE1%J4h*_hHgcaI)5az`qTee&_JJ9sHBSH=X}*_?uPyJO1w$#!oZ=u&NIL o{KMY(9sc(w{#SU0;Vr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) +end +``` + +The given function is defined in a spherical coordinate system and calculates values based on the radial position r and angular position theta. The function behaves differently inside, outside, and between two specified radii, r_inner and r_outer. +The function is defined using conditional statements (if) to determine the value based on r: +Inside the Inner Radius (rr_outer): Like the inner radius case, but here the constant tsurf is added to the sinusoidal perturbation term. +Formula: + +```{math} +t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , +``` + +Otherwise (For r Values Between r_inner and r_outer): Only the sinusoidal perturbation term is calculated. +Formula: + +```{math} +p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , +``` + +This is the result for a quarter of shell: + +```{figure-md} fig:temperature + + +Temperature for the above muparser function. +``` + +However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. +For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. +Therefore, we may use the following mathematical function: + +```{math} +temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , +``` + +And + + +```{math} +temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , +``` + +In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. +The final result will be as following: + +``` + + +Temperature distribution in ASCII format. +``` + + +Now, let's write a Python script to utilize the function and export it in ASCII format + +``` +# The script imports necessary libraries and sets up parameters for our temperature model. + +import matplotlib.pyplot as plt +import numpy as np +import math + +# Parameters +r_inner = 3481000 # Internal radius in meters +r_outer = 6371000 # External radius in meters +p_large = 400.0 # Amplitude of the large perturbations +p_small = 30.0 # Amplitude of the small perturbations +frequency_large = 3 # Frequency of the large perturbations +frequency_small = 30 # Frequency of the small perturbations +spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees +start_angle_degrees = 330 # Starting angle for the perturbation in degrees + +# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. + +def temperature_function_degrees_array(r, theta_degrees): + # Adjust theta to shift the starting angle of the perturbation + adjusted_theta_degrees = theta_degrees + start_angle_degrees + adjusted_theta_degrees = adjusted_theta_degrees % 360 + + # Initialize the temperature array + temp = np.zeros_like(r) + + # Determine the large perturbation using a step function approach + + large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) + temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) + + # Apply small perturbations where large perturbations are not applied + small_perturbation_mask = ~large_perturbation_mask + temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) + + return temp + +# Here we generate data for visualization +theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees +radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer + +# Here we create a grid for plotting + +R, Theta = np.meshgrid(radius, theta) +Temp = temperature_function_degrees_array(R, Theta) + + +# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. +# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. +# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: +# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. +# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. +# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. +# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. +#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. +# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. +# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). +# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. + + + +def write_ascii_data(radius, theta_degrees, temperatures, filename): + with open(filename, 'w') as file: + file.write("# Test data for ascii data initial conditions.\n") + file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") + file.write("# POINTS: 100 360 1\n") + file.write("# Columns: r phi temperature [K]\n") + + for j in range(len(theta_degrees)): + for i in range(len(radius)): + r = radius[i] + phi = theta_degrees[j] + temp = temperatures[j, i] + + # Improved formatting + r_str = f"{r:.1f}" + phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" + temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" + + # Column alignment with offset for the second column + file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") + + +# Conversion of polar coordinates to Cartesian coordinates for plotting +X = R * np.cos(np.radians(Theta)) +Y = R * np.sin(np.radians(Theta)) + + +# Plotting +plt.figure(figsize=(8, 6)) +contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') +plt.colorbar(contour, label='Temperature') +plt.title('Temperature distribution') +plt.xlabel('Coordinate X (m)') +plt.ylabel('Coordinate Y (m)') +plt.axis('equal') +plt.show() + + +# Use the function write_ascii_data to save data +write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') + +# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. + +import math + +def convert_to_radians(degrees): + """Convert degrees to radians.""" + return degrees * (math.pi / 180) + +def convert_file_angles(input_file_path, output_file_path): + """Convert the angles in the second column of the file from degrees to radians.""" + with open(input_file_path, 'r') as file: + content = file.readlines() + + converted_lines = content[:4] # Keep the header lines unchanged + for line in content[4:]: + columns = line.split() + if len(columns) == 3: + radius, angle_deg, temperature = columns + angle_rad = convert_to_radians(float(angle_deg)) + converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" + converted_lines.append(converted_line) + else: + converted_lines.append(line) + + with open(output_file_path, 'w') as file: + file.writelines(converted_lines) + +# Example usage +input_file_path = 'perturbation_ascii.txt' # Replace with your input file path +output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path + +convert_file_angles(input_file_path, output_file_path) + +``` + + +If everything has been done correctly, the ASCII file should appear as follows: + + +``` + +# Test data for ascii data initial conditions. +# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" +# POINTS: 100 360 1 +# Columns: r phi temperature [K] +3481000.0 0.00000000 0 +3510191.9 0.00000000 0 +3539383.8 0.00000000 0 +3568575.8 0.00000000 0 +3597767.7 0.00000000 0 +3626959.6 0.00000000 0 +3656151.5 0.00000000 0 + + +``` + +For each radius value and for each angular value, a certain temperature will be established. +Once executed, the script will generate a file named `perturbation_ascii.txt`. Before running our simulation, we should move our file to the following directory: + +``` +`$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/` +``` + + + +To implement it in our simulation (.prm file), we initialize the temperature model as follows: + +``` + +# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. +subsection Initial temperature model + set List of model names = adiabatic, ascii data + subsection Adiabatic + set Age bottom boundary layer = 1e9 + set Age top boundary layer = 1e9 + + subsection Function + set Function expression = 0 + end + + end + +#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. + subsection Ascii data model + set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ + set Data file name = perturbation_ ascii.txt + end +end + +``` + + + +Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. + +``` + +subsection Material model + set Model name = Steinberger + set Material averaging = harmonic average + + subsection Steinberger model + + set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ + set Lateral viscosity file name = temp-viscosity-prefactor.txt + set Material file names = pyr-ringwood88.txt + set Radial viscosity file name = radial-visc-simple.txt + set Latent heat = false + + # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". + set Maximum lateral viscosity variation = 1e2 + set Maximum viscosity = 5e23 + set Minimum viscosity = 1e19 + set Use lateral average temperature for viscosity = false + set Thermal conductivity formulation = p-T-dependent + #set Thermal conductivity = 4.17 + + set Composition viscosity prefactors = 1 + + end +end +``` + +The simulation will take some time to run, but this will be the final result: + +``` + + + +Temperature distribution with aspect ratio adjustment. +``` + + + +You can see the complete video in the following link: + +https://www.youtube.com/watch?v=6KVsunMhpj0 + diff --git a/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex new file mode 100644 index 00000000000..87b58891496 --- /dev/null +++ b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex @@ -0,0 +1,328 @@ + + +\documentclass{article} +\usepackage{amsmath} +\usepackage{graphicx} +\usepackage{hyperref} + +\begin{document} + +\section*{Using ASCII file to compute a personalized temperature distribution} + +\textit{This section was contributed by Francesco Radica.} + +In this cookbook, we will explore how to implement complex temperature perturbations in a simulation using Steinberger's material model. Specifically, we'll modify a temperature function originally developed for the CITCOM simulation program, designed to initiate mantle convection through an ASCII file. Additionally, we will implement a stagnant lid type subduction, aiming for a viscosity profile that is as realistic as possible. + +ASPECT employs the muparser language for writing mathematical functions, which are useful for describing various features such as temperature perturbation functions. For the simulation program CITCOM, a particular mathematical function is well-known for generating perturbations. We will thus apply this function to our adiabatic temperature profile, to which temperature will be added and subtracted according to the mathematical function: + +\begin{verbatim} +subsection Initial temperature model + set List of model names = adiabatic, function + subsection Adiabatic + set Age bottom boundary layer = 5e8 + set Age top boundary layer = 5e8 + + subsection Function + set Function expression = 0 + end + end + +subsection Function + set Coordinate system = spherical + set Variable names = r,theta + + set Function constants = r_inner=3481000, r_outer=6371000, tcmb=3700, tsurf=300, w=2*pi, p=300.0, frequency=100 + set Function expression = if(rr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) +end +\end{verbatim} + +The given function is defined in a spherical coordinate system and calculates values based on the radial position \(r\) and angular position \(\theta\). The function behaves differently inside, outside, and between two specified radii, \(r_{\text{inner}}\) and \(r_{\text{outer}}\). +The function is defined using conditional statements (if) to determine the value based on \(r\): +Inside the Inner Radius (\(r < r_{\text{inner}}\)): The function calculates a value by adding the constant \(t_{\text{cmb}}\) to a sinusoidal perturbation term. This perturbation term depends on the radial position \(r\), the angular position \(\theta\), and the constants \(p\) and frequency. +Formula: + +\begin{equation} +t_\text{cmb} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , +\end{equation} + +Outside the Outer Radius (\(r > r_{\text{outer}}\)): Like the inner radius case, but here the constant \(t_{\text{surf}}\) is added to the sinusoidal perturbation term. +Formula: + +\begin{equation} +t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , +\end{equation} + +Otherwise (For \(r\) Values Between \(r_{\text{inner}}\) and \(r_{\text{outer}}\)): Only the sinusoidal perturbation term is calculated. +Formula: + +\begin{equation} +p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , +\end{equation} + +This is the result for a quarter of shell: + +\begin{figure}[h!] +\centering +\includegraphics[width=0.48\textwidth]{temperature.png} +\caption{Temperature for the above muparser function.} +\label{fig:temperature} +\end{figure} + +However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. +For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. +Therefore, we may use the following mathematical function: + +\begin{equation} +temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , +\end{equation} + +And + +\begin{equation} +temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , +\end{equation} + +In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. +The final result will be as following: + +\begin{figure}[h!] +\centering +\includegraphics[width=0.48\textwidth]{ascii_temperature.png} +\caption{Temperature distribution in ASCII format.} +\label{fig:ascii-temperature} +\end{figure} + +Now, let's write a Python script to utilize the function and export it in ASCII format: + +\begin{verbatim} +# The script imports necessary libraries and sets up parameters for our temperature model. + +import matplotlib.pyplot as plt +import numpy as np +import math + +# Parameters +r_inner = 3481000 # Internal radius in meters +r_outer = 6371000 # External radius in meters +p_large = 400.0 # Amplitude of the large perturbations +p_small = 30.0 # Amplitude of the small perturbations +frequency_large = 3 # Frequency of the large perturbations +frequency_small = 30 # Frequency of the small perturbations +spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees +start_angle_degrees = 330 # Starting angle for the perturbation in degrees + +# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. + +def temperature_function_degrees_array(r, theta_degrees): + # Adjust theta to shift the starting angle of the perturbation + adjusted_theta_degrees = theta_degrees + start_angle_degrees + adjusted_theta_degrees = adjusted_theta_degrees % 360 + + # Initialize the temperature array + temp = np.zeros_like(r) + + # Determine the large perturbation using a step function approach + + large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) + temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) + + # Apply small perturbations where large perturbations are not applied + small_perturbation_mask = ~large_perturbation_mask + temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) + + return temp + +# Here we generate data for visualization +theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees +radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer + +# Here we create a grid for plotting + +R, Theta = np.meshgrid(radius, theta) +Temp = temperature_function_de + +grees_array(R, Theta) + + +# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. +# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. +# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: +# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. +# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. +# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. +# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. +#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. +# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. +# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). +# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. + + + +def write_ascii_data(radius, theta_degrees, temperatures, filename): + with open(filename, 'w') as file: + file.write("# Test data for ascii data initial conditions.\n") + file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") + file.write("# POINTS: 100 360 1\n") + file.write("# Columns: r phi temperature [K]\n") + + for j in range(len(theta_degrees)): + for i in range(len(radius)): + r = radius[i] + phi = theta_degrees[j] + temp = temperatures[j, i] + + # Improved formatting + r_str = f"{r:.1f}" + phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" + temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" + + # Column alignment with offset for the second column + file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") + + +# Conversion of polar coordinates to Cartesian coordinates for plotting +X = R * np.cos(np.radians(Theta)) +Y = R * np.sin(np.radians(Theta)) + + +# Plotting +plt.figure(figsize=(8, 6)) +contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') +plt.colorbar(contour, label='Temperature') +plt.title('Temperature distribution') +plt.xlabel('Coordinate X (m)') +plt.ylabel('Coordinate Y (m)') +plt.axis('equal') +plt.show() + + +# Use the function write_ascii_data to save data +write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') + +# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. + +import math + +def convert_to_radians(degrees): + """Convert degrees to radians.""" + return degrees * (math.pi / 180) + +def convert_file_angles(input_file_path, output_file_path): + """Convert the angles in the second column of the file from degrees to radians.""" + with open(input_file_path, 'r') as file: + content = file.readlines() + + converted_lines = content[:4] # Keep the header lines unchanged + for line in content[4:]: + columns = line.split() + if len(columns) == 3: + radius, angle_deg, temperature = columns + angle_rad = convert_to_radians(float(angle_deg)) + converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" + converted_lines.append(converted_line) + else: + converted_lines.append(line) + + with open(output_file_path, 'w') as file: + file.writelines(converted_lines) + +# Example usage +input_file_path = 'perturbation_ascii.txt' # Replace with your input file path +output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path + +convert_file_angles(input_file_path, output_file_path) + +\end{verbatim} + +If everything has been done correctly, the ASCII file should appear as follows: + +\begin{verbatim} +# Test data for ascii data initial conditions. +# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" +# POINTS: 100 360 1 +# Columns: r phi temperature [K] +3481000.0 0.00000000 0 +3510191.9 0.00000000 0 +3539383.8 0.00000000 0 +3568575.8 0.00000000 0 +3597767.7 0.00000000 0 +3626959.6 0.00000000 0 +3656151.5 0.00000000 0 +\end{verbatim} + +For each radius value and for each angular value, a certain temperature will be established. +Once executed, the script will generate a file named \texttt{perturbation\_ascii.txt}. Before running our simulation, we should move our file to the following directory: + +\begin{verbatim} +$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ +\end{verbatim} + +To implement it in our simulation (\texttt{.prm} file), we initialize the temperature model as follows: + +\begin{verbatim} +# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. +subsection Initial temperature model + set List of model names = adiabatic, ascii data + subsection Adiabatic + set Age bottom boundary layer = 1e9 + set Age top boundary layer = 1e9 + + subsection Function + set Function expression = 0 + end + + end + +#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. + subsection Ascii data model + set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ + set Data file name = perturbation_ ascii.txt + end +end +\end{verbatim} + +Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. + +\begin{verbatim} +subsection Material model + set Model name = Steinberger + set Material averaging = harmonic average + + subsection Steinberger model + + set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ + set Lateral viscosity file name = temp-viscosity-prefactor.txt + set Material file names = pyr-ringwood88.txt + set Radial viscosity file name = radial-visc-simple.txt + set Latent heat = false + + # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". + set Maximum lateral viscosity variation = 1e2 + set Maximum viscosity = 5e23 + set Minimum viscosity = 1e19 + set Use lateral average temperature for viscosity = false + set Thermal conductivity formulation = p-T-dependent + #set Thermal conductivity = 4.17 + + set Composition viscosity prefactors = 1 + + + + end +end +\end{verbatim} + +The simulation will take some time to run, but this will be the final result: + +\begin{figure}[h!] +\centering +\includegraphics[width=0.48\textwidth]{ascii_temperature_aspect.png} +\caption{Temperature distribution with aspect ratio adjustment.} +\label{fig:ascii-temperature-aspect} +\end{figure} + +You can see the complete video in the following link: +\url{https://www.youtube.com/watch?v=6KVsunMhpj0} + +\end{document} +``` \ No newline at end of file diff --git a/cookbooks/ascii_perturbation/perturbation.py b/cookbooks/ascii_perturbation/perturbation.py new file mode 100644 index 00000000000..ab5d46a683a --- /dev/null +++ b/cookbooks/ascii_perturbation/perturbation.py @@ -0,0 +1,114 @@ +import matplotlib.pyplot as plt +import numpy as np +import math + +# Parametri +r_inner = 3481000 # Raggio interno in metri +r_outer = 6371000 # Raggio esterno in metri +p_large = 700.0 # Ampiezza delle grandi perturbazioni +p_small = 30.0 # Ampiezza delle piccole perturbazioni +frequency_large = 3 # Frequenza delle grandi perturbazioni +frequency_small = 30 # Frequenza delle piccole perturbazioni +spread_angle_large_degrees = 90 # Angolo di diffusione delle grandi perturbazioni in gradi +start_angle_degrees = 270 # Angolo di partenza per la perturbazione in gradi + +# Funzione di temperatura modificata per utilizzare i gradi e gestire gli array +def temperature_function_degrees_array(r, theta_degrees): + # Aggiusta theta per spostare l'angolo di inizio della perturbazione + adjusted_theta_degrees = theta_degrees + start_angle_degrees + adjusted_theta_degrees = adjusted_theta_degrees % 360 + + # Inizializza l'array della temperatura + temp = np.zeros_like(r) + + # Determina la grande perturbazione usando un approccio a funzione gradino + large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) + temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner) + math.pi) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) + + # Applica piccole perturbazioni dove non si applicano le grandi perturbazioni + small_perturbation_mask = ~large_perturbation_mask + temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) + + return temp + + + + +# Generazione dei dati per la visualizzazione +theta = np.linspace(0, 360, 360) # Angoli da 0 a 360 gradi +radius = np.linspace(r_inner, r_outer, 100) # Raggi da r_inner a r_outer + +# Creazione di una griglia per il plotting +R, Theta = np.meshgrid(radius, theta) +Temp = temperature_function_degrees_array(R, Theta) + +def write_ascii_data(radius, theta_degrees, temperatures, filename): + with open(filename, 'w') as file: + file.write("# Test data for ascii data initial conditions.\n") + file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") + file.write("# POINTS: 100 360 1\n") + file.write("# Columns: r phi temperature [K]\n") + + for j in range(len(theta_degrees)): + for i in range(len(radius)): + r = radius[i] + phi = theta_degrees[j] + temp = temperatures[j, i] + + # Formattazione migliorata + r_str = f"{r:.1f}" + phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" + temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" + + # Allineamento delle colonne con spostamento della seconda colonna + file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") + + +# Conversione delle coordinate polari in coordinate cartesiane per il plotting +X = R * np.cos(np.radians(Theta)) +Y = R * np.sin(np.radians(Theta)) + +# Plotting +plt.figure(figsize=(8, 6)) +contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') +plt.colorbar(contour, label='Temperatura') +plt.title('Distribuzione della Temperatura in Coordinate Polari') +plt.xlabel('Coordinata X (m)') +plt.ylabel('Coordinata Y (m)') +plt.axis('equal') +plt.show() + + +# Uso della funzione write_ascii_data per salvare i dati +write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') + +import math + +def convert_to_radians(degrees): + """Convert degrees to radians.""" + return degrees * (math.pi / 180) + +def convert_file_angles(input_file_path, output_file_path): + """Convert the angles in the second column of the file from degrees to radians.""" + with open(input_file_path, 'r') as file: + content = file.readlines() + + converted_lines = content[:4] # Keep the header lines unchanged + for line in content[4:]: + columns = line.split() + if len(columns) == 3: + radius, angle_deg, temperature = columns + angle_rad = convert_to_radians(float(angle_deg)) + converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" + converted_lines.append(converted_line) + else: + converted_lines.append(line) + + with open(output_file_path, 'w') as file: + file.writelines(converted_lines) + +# Example usage +input_file_path = 'perturbation_ascii.txt' # Replace with your input file path +output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path + +convert_file_angles(input_file_path, output_file_path) diff --git a/cookbooks/ascii_perturbation/perturbation_ascii.txt b/cookbooks/ascii_perturbation/perturbation_ascii.txt new file mode 100644 index 00000000000..d2cfd20bd2f --- /dev/null +++ b/cookbooks/ascii_perturbation/perturbation_ascii.txt @@ -0,0 +1,36004 @@ +# Test data for ascii data 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file mode 100644 index 0000000000000000000000000000000000000000..1215360c558324f168a348f977b46d5a160ee437 GIT binary patch literal 162 zcmWgj%}g%JFV0UZQSeVo%S=vH2rW)6VjuuS8GIQs8Il=_81fm4fjEt!gh7G9A4sQx Q#Z!U2P@qgIPz9v`0A Date: Tue, 11 Jun 2024 17:46:54 +0200 Subject: [PATCH 2/7] Update ~$torial_ascii_MERGE.docx --- .../ascii_perturbation/~$torial_ascii_MERGE.docx | Bin 162 -> 1 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/cookbooks/ascii_perturbation/~$torial_ascii_MERGE.docx b/cookbooks/ascii_perturbation/~$torial_ascii_MERGE.docx index 1215360c558324f168a348f977b46d5a160ee437..8b137891791fe96927ad78e64b0aad7bded08bdc 100644 GIT binary patch literal 1 Icmd-A000XB3jhEB literal 162 zcmWgj%}g%JFV0UZQSeVo%S=vH2rW)6VjuuS8GIQs8Il=_81fm4fjEt!gh7G9A4sQx Q#Z!U2P@qgIPz9v`0A Date: Tue, 11 Jun 2024 17:47:43 +0200 Subject: [PATCH 3/7] Delete cookbooks/ascii_perturbation directory --- .../ascii_perturbation/ascii_perturbation.prm | 179 - .../documentation/ascii_temperature.png | Bin 334131 -> 0 bytes .../ascii_temperature_aspect.png | Bin 243837 -> 0 bytes .../documentation/perturbation.txt | 36004 ---------------- .../documentation/temperature.png | Bin 190985 -> 0 bytes .../documentation/tutorial_a.docx | Bin 27089 -> 0 bytes .../documentation/tutorial_ascii.md | 329 - .../documentation/tutorial_ascii.tex | 328 - cookbooks/ascii_perturbation/perturbation.py | 114 - .../ascii_perturbation/perturbation_ascii.txt | 36004 ---------------- cookbooks/ascii_perturbation/~$torial_a.docx | Bin 162 -> 0 bytes .../~$torial_ascii_MERGE.docx | 1 - 12 files changed, 72959 deletions(-) delete mode 100644 cookbooks/ascii_perturbation/ascii_perturbation.prm delete mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature.png delete mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature_aspect.png delete mode 100644 cookbooks/ascii_perturbation/documentation/perturbation.txt delete mode 100644 cookbooks/ascii_perturbation/documentation/temperature.png delete mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_a.docx delete mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.md delete mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex delete mode 100644 cookbooks/ascii_perturbation/perturbation.py delete mode 100644 cookbooks/ascii_perturbation/perturbation_ascii.txt delete mode 100644 cookbooks/ascii_perturbation/~$torial_a.docx delete mode 100644 cookbooks/ascii_perturbation/~$torial_ascii_MERGE.docx diff --git a/cookbooks/ascii_perturbation/ascii_perturbation.prm b/cookbooks/ascii_perturbation/ascii_perturbation.prm deleted file mode 100644 index 618deb32f05..00000000000 --- a/cookbooks/ascii_perturbation/ascii_perturbation.prm +++ /dev/null @@ -1,179 +0,0 @@ - -set Dimension = 2 -#set Resume computation = auto -set Start time = 0 -set End time = 5e8 -set Use years in output instead of seconds = true -set Adiabatic surface temperature = 1623 -set Use conduction timestep = true -set Output directory = ascii_perturbation - - -set CFL number = 1 -set Nonlinear solver scheme = single Advection, single Stokes -subsection Solver parameters - subsection Stokes solver parameters - set Linear solver tolerance = 1e-5 - set Number of cheap Stokes solver steps = 2000 # 200 - end -end - -subsection Formulation - set Mass conservation = projected density field - set Temperature equation = real density -end - -subsection Checkpointing - set Steps between checkpoint = 100 -end - - -subsection Geometry model - set Model name = spherical shell - - subsection Spherical shell - set Inner radius = 3481000 - set Outer radius = 6371000 - end -end - - -subsection Boundary temperature model - set Fixed temperature boundary indicators = top, bottom - set List of model names = spherical constant - subsection Spherical constant - set Inner temperature = 3700 - set Outer temperature = 273 - end -end - - -subsection Boundary velocity model - set Tangential velocity boundary indicators = bottom, top -end - - -subsection Gravity model - set Model name = ascii data -end - - -# Here we initialize the temeprature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. - -subsection Initial temperature model - set List of model names = adiabatic, ascii data - subsection Adiabatic - set Age bottom boundary layer = 1e9 - set Age top boundary layer = 1e9 - - subsection Function - set Function expression = 0 - end - - end - -# Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. - - subsection Ascii data model - set Data directory = $ASPECT_SOURCE_DIR/data/cookbooks/ascii_perturbation - set Data file name = perturbation_ascii.txt - end -end - - -subsection Material model - set Model name = Steinberger - set Material averaging = harmonic average - - subsection Steinberger model - - set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ - set Lateral viscosity file name = temp-viscosity-prefactor.txt - set Material file names = pyr-ringwood88.txt - set Radial viscosity file name = radial-visc-simple.txt - set Latent heat = false - - # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". - - set Maximum lateral viscosity variation = 1e2 - set Maximum viscosity = 5e23 - set Minimum viscosity = 1e19 - - - set Use lateral average temperature for viscosity = false - set Thermal conductivity formulation = p-T-dependent - - set Composition viscosity prefactors = 1 - - end -end - - -subsection Heating model - set List of model names = adiabatic heating, shear heating -end - - -# We refine the mesh near the boundaries, and where temperature variations are -# large. In addition, we make sure that in the transition zone, where both the -# viscosity and the density change a lot, we use the highest refinement level. -subsection Mesh refinement - set Initial adaptive refinement = 1 - set Initial global refinement = 5 - set Refinement fraction = 0.95 - set Coarsening fraction = 0.05 - set Strategy = temperature, boundary, minimum refinement function - set Time steps between mesh refinement = 5 - - subsection Boundary - set Boundary refinement indicators = top, bottom - end - - subsection Minimum refinement function - set Coordinate system = depth - set Variable names = depth, phi - set Function expression = if(depth<700000, 6, 5) - end -end - -subsection Boundary temperature model - set Fixed temperature boundary indicators = 0,1 -end - - -subsection Nullspace removal - set Remove nullspace = net rotation -end - -subsection Compositional fields - set Number of fields = 1 - set Names of fields = density_field - set Types of fields = density - set Compositional field methods = prescribed field -end - - - -subsection Initial composition model - set Model name = function - subsection Function - set Variable names = x,y - set Function constants = r_inner=3481000, r_outer=6371000 - set Function expression = if(sqrt(x^2+y^2)NnjvAa1S9saCZ+7+}&+(cZcBa4g&-Y5Fki!cXxLgU~qTYlk2{( z_j&hP&xid3_SBlG9#(hLl$_@wRfH?ZNdVpvyn}&(0Z4xPsssZAZvX=WSA~oS{mIKR zks!2!byAWLfvFfHfP-IOrRC^?z&lT-g7)V=mmkXTuxh!vA{=SM~R@{-6r!yEBAsET8!Yb~tN7+cZreg6gkHLeiJ5g^i6lBWC!r-Ks z%1cU0${OB%0e;n;RDG}8TUB*%@TFqks3&N#w;XQ{HO$`tM)CbC99#lbyW8vfY1xU> zxX-D;?kLkH%QXMx38bQ;w4%aE&TSrYa*!7zQkrL(`@a^0Xe$Hv=u`!i5`zD|R3Vna zs*whj2K;ZOt{}kD{}-j$yiqCQ|5{+xa{ku~O9TG@OaHG1`~Tida}od@-+M4bLhwPc z>3%oUtJG~$47V`n<*L|XFoBZ)tS-IbypM1?*6(Tis#x&(XYqnGL*u9CBQrti;S~DA zfXc`oM!)-E=P~ZRg5SS?yC{0o*Zg;67!aH15*Qo`LFxud16+Ov+_s+jSRDSU2i>gq z5!z)5T*SwgOUKVgR`X_$c`C++C*R%HKYMvDbd#iv@t(GT%J=y8xGmbBZ=}`reO%DJ zZ9X%>pmS~bU!AzMH`Am%+8_PyFA5d7%7dKxy?VjxtH*bv3-a+FD8@?FuevTbVdkZ1 zvn%{ls#4gQno@?#dQ|}`fO2EN2#BB8rtN;0Ux`k)>65PSJ?ZqozIoH$Npta^-&OAC zTW@3mw3PwDD7Zx)m%EyNkvQ~P9*AxT5i|nZif&zZcXwarjm*udN7I-o=yjW%lilg` z+g6;h%r-+pL$O-sof~eJtfo1ZtrK16d9Rz-pDXOr@${bR)*IRB)xrAzK9w!I0-(yJ z>{ZKiwnJ;aV^V@N`_3v<@M#mBlsKUcn<=(!!)6H0rKR|+&_AW);b#C%n{Gu;@~^s5 z=%n1Q45)rBNSqrtb$qs34X*gP7|QLm+Yo0I<|3U%q>YWQ77TP8EF-Pv0e6LID(+uP?V$$$cP#i&K|Mufk=!cK&Sdi^1?kQUka4$JJ@h z_WRKgL@H!-zq{^iPCk|_y{9eQ%pzfhAmIZ&uVYgpcfV7wb$KtrePOv8w&TTdU)QGH z46CJ2{O8h)&ptdC1Nl=e_m{G)cKHYp{THzQl>Y0(JPF?p@5|kG^yMbH&p?fTtk=r+ z)WATPVf+2DU6kJk>B@2B!D09NtLMQbf%nC{hFgR`Z#ARM0N}*)JFj!=kVq6 z)J_LTDEZng_!L;lkD7FM7Ak0cH%OH;Ws;Xz9fY>@cOF0j(7pZ7|E&8yBFYa*ufL4B z5fBG94>L3uplADfY9)i?1n&o9r`H~jwjF_ES?Mu62PMwOb$*AmoTk5zVh%}P@A@lb zBA%f`Twa36;cEt~Tg+u=V?X~%yxz}8r4)LQeb-yrwe=SqQ~&<;OVBOfrLhGaWO5R} z?PbrejaAXlK;Gv-@IJ!!Tl)qA<9>YJC#ERhvp~`kJukvovk1@Y<@y`YZA(8F>GQq> ziicBS)bS~f=_{DgkNL@z(W^04e(lHJ)}G*NqebWT>7cxCL?v0u?RHV7t>sJLUiS0ta%CR(WsRAuz%xXiyLI`b*$wox)6ILiH}2+{<8uSq zEPfUx#*Z#2so~tzTBSj zfobF+M@@$nAr_Jv67XP>jIP&`{FqvXKP#4HV~Hv;L@Ca`&xiViw{fCq9MAmF(Hn!< zm)%YB>V6o^QW6NnBm|jdU$-+Pws6;&xy0~Y42)rnyNA5Q>}NR+(ezET@Lw*!`oj}6 zx$Z=O`rk(els!_#fj z*E9zce{R3#<3FcFrDjo{=jD9RAYEG_{BWS&Zh1GX|Kd1(7Wjh3z4LzfwU4uP@*Wze zYp$H!%@QwUMlADxHf<5Hdj8es^-ao%c!NIarf}c&Sw}r zEabAfJC=EPyA$9g&|!~%oK5<27Rt}YuK0h#DO(5bF2UbC$YBro057Az;Kks5J`u6)SOJx3D86{W zRSoME8kE-JjYB`{ek^W%ecrv#G7~KJ&!Bz!1I!LD={L-#K2`BlHRl+JBj1Sq~~g?+_mp^hZN zx_rPlkWYn$d%xbAVc28~=B!|4m}~w_2979YPklIj}d0IZr+M8#%8} zd$-Bg4~Lbvsjk2tDd;oR;Mi=!|{s{&RLpU_dJfA0n5Qo`Dx9A$`undsHPVAq}7c^0rRP@h;(sw_ziovJdfG zXpUzD4bjE(S@QVtAg1ZG6V{Jl${KOO3N?;YU!&N-N14^>QzL4$<1@LlCeAaOH`1kS|0N(jC{W*Ri+Not0}c=r`KO%WLOpz6AJ?VZn>N0)xs9z9Fh-P(vfmI6we2d+HD&wpsI|Tl>lPKe2TR}0DEvmJE=bX9RPJ}C z9l$yJcGRv{k99PtaQ*4?jUD#K8~JFHezd)Vqc8N@w3=;lGPfpQ@)kR;8pnOc9<3Lo zgJX~zh|C1X-Oc!-_t%GlQkK+1=!o4`91_nKrN3%-@e7T8)E73e+QaazW%bUTaBA0THz z>b`73ae}UXHI*Qk24Z99WA*S0l#OJyzI@fS^B@;lfsXG3cZ#J)^cb8<

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z1Tlch$8r;~`e!w6PcnE_MM)kYy8O?@EcBec(GZC1%?X5x331ecc;_fO*xEU=8rnMi zq2!Pt>i_SZ1Lw|%$d_q`jVJ)@?F-S?1i5UCCuDRFjW^G#m_ZA$1PxI(FyMxC#P^G$HE1} zKw^$Kj8*(qvk*{+zNfGePcF>TOgq}HpJf(NWoAIK&6r}j2;F2Z}aa_0&Q$GA!H!Y6-lFpJlKP@pIKxLgb0u&`Z7*{8IjhV|9IWgNA zoIxI=_3%Kl#GivM+xuOdHm9{8Xt zWgBR1c*Zusq6{x_ff1~*5a@Nrkj0xcD)&`9HNUVK=oC~u9v+ByjQ`CbR!p8|NhSvv z?!8_y0fm1rSM7;m-uEIW?(@q^&zQ;Yl*J!-xB2MX!vQ6pL{rFBL19KHM3GRIc)7cE z@71&Y{*v;m$66G4l3=kY`*$A-H6Ck2&>2AT&aWiqs74g{D3-jfQ&1 zZvE)Jpz2-3xB%#Q^Iu!oS;&+FSpDZvX{=?!|_mAJghL+Z`%{9yEoAE1%J4h*_hHgcaI)5az`qTee&_JJ9sHBSH=X}*_?uPyJO1w$#!oZ=u&NIL o{KMY(9sc(w{#SU0;Vr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) -end -``` - -The given function is defined in a spherical coordinate system and calculates values based on the radial position r and angular position theta. The function behaves differently inside, outside, and between two specified radii, r_inner and r_outer. -The function is defined using conditional statements (if) to determine the value based on r: -Inside the Inner Radius (rr_outer): Like the inner radius case, but here the constant tsurf is added to the sinusoidal perturbation term. -Formula: - -```{math} -t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , -``` - -Otherwise (For r Values Between r_inner and r_outer): Only the sinusoidal perturbation term is calculated. -Formula: - -```{math} -p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , -``` - -This is the result for a quarter of shell: - -```{figure-md} fig:temperature - - -Temperature for the above muparser function. -``` - -However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. -For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. -Therefore, we may use the following mathematical function: - -```{math} -temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , -``` - -And - - -```{math} -temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , -``` - -In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. -The final result will be as following: - -``` - - -Temperature distribution in ASCII format. -``` - - -Now, let's write a Python script to utilize the function and export it in ASCII format - -``` -# The script imports necessary libraries and sets up parameters for our temperature model. - -import matplotlib.pyplot as plt -import numpy as np -import math - -# Parameters -r_inner = 3481000 # Internal radius in meters -r_outer = 6371000 # External radius in meters -p_large = 400.0 # Amplitude of the large perturbations -p_small = 30.0 # Amplitude of the small perturbations -frequency_large = 3 # Frequency of the large perturbations -frequency_small = 30 # Frequency of the small perturbations -spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees -start_angle_degrees = 330 # Starting angle for the perturbation in degrees - -# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. - -def temperature_function_degrees_array(r, theta_degrees): - # Adjust theta to shift the starting angle of the perturbation - adjusted_theta_degrees = theta_degrees + start_angle_degrees - adjusted_theta_degrees = adjusted_theta_degrees % 360 - - # Initialize the temperature array - temp = np.zeros_like(r) - - # Determine the large perturbation using a step function approach - - large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) - temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) - - # Apply small perturbations where large perturbations are not applied - small_perturbation_mask = ~large_perturbation_mask - temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) - - return temp - -# Here we generate data for visualization -theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees -radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer - -# Here we create a grid for plotting - -R, Theta = np.meshgrid(radius, theta) -Temp = temperature_function_degrees_array(R, Theta) - - -# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. -# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. -# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: -# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. -# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. -# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. -# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. -#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. -# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. -# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). -# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. - - - -def write_ascii_data(radius, theta_degrees, temperatures, filename): - with open(filename, 'w') as file: - file.write("# Test data for ascii data initial conditions.\n") - file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") - file.write("# POINTS: 100 360 1\n") - file.write("# Columns: r phi temperature [K]\n") - - for j in range(len(theta_degrees)): - for i in range(len(radius)): - r = radius[i] - phi = theta_degrees[j] - temp = temperatures[j, i] - - # Improved formatting - r_str = f"{r:.1f}" - phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" - temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" - - # Column alignment with offset for the second column - file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") - - -# Conversion of polar coordinates to Cartesian coordinates for plotting -X = R * np.cos(np.radians(Theta)) -Y = R * np.sin(np.radians(Theta)) - - -# Plotting -plt.figure(figsize=(8, 6)) -contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') -plt.colorbar(contour, label='Temperature') -plt.title('Temperature distribution') -plt.xlabel('Coordinate X (m)') -plt.ylabel('Coordinate Y (m)') -plt.axis('equal') -plt.show() - - -# Use the function write_ascii_data to save data -write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') - -# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. - -import math - -def convert_to_radians(degrees): - """Convert degrees to radians.""" - return degrees * (math.pi / 180) - -def convert_file_angles(input_file_path, output_file_path): - """Convert the angles in the second column of the file from degrees to radians.""" - with open(input_file_path, 'r') as file: - content = file.readlines() - - converted_lines = content[:4] # Keep the header lines unchanged - for line in content[4:]: - columns = line.split() - if len(columns) == 3: - radius, angle_deg, temperature = columns - angle_rad = convert_to_radians(float(angle_deg)) - converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" - converted_lines.append(converted_line) - else: - converted_lines.append(line) - - with open(output_file_path, 'w') as file: - file.writelines(converted_lines) - -# Example usage -input_file_path = 'perturbation_ascii.txt' # Replace with your input file path -output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path - -convert_file_angles(input_file_path, output_file_path) - -``` - - -If everything has been done correctly, the ASCII file should appear as follows: - - -``` - -# Test data for ascii data initial conditions. -# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" -# POINTS: 100 360 1 -# Columns: r phi temperature [K] -3481000.0 0.00000000 0 -3510191.9 0.00000000 0 -3539383.8 0.00000000 0 -3568575.8 0.00000000 0 -3597767.7 0.00000000 0 -3626959.6 0.00000000 0 -3656151.5 0.00000000 0 - - -``` - -For each radius value and for each angular value, a certain temperature will be established. -Once executed, the script will generate a file named `perturbation_ascii.txt`. Before running our simulation, we should move our file to the following directory: - -``` -`$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/` -``` - - - -To implement it in our simulation (.prm file), we initialize the temperature model as follows: - -``` - -# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. -subsection Initial temperature model - set List of model names = adiabatic, ascii data - subsection Adiabatic - set Age bottom boundary layer = 1e9 - set Age top boundary layer = 1e9 - - subsection Function - set Function expression = 0 - end - - end - -#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. - subsection Ascii data model - set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ - set Data file name = perturbation_ ascii.txt - end -end - -``` - - - -Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. - -``` - -subsection Material model - set Model name = Steinberger - set Material averaging = harmonic average - - subsection Steinberger model - - set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ - set Lateral viscosity file name = temp-viscosity-prefactor.txt - set Material file names = pyr-ringwood88.txt - set Radial viscosity file name = radial-visc-simple.txt - set Latent heat = false - - # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". - set Maximum lateral viscosity variation = 1e2 - set Maximum viscosity = 5e23 - set Minimum viscosity = 1e19 - set Use lateral average temperature for viscosity = false - set Thermal conductivity formulation = p-T-dependent - #set Thermal conductivity = 4.17 - - set Composition viscosity prefactors = 1 - - end -end -``` - -The simulation will take some time to run, but this will be the final result: - -``` - - - -Temperature distribution with aspect ratio adjustment. -``` - - - -You can see the complete video in the following link: - -https://www.youtube.com/watch?v=6KVsunMhpj0 - diff --git a/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex deleted file mode 100644 index 87b58891496..00000000000 --- a/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex +++ /dev/null @@ -1,328 +0,0 @@ - - -\documentclass{article} -\usepackage{amsmath} -\usepackage{graphicx} -\usepackage{hyperref} - -\begin{document} - -\section*{Using ASCII file to compute a personalized temperature distribution} - -\textit{This section was contributed by Francesco Radica.} - -In this cookbook, we will explore how to implement complex temperature perturbations in a simulation using Steinberger's material model. Specifically, we'll modify a temperature function originally developed for the CITCOM simulation program, designed to initiate mantle convection through an ASCII file. Additionally, we will implement a stagnant lid type subduction, aiming for a viscosity profile that is as realistic as possible. - -ASPECT employs the muparser language for writing mathematical functions, which are useful for describing various features such as temperature perturbation functions. For the simulation program CITCOM, a particular mathematical function is well-known for generating perturbations. We will thus apply this function to our adiabatic temperature profile, to which temperature will be added and subtracted according to the mathematical function: - -\begin{verbatim} -subsection Initial temperature model - set List of model names = adiabatic, function - subsection Adiabatic - set Age bottom boundary layer = 5e8 - set Age top boundary layer = 5e8 - - subsection Function - set Function expression = 0 - end - end - -subsection Function - set Coordinate system = spherical - set Variable names = r,theta - - set Function constants = r_inner=3481000, r_outer=6371000, tcmb=3700, tsurf=300, w=2*pi, p=300.0, frequency=100 - set Function expression = if(rr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) -end -\end{verbatim} - -The given function is defined in a spherical coordinate system and calculates values based on the radial position \(r\) and angular position \(\theta\). The function behaves differently inside, outside, and between two specified radii, \(r_{\text{inner}}\) and \(r_{\text{outer}}\). -The function is defined using conditional statements (if) to determine the value based on \(r\): -Inside the Inner Radius (\(r < r_{\text{inner}}\)): The function calculates a value by adding the constant \(t_{\text{cmb}}\) to a sinusoidal perturbation term. This perturbation term depends on the radial position \(r\), the angular position \(\theta\), and the constants \(p\) and frequency. -Formula: - -\begin{equation} -t_\text{cmb} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , -\end{equation} - -Outside the Outer Radius (\(r > r_{\text{outer}}\)): Like the inner radius case, but here the constant \(t_{\text{surf}}\) is added to the sinusoidal perturbation term. -Formula: - -\begin{equation} -t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , -\end{equation} - -Otherwise (For \(r\) Values Between \(r_{\text{inner}}\) and \(r_{\text{outer}}\)): Only the sinusoidal perturbation term is calculated. -Formula: - -\begin{equation} -p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , -\end{equation} - -This is the result for a quarter of shell: - -\begin{figure}[h!] -\centering -\includegraphics[width=0.48\textwidth]{temperature.png} -\caption{Temperature for the above muparser function.} -\label{fig:temperature} -\end{figure} - -However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. -For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. -Therefore, we may use the following mathematical function: - -\begin{equation} -temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , -\end{equation} - -And - -\begin{equation} -temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , -\end{equation} - -In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. -The final result will be as following: - -\begin{figure}[h!] -\centering -\includegraphics[width=0.48\textwidth]{ascii_temperature.png} -\caption{Temperature distribution in ASCII format.} -\label{fig:ascii-temperature} -\end{figure} - -Now, let's write a Python script to utilize the function and export it in ASCII format: - -\begin{verbatim} -# The script imports necessary libraries and sets up parameters for our temperature model. - -import matplotlib.pyplot as plt -import numpy as np -import math - -# Parameters -r_inner = 3481000 # Internal radius in meters -r_outer = 6371000 # External radius in meters -p_large = 400.0 # Amplitude of the large perturbations -p_small = 30.0 # Amplitude of the small perturbations -frequency_large = 3 # Frequency of the large perturbations -frequency_small = 30 # Frequency of the small perturbations -spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees -start_angle_degrees = 330 # Starting angle for the perturbation in degrees - -# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. - -def temperature_function_degrees_array(r, theta_degrees): - # Adjust theta to shift the starting angle of the perturbation - adjusted_theta_degrees = theta_degrees + start_angle_degrees - adjusted_theta_degrees = adjusted_theta_degrees % 360 - - # Initialize the temperature array - temp = np.zeros_like(r) - - # Determine the large perturbation using a step function approach - - large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) - temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) - - # Apply small perturbations where large perturbations are not applied - small_perturbation_mask = ~large_perturbation_mask - temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) - - return temp - -# Here we generate data for visualization -theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees -radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer - -# Here we create a grid for plotting - -R, Theta = np.meshgrid(radius, theta) -Temp = temperature_function_de - -grees_array(R, Theta) - - -# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. -# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. -# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: -# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. -# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. -# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. -# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. -#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. -# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. -# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). -# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. - - - -def write_ascii_data(radius, theta_degrees, temperatures, filename): - with open(filename, 'w') as file: - file.write("# Test data for ascii data initial conditions.\n") - file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") - file.write("# POINTS: 100 360 1\n") - file.write("# Columns: r phi temperature [K]\n") - - for j in range(len(theta_degrees)): - for i in range(len(radius)): - r = radius[i] - phi = theta_degrees[j] - temp = temperatures[j, i] - - # Improved formatting - r_str = f"{r:.1f}" - phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" - temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" - - # Column alignment with offset for the second column - file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") - - -# Conversion of polar coordinates to Cartesian coordinates for plotting -X = R * np.cos(np.radians(Theta)) -Y = R * np.sin(np.radians(Theta)) - - -# Plotting -plt.figure(figsize=(8, 6)) -contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') -plt.colorbar(contour, label='Temperature') -plt.title('Temperature distribution') -plt.xlabel('Coordinate X (m)') -plt.ylabel('Coordinate Y (m)') -plt.axis('equal') -plt.show() - - -# Use the function write_ascii_data to save data -write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') - -# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. - -import math - -def convert_to_radians(degrees): - """Convert degrees to radians.""" - return degrees * (math.pi / 180) - -def convert_file_angles(input_file_path, output_file_path): - """Convert the angles in the second column of the file from degrees to radians.""" - with open(input_file_path, 'r') as file: - content = file.readlines() - - converted_lines = content[:4] # Keep the header lines unchanged - for line in content[4:]: - columns = line.split() - if len(columns) == 3: - radius, angle_deg, temperature = columns - angle_rad = convert_to_radians(float(angle_deg)) - converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" - converted_lines.append(converted_line) - else: - converted_lines.append(line) - - with open(output_file_path, 'w') as file: - file.writelines(converted_lines) - -# Example usage -input_file_path = 'perturbation_ascii.txt' # Replace with your input file path -output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path - -convert_file_angles(input_file_path, output_file_path) - -\end{verbatim} - -If everything has been done correctly, the ASCII file should appear as follows: - -\begin{verbatim} -# Test data for ascii data initial conditions. -# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" -# POINTS: 100 360 1 -# Columns: r phi temperature [K] -3481000.0 0.00000000 0 -3510191.9 0.00000000 0 -3539383.8 0.00000000 0 -3568575.8 0.00000000 0 -3597767.7 0.00000000 0 -3626959.6 0.00000000 0 -3656151.5 0.00000000 0 -\end{verbatim} - -For each radius value and for each angular value, a certain temperature will be established. -Once executed, the script will generate a file named \texttt{perturbation\_ascii.txt}. Before running our simulation, we should move our file to the following directory: - -\begin{verbatim} -$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ -\end{verbatim} - -To implement it in our simulation (\texttt{.prm} file), we initialize the temperature model as follows: - -\begin{verbatim} -# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. -subsection Initial temperature model - set List of model names = adiabatic, ascii data - subsection Adiabatic - set Age bottom boundary layer = 1e9 - set Age top boundary layer = 1e9 - - subsection Function - set Function expression = 0 - end - - end - -#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. - subsection Ascii data model - set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ - set Data file name = perturbation_ ascii.txt - end -end -\end{verbatim} - -Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. - -\begin{verbatim} -subsection Material model - set Model name = Steinberger - set Material averaging = harmonic average - - subsection Steinberger model - - set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ - set Lateral viscosity file name = temp-viscosity-prefactor.txt - set Material file names = pyr-ringwood88.txt - set Radial viscosity file name = radial-visc-simple.txt - set Latent heat = false - - # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". - set Maximum lateral viscosity variation = 1e2 - set Maximum viscosity = 5e23 - set Minimum viscosity = 1e19 - set Use lateral average temperature for viscosity = false - set Thermal conductivity formulation = p-T-dependent - #set Thermal conductivity = 4.17 - - set Composition viscosity prefactors = 1 - - - - end -end -\end{verbatim} - -The simulation will take some time to run, but this will be the final result: - -\begin{figure}[h!] -\centering -\includegraphics[width=0.48\textwidth]{ascii_temperature_aspect.png} -\caption{Temperature distribution with aspect ratio adjustment.} -\label{fig:ascii-temperature-aspect} -\end{figure} - -You can see the complete video in the following link: -\url{https://www.youtube.com/watch?v=6KVsunMhpj0} - -\end{document} -``` \ No newline at end of file diff --git a/cookbooks/ascii_perturbation/perturbation.py b/cookbooks/ascii_perturbation/perturbation.py deleted file mode 100644 index ab5d46a683a..00000000000 --- a/cookbooks/ascii_perturbation/perturbation.py +++ /dev/null @@ -1,114 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -import math - -# Parametri -r_inner = 3481000 # Raggio interno in metri -r_outer = 6371000 # Raggio esterno in metri -p_large = 700.0 # Ampiezza delle grandi perturbazioni -p_small = 30.0 # Ampiezza delle piccole perturbazioni -frequency_large = 3 # Frequenza delle grandi perturbazioni -frequency_small = 30 # Frequenza delle piccole perturbazioni -spread_angle_large_degrees = 90 # Angolo di diffusione delle grandi perturbazioni in gradi -start_angle_degrees = 270 # Angolo di partenza per la perturbazione in gradi - -# Funzione di temperatura modificata per utilizzare i gradi e gestire gli array -def temperature_function_degrees_array(r, theta_degrees): - # Aggiusta theta per spostare l'angolo di inizio della perturbazione - adjusted_theta_degrees = theta_degrees + start_angle_degrees - adjusted_theta_degrees = adjusted_theta_degrees % 360 - - # Inizializza l'array della temperatura - temp = np.zeros_like(r) - - # Determina la grande perturbazione usando un approccio a funzione gradino - large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) - temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner) + math.pi) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) - - # Applica piccole perturbazioni dove non si applicano le grandi perturbazioni - small_perturbation_mask = ~large_perturbation_mask - temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) - - return temp - - - - -# Generazione dei dati per la visualizzazione -theta = np.linspace(0, 360, 360) # Angoli da 0 a 360 gradi -radius = np.linspace(r_inner, r_outer, 100) # Raggi da r_inner a r_outer - -# Creazione di una griglia per il plotting -R, Theta = np.meshgrid(radius, theta) -Temp = temperature_function_degrees_array(R, Theta) - -def write_ascii_data(radius, theta_degrees, temperatures, filename): - with open(filename, 'w') as file: - file.write("# Test data for ascii data initial conditions.\n") - file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") - file.write("# POINTS: 100 360 1\n") - file.write("# Columns: r phi temperature [K]\n") - - for j in range(len(theta_degrees)): - for i in range(len(radius)): - r = radius[i] - phi = theta_degrees[j] - temp = temperatures[j, i] - - # Formattazione migliorata - r_str = f"{r:.1f}" - phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" - temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" - - # Allineamento delle colonne con spostamento della seconda colonna - file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") - - -# Conversione delle coordinate polari in coordinate cartesiane per il plotting -X = R * np.cos(np.radians(Theta)) -Y = R * np.sin(np.radians(Theta)) - -# Plotting -plt.figure(figsize=(8, 6)) -contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') -plt.colorbar(contour, label='Temperatura') -plt.title('Distribuzione della Temperatura in Coordinate Polari') -plt.xlabel('Coordinata X (m)') -plt.ylabel('Coordinata Y (m)') -plt.axis('equal') -plt.show() - - -# Uso della funzione write_ascii_data per salvare i dati -write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') - -import math - -def convert_to_radians(degrees): - """Convert degrees to radians.""" - return degrees * (math.pi / 180) - -def convert_file_angles(input_file_path, output_file_path): - """Convert the angles in the second column of the file from degrees to radians.""" - with open(input_file_path, 'r') as file: - content = file.readlines() - - converted_lines = content[:4] # Keep the header lines unchanged - for line in content[4:]: - columns = line.split() - if len(columns) == 3: - radius, angle_deg, temperature = columns - angle_rad = convert_to_radians(float(angle_deg)) - converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" - converted_lines.append(converted_line) - else: - converted_lines.append(line) - - with open(output_file_path, 'w') as file: - file.writelines(converted_lines) - -# Example usage -input_file_path = 'perturbation_ascii.txt' # Replace with your input file path -output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path - -convert_file_angles(input_file_path, output_file_path) diff --git a/cookbooks/ascii_perturbation/perturbation_ascii.txt b/cookbooks/ascii_perturbation/perturbation_ascii.txt deleted file mode 100644 index d2cfd20bd2f..00000000000 --- a/cookbooks/ascii_perturbation/perturbation_ascii.txt +++ /dev/null @@ -1,36004 +0,0 @@ -# Test data for ascii data 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deleted file mode 100644 index 1215360c558324f168a348f977b46d5a160ee437..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 162 zcmWgj%}g%JFV0UZQSeVo%S=vH2rW)6VjuuS8GIQs8Il=_81fm4fjEt!gh7G9A4sQx Q#Z!U2P@qgIPz9v`0A Date: Tue, 11 Jun 2024 17:48:08 +0200 Subject: [PATCH 4/7] Add files via upload --- .../ascii_perturbation/ascii_perturbation.prm | 179 + .../documentation/ascii_temperature.png | Bin 0 -> 334131 bytes .../ascii_temperature_aspect.png | Bin 0 -> 243837 bytes .../documentation/perturbation.txt | 36004 ++++++++++++++++ .../documentation/temperature.png | Bin 0 -> 190985 bytes .../documentation/tutorial_a.docx | Bin 0 -> 27089 bytes .../documentation/tutorial_ascii.md | 329 + .../documentation/tutorial_ascii.tex | 328 + cookbooks/ascii_perturbation/perturbation.py | 114 + .../ascii_perturbation/perturbation_ascii.txt | 36004 ++++++++++++++++ 10 files changed, 72958 insertions(+) create mode 100644 cookbooks/ascii_perturbation/ascii_perturbation.prm create mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature.png create mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature_aspect.png create mode 100644 cookbooks/ascii_perturbation/documentation/perturbation.txt create mode 100644 cookbooks/ascii_perturbation/documentation/temperature.png create mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_a.docx create mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.md create mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex create mode 100644 cookbooks/ascii_perturbation/perturbation.py create mode 100644 cookbooks/ascii_perturbation/perturbation_ascii.txt diff --git a/cookbooks/ascii_perturbation/ascii_perturbation.prm b/cookbooks/ascii_perturbation/ascii_perturbation.prm new file mode 100644 index 00000000000..618deb32f05 --- /dev/null +++ b/cookbooks/ascii_perturbation/ascii_perturbation.prm @@ -0,0 +1,179 @@ + +set Dimension = 2 +#set Resume computation = auto +set Start time = 0 +set End time = 5e8 +set Use years in output instead of seconds = true +set Adiabatic surface temperature = 1623 +set Use conduction timestep = true +set Output directory = ascii_perturbation + + +set CFL number = 1 +set Nonlinear solver scheme = single Advection, single Stokes +subsection Solver parameters + subsection Stokes solver parameters + set Linear solver tolerance = 1e-5 + set Number of cheap Stokes solver steps = 2000 # 200 + end +end + +subsection Formulation + set Mass conservation = projected density field + set Temperature equation = real density +end + +subsection Checkpointing + set Steps between checkpoint = 100 +end + + +subsection Geometry model + set Model name = spherical shell + + subsection Spherical shell + set Inner radius = 3481000 + set Outer radius = 6371000 + end +end + + +subsection Boundary temperature model + set Fixed temperature boundary indicators = top, bottom + set List of model names = spherical constant + subsection Spherical constant + set Inner temperature = 3700 + set Outer temperature = 273 + end +end + + +subsection Boundary velocity model + set Tangential velocity boundary indicators = bottom, top +end + + +subsection Gravity model + set Model name = ascii data +end + + +# Here we initialize the temeprature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. + +subsection Initial temperature model + set List of model names = adiabatic, ascii data + subsection Adiabatic + set Age bottom boundary layer = 1e9 + set Age top boundary layer = 1e9 + + subsection Function + set Function expression = 0 + end + + end + +# Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. + + subsection Ascii data model + set Data directory = $ASPECT_SOURCE_DIR/data/cookbooks/ascii_perturbation + set Data file name = perturbation_ascii.txt + end +end + + +subsection Material model + set Model name = Steinberger + set Material averaging = harmonic average + + subsection Steinberger model + + set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ + set Lateral viscosity file name = temp-viscosity-prefactor.txt + set Material file names = pyr-ringwood88.txt + set Radial viscosity file name = radial-visc-simple.txt + set Latent heat = false + + # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". + + set Maximum lateral viscosity variation = 1e2 + set Maximum viscosity = 5e23 + set Minimum viscosity = 1e19 + + + set Use lateral average temperature for viscosity = false + set Thermal conductivity formulation = p-T-dependent + + set Composition viscosity prefactors = 1 + + end +end + + +subsection Heating model + set List of model names = adiabatic heating, shear heating +end + + +# We refine the mesh near the boundaries, and where temperature variations are +# large. In addition, we make sure that in the transition zone, where both the +# viscosity and the density change a lot, we use the highest refinement level. +subsection Mesh refinement + set Initial adaptive refinement = 1 + set Initial global refinement = 5 + set Refinement fraction = 0.95 + set Coarsening fraction = 0.05 + set Strategy = temperature, boundary, minimum refinement function + set Time steps between mesh refinement = 5 + + subsection Boundary + set Boundary refinement indicators = top, bottom + end + + subsection Minimum refinement function + set Coordinate system = depth + set Variable names = depth, phi + set Function expression = if(depth<700000, 6, 5) + end +end + +subsection Boundary temperature model + set Fixed temperature boundary indicators = 0,1 +end + + +subsection Nullspace removal + set Remove nullspace = net rotation +end + +subsection Compositional fields + set Number of fields = 1 + set Names of fields = density_field + set Types of fields = density + set Compositional field methods = prescribed field +end + + + +subsection Initial composition model + set Model name = function + subsection Function + set Variable names = x,y + set Function constants = r_inner=3481000, r_outer=6371000 + set Function expression = if(sqrt(x^2+y^2)NnjvAa1S9saCZ+7+}&+(cZcBa4g&-Y5Fki!cXxLgU~qTYlk2{( z_j&hP&xid3_SBlG9#(hLl$_@wRfH?ZNdVpvyn}&(0Z4xPsssZAZvX=WSA~oS{mIKR zks!2!byAWLfvFfHfP-IOrRC^?z&lT-g7)V=mmkXTuxh!vA{=SM~R@{-6r!yEBAsET8!Yb~tN7+cZreg6gkHLeiJ5g^i6lBWC!r-Ks z%1cU0${OB%0e;n;RDG}8TUB*%@TFqks3&N#w;XQ{HO$`tM)CbC99#lbyW8vfY1xU> zxX-D;?kLkH%QXMx38bQ;w4%aE&TSrYa*!7zQkrL(`@a^0Xe$Hv=u`!i5`zD|R3Vna zs*whj2K;ZOt{}kD{}-j$yiqCQ|5{+xa{ku~O9TG@OaHG1`~Tida}od@-+M4bLhwPc z>3%oUtJG~$47V`n<*L|XFoBZ)tS-IbypM1?*6(Tis#x&(XYqnGL*u9CBQrti;S~DA zfXc`oM!)-E=P~ZRg5SS?yC{0o*Zg;67!aH15*Qo`LFxud16+Ov+_s+jSRDSU2i>gq z5!z)5T*SwgOUKVgR`X_$c`C++C*R%HKYMvDbd#iv@t(GT%J=y8xGmbBZ=}`reO%DJ zZ9X%>pmS~bU!AzMH`Am%+8_PyFA5d7%7dKxy?VjxtH*bv3-a+FD8@?FuevTbVdkZ1 zvn%{ls#4gQno@?#dQ|}`fO2EN2#BB8rtN;0Ux`k)>65PSJ?ZqozIoH$Npta^-&OAC zTW@3mw3PwDD7Zx)m%EyNkvQ~P9*AxT5i|nZif&zZcXwarjm*udN7I-o=yjW%lilg` z+g6;h%r-+pL$O-sof~eJtfo1ZtrK16d9Rz-pDXOr@${bR)*IRB)xrAzK9w!I0-(yJ z>{ZKiwnJ;aV^V@N`_3v<@M#mBlsKUcn<=(!!)6H0rKR|+&_AW);b#C%n{Gu;@~^s5 z=%n1Q45)rBNSqrtb$qs34X*gP7|QLm+Yo0I<|3U%q>YWQ77TP8EF-Pv0e6LID(+uP?V$$$cP#i&K|Mufk=!cK&Sdi^1?kQUka4$JJ@h z_WRKgL@H!-zq{^iPCk|_y{9eQ%pzfhAmIZ&uVYgpcfV7wb$KtrePOv8w&TTdU)QGH z46CJ2{O8h)&ptdC1Nl=e_m{G)cKHYp{THzQl>Y0(JPF?p@5|kG^yMbH&p?fTtk=r+ z)WATPVf+2DU6kJk>B@2B!D09NtLMQbf%nC{hFgR`Z#ARM0N}*)JFj!=kVq6 z)J_LTDEZng_!L;lkD7FM7Ak0cH%OH;Ws;Xz9fY>@cOF0j(7pZ7|E&8yBFYa*ufL4B z5fBG94>L3uplADfY9)i?1n&o9r`H~jwjF_ES?Mu62PMwOb$*AmoTk5zVh%}P@A@lb zBA%f`Twa36;cEt~Tg+u=V?X~%yxz}8r4)LQeb-yrwe=SqQ~&<;OVBOfrLhGaWO5R} z?PbrejaAXlK;Gv-@IJ!!Tl)qA<9>YJC#ERhvp~`kJukvovk1@Y<@y`YZA(8F>GQq> ziicBS)bS~f=_{DgkNL@z(W^04e(lHJ)}G*NqebWT>7cxCL?v0u?RHV7t>sJLUiS0ta%CR(WsRAuz%xXiyLI`b*$wox)6ILiH}2+{<8uSq zEPfUx#*Z#2so~tzTBSj zfobF+M@@$nAr_Jv67XP>jIP&`{FqvXKP#4HV~Hv;L@Ca`&xiViw{fCq9MAmF(Hn!< zm)%YB>V6o^QW6NnBm|jdU$-+Pws6;&xy0~Y42)rnyNA5Q>}NR+(ezET@Lw*!`oj}6 zx$Z=O`rk(els!_#fj z*E9zce{R3#<3FcFrDjo{=jD9RAYEG_{BWS&Zh1GX|Kd1(7Wjh3z4LzfwU4uP@*Wze zYp$H!%@QwUMlADxHf<5Hdj8es^-ao%c!NIarf}c&Sw}r zEabAfJC=EPyA$9g&|!~%oK5<27Rt}YuK0h#DO(5bF2UbC$YBro057Az;Kks5J`u6)SOJx3D86{W zRSoME8kE-JjYB`{ek^W%ecrv#G7~KJ&!Bz!1I!LD={L-#K2`BlHRl+JBj1Sq~~g?+_mp^hZN zx_rPlkWYn$d%xbAVc28~=B!|4m}~w_2979YPklIj}d0IZr+M8#%8} zd$-Bg4~Lbvsjk2tDd;oR;Mi=!|{s{&RLpU_dJfA0n5Qo`Dx9A$`undsHPVAq}7c^0rRP@h;(sw_ziovJdfG zXpUzD4bjE(S@QVtAg1ZG6V{Jl${KOO3N?;YU!&N-N14^>QzL4$<1@LlCeAaOH`1kS|0N(jC{W*Ri+Not0}c=r`KO%WLOpz6AJ?VZn>N0)xs9z9Fh-P(vfmI6we2d+HD&wpsI|Tl>lPKe2TR}0DEvmJE=bX9RPJ}C z9l$yJcGRv{k99PtaQ*4?jUD#K8~JFHezd)Vqc8N@w3=;lGPfpQ@)kR;8pnOc9<3Lo zgJX~zh|C1X-Oc!-_t%GlQkK+1=!o4`91_nKrN3%-@e7T8)E73e+QaazW%bUTaBA0THz z>b`73ae}UXHI*Qk24Z99WA*S0l#OJyzI@fS^B@;lfsXG3cZ#J)^cb8<

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z1Tlch$8r;~`e!w6PcnE_MM)kYy8O?@EcBec(GZC1%?X5x331ecc;_fO*xEU=8rnMi zq2!Pt>i_SZ1Lw|%$d_q`jVJ)@?F-S?1i5UCCuDRFjW^G#m_ZA$1PxI(FyMxC#P^G$HE1} zKw^$Kj8*(qvk*{+zNfGePcF>TOgq}HpJf(NWoAIK&6r}j2;F2Z}aa_0&Q$GA!H!Y6-lFpJlKP@pIKxLgb0u&`Z7*{8IjhV|9IWgNA zoIxI=_3%Kl#GivM+xuOdHm9{8Xt zWgBR1c*Zusq6{x_ff1~*5a@Nrkj0xcD)&`9HNUVK=oC~u9v+ByjQ`CbR!p8|NhSvv z?!8_y0fm1rSM7;m-uEIW?(@q^&zQ;Yl*J!-xB2MX!vQ6pL{rFBL19KHM3GRIc)7cE z@71&Y{*v;m$66G4l3=kY`*$A-H6Ck2&>2AT&aWiqs74g{D3-jfQ&1 zZvE)Jpz2-3xB%#Q^Iu!oS;&+FSpDZvX{=?!|_mAJghL+Z`%{9yEoAE1%J4h*_hHgcaI)5az`qTee&_JJ9sHBSH=X}*_?uPyJO1w$#!oZ=u&NIL o{KMY(9sc(w{#SU0;Vr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) +end +``` + +The given function is defined in a spherical coordinate system and calculates values based on the radial position r and angular position theta. The function behaves differently inside, outside, and between two specified radii, r_inner and r_outer. +The function is defined using conditional statements (if) to determine the value based on r: +Inside the Inner Radius (rr_outer): Like the inner radius case, but here the constant tsurf is added to the sinusoidal perturbation term. +Formula: + +```{math} +t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , +``` + +Otherwise (For r Values Between r_inner and r_outer): Only the sinusoidal perturbation term is calculated. +Formula: + +```{math} +p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , +``` + +This is the result for a quarter of shell: + +```{figure-md} fig:temperature + + +Temperature for the above muparser function. +``` + +However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. +For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. +Therefore, we may use the following mathematical function: + +```{math} +temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , +``` + +And + + +```{math} +temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , +``` + +In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. +The final result will be as following: + +``` + + +Temperature distribution in ASCII format. +``` + + +Now, let's write a Python script to utilize the function and export it in ASCII format + +``` +# The script imports necessary libraries and sets up parameters for our temperature model. + +import matplotlib.pyplot as plt +import numpy as np +import math + +# Parameters +r_inner = 3481000 # Internal radius in meters +r_outer = 6371000 # External radius in meters +p_large = 400.0 # Amplitude of the large perturbations +p_small = 30.0 # Amplitude of the small perturbations +frequency_large = 3 # Frequency of the large perturbations +frequency_small = 30 # Frequency of the small perturbations +spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees +start_angle_degrees = 330 # Starting angle for the perturbation in degrees + +# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. + +def temperature_function_degrees_array(r, theta_degrees): + # Adjust theta to shift the starting angle of the perturbation + adjusted_theta_degrees = theta_degrees + start_angle_degrees + adjusted_theta_degrees = adjusted_theta_degrees % 360 + + # Initialize the temperature array + temp = np.zeros_like(r) + + # Determine the large perturbation using a step function approach + + large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) + temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) + + # Apply small perturbations where large perturbations are not applied + small_perturbation_mask = ~large_perturbation_mask + temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) + + return temp + +# Here we generate data for visualization +theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees +radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer + +# Here we create a grid for plotting + +R, Theta = np.meshgrid(radius, theta) +Temp = temperature_function_degrees_array(R, Theta) + + +# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. +# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. +# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: +# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. +# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. +# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. +# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. +#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. +# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. +# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). +# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. + + + +def write_ascii_data(radius, theta_degrees, temperatures, filename): + with open(filename, 'w') as file: + file.write("# Test data for ascii data initial conditions.\n") + file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") + file.write("# POINTS: 100 360 1\n") + file.write("# Columns: r phi temperature [K]\n") + + for j in range(len(theta_degrees)): + for i in range(len(radius)): + r = radius[i] + phi = theta_degrees[j] + temp = temperatures[j, i] + + # Improved formatting + r_str = f"{r:.1f}" + phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" + temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" + + # Column alignment with offset for the second column + file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") + + +# Conversion of polar coordinates to Cartesian coordinates for plotting +X = R * np.cos(np.radians(Theta)) +Y = R * np.sin(np.radians(Theta)) + + +# Plotting +plt.figure(figsize=(8, 6)) +contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') +plt.colorbar(contour, label='Temperature') +plt.title('Temperature distribution') +plt.xlabel('Coordinate X (m)') +plt.ylabel('Coordinate Y (m)') +plt.axis('equal') +plt.show() + + +# Use the function write_ascii_data to save data +write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') + +# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. + +import math + +def convert_to_radians(degrees): + """Convert degrees to radians.""" + return degrees * (math.pi / 180) + +def convert_file_angles(input_file_path, output_file_path): + """Convert the angles in the second column of the file from degrees to radians.""" + with open(input_file_path, 'r') as file: + content = file.readlines() + + converted_lines = content[:4] # Keep the header lines unchanged + for line in content[4:]: + columns = line.split() + if len(columns) == 3: + radius, angle_deg, temperature = columns + angle_rad = convert_to_radians(float(angle_deg)) + converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" + converted_lines.append(converted_line) + else: + converted_lines.append(line) + + with open(output_file_path, 'w') as file: + file.writelines(converted_lines) + +# Example usage +input_file_path = 'perturbation_ascii.txt' # Replace with your input file path +output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path + +convert_file_angles(input_file_path, output_file_path) + +``` + + +If everything has been done correctly, the ASCII file should appear as follows: + + +``` + +# Test data for ascii data initial conditions. +# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" +# POINTS: 100 360 1 +# Columns: r phi temperature [K] +3481000.0 0.00000000 0 +3510191.9 0.00000000 0 +3539383.8 0.00000000 0 +3568575.8 0.00000000 0 +3597767.7 0.00000000 0 +3626959.6 0.00000000 0 +3656151.5 0.00000000 0 + + +``` + +For each radius value and for each angular value, a certain temperature will be established. +Once executed, the script will generate a file named `perturbation_ascii.txt`. Before running our simulation, we should move our file to the following directory: + +``` +`$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/` +``` + + + +To implement it in our simulation (.prm file), we initialize the temperature model as follows: + +``` + +# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. +subsection Initial temperature model + set List of model names = adiabatic, ascii data + subsection Adiabatic + set Age bottom boundary layer = 1e9 + set Age top boundary layer = 1e9 + + subsection Function + set Function expression = 0 + end + + end + +#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. + subsection Ascii data model + set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ + set Data file name = perturbation_ ascii.txt + end +end + +``` + + + +Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. + +``` + +subsection Material model + set Model name = Steinberger + set Material averaging = harmonic average + + subsection Steinberger model + + set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ + set Lateral viscosity file name = temp-viscosity-prefactor.txt + set Material file names = pyr-ringwood88.txt + set Radial viscosity file name = radial-visc-simple.txt + set Latent heat = false + + # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". + set Maximum lateral viscosity variation = 1e2 + set Maximum viscosity = 5e23 + set Minimum viscosity = 1e19 + set Use lateral average temperature for viscosity = false + set Thermal conductivity formulation = p-T-dependent + #set Thermal conductivity = 4.17 + + set Composition viscosity prefactors = 1 + + end +end +``` + +The simulation will take some time to run, but this will be the final result: + +``` + + + +Temperature distribution with aspect ratio adjustment. +``` + + + +You can see the complete video in the following link: + +https://www.youtube.com/watch?v=6KVsunMhpj0 + diff --git a/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex new file mode 100644 index 00000000000..87b58891496 --- /dev/null +++ b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex @@ -0,0 +1,328 @@ + + +\documentclass{article} +\usepackage{amsmath} +\usepackage{graphicx} +\usepackage{hyperref} + +\begin{document} + +\section*{Using ASCII file to compute a personalized temperature distribution} + +\textit{This section was contributed by Francesco Radica.} + +In this cookbook, we will explore how to implement complex temperature perturbations in a simulation using Steinberger's material model. Specifically, we'll modify a temperature function originally developed for the CITCOM simulation program, designed to initiate mantle convection through an ASCII file. Additionally, we will implement a stagnant lid type subduction, aiming for a viscosity profile that is as realistic as possible. + +ASPECT employs the muparser language for writing mathematical functions, which are useful for describing various features such as temperature perturbation functions. For the simulation program CITCOM, a particular mathematical function is well-known for generating perturbations. We will thus apply this function to our adiabatic temperature profile, to which temperature will be added and subtracted according to the mathematical function: + +\begin{verbatim} +subsection Initial temperature model + set List of model names = adiabatic, function + subsection Adiabatic + set Age bottom boundary layer = 5e8 + set Age top boundary layer = 5e8 + + subsection Function + set Function expression = 0 + end + end + +subsection Function + set Coordinate system = spherical + set Variable names = r,theta + + set Function constants = r_inner=3481000, r_outer=6371000, tcmb=3700, tsurf=300, w=2*pi, p=300.0, frequency=100 + set Function expression = if(rr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) +end +\end{verbatim} + +The given function is defined in a spherical coordinate system and calculates values based on the radial position \(r\) and angular position \(\theta\). The function behaves differently inside, outside, and between two specified radii, \(r_{\text{inner}}\) and \(r_{\text{outer}}\). +The function is defined using conditional statements (if) to determine the value based on \(r\): +Inside the Inner Radius (\(r < r_{\text{inner}}\)): The function calculates a value by adding the constant \(t_{\text{cmb}}\) to a sinusoidal perturbation term. This perturbation term depends on the radial position \(r\), the angular position \(\theta\), and the constants \(p\) and frequency. +Formula: + +\begin{equation} +t_\text{cmb} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , +\end{equation} + +Outside the Outer Radius (\(r > r_{\text{outer}}\)): Like the inner radius case, but here the constant \(t_{\text{surf}}\) is added to the sinusoidal perturbation term. +Formula: + +\begin{equation} +t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , +\end{equation} + +Otherwise (For \(r\) Values Between \(r_{\text{inner}}\) and \(r_{\text{outer}}\)): Only the sinusoidal perturbation term is calculated. +Formula: + +\begin{equation} +p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , +\end{equation} + +This is the result for a quarter of shell: + +\begin{figure}[h!] +\centering +\includegraphics[width=0.48\textwidth]{temperature.png} +\caption{Temperature for the above muparser function.} +\label{fig:temperature} +\end{figure} + +However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. +For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. +Therefore, we may use the following mathematical function: + +\begin{equation} +temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , +\end{equation} + +And + +\begin{equation} +temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , +\end{equation} + +In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. +The final result will be as following: + +\begin{figure}[h!] +\centering +\includegraphics[width=0.48\textwidth]{ascii_temperature.png} +\caption{Temperature distribution in ASCII format.} +\label{fig:ascii-temperature} +\end{figure} + +Now, let's write a Python script to utilize the function and export it in ASCII format: + +\begin{verbatim} +# The script imports necessary libraries and sets up parameters for our temperature model. + +import matplotlib.pyplot as plt +import numpy as np +import math + +# Parameters +r_inner = 3481000 # Internal radius in meters +r_outer = 6371000 # External radius in meters +p_large = 400.0 # Amplitude of the large perturbations +p_small = 30.0 # Amplitude of the small perturbations +frequency_large = 3 # Frequency of the large perturbations +frequency_small = 30 # Frequency of the small perturbations +spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees +start_angle_degrees = 330 # Starting angle for the perturbation in degrees + +# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. + +def temperature_function_degrees_array(r, theta_degrees): + # Adjust theta to shift the starting angle of the perturbation + adjusted_theta_degrees = theta_degrees + start_angle_degrees + adjusted_theta_degrees = adjusted_theta_degrees % 360 + + # Initialize the temperature array + temp = np.zeros_like(r) + + # Determine the large perturbation using a step function approach + + large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) + temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) + + # Apply small perturbations where large perturbations are not applied + small_perturbation_mask = ~large_perturbation_mask + temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) + + return temp + +# Here we generate data for visualization +theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees +radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer + +# Here we create a grid for plotting + +R, Theta = np.meshgrid(radius, theta) +Temp = temperature_function_de + +grees_array(R, Theta) + + +# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. +# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. +# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: +# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. +# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. +# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. +# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. +#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. +# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. +# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). +# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. + + + +def write_ascii_data(radius, theta_degrees, temperatures, filename): + with open(filename, 'w') as file: + file.write("# Test data for ascii data initial conditions.\n") + file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") + file.write("# POINTS: 100 360 1\n") + file.write("# Columns: r phi temperature [K]\n") + + for j in range(len(theta_degrees)): + for i in range(len(radius)): + r = radius[i] + phi = theta_degrees[j] + temp = temperatures[j, i] + + # Improved formatting + r_str = f"{r:.1f}" + phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" + temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" + + # Column alignment with offset for the second column + file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") + + +# Conversion of polar coordinates to Cartesian coordinates for plotting +X = R * np.cos(np.radians(Theta)) +Y = R * np.sin(np.radians(Theta)) + + +# Plotting +plt.figure(figsize=(8, 6)) +contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') +plt.colorbar(contour, label='Temperature') +plt.title('Temperature distribution') +plt.xlabel('Coordinate X (m)') +plt.ylabel('Coordinate Y (m)') +plt.axis('equal') +plt.show() + + +# Use the function write_ascii_data to save data +write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') + +# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. + +import math + +def convert_to_radians(degrees): + """Convert degrees to radians.""" + return degrees * (math.pi / 180) + +def convert_file_angles(input_file_path, output_file_path): + """Convert the angles in the second column of the file from degrees to radians.""" + with open(input_file_path, 'r') as file: + content = file.readlines() + + converted_lines = content[:4] # Keep the header lines unchanged + for line in content[4:]: + columns = line.split() + if len(columns) == 3: + radius, angle_deg, temperature = columns + angle_rad = convert_to_radians(float(angle_deg)) + converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" + converted_lines.append(converted_line) + else: + converted_lines.append(line) + + with open(output_file_path, 'w') as file: + file.writelines(converted_lines) + +# Example usage +input_file_path = 'perturbation_ascii.txt' # Replace with your input file path +output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path + +convert_file_angles(input_file_path, output_file_path) + +\end{verbatim} + +If everything has been done correctly, the ASCII file should appear as follows: + +\begin{verbatim} +# Test data for ascii data initial conditions. +# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" +# POINTS: 100 360 1 +# Columns: r phi temperature [K] +3481000.0 0.00000000 0 +3510191.9 0.00000000 0 +3539383.8 0.00000000 0 +3568575.8 0.00000000 0 +3597767.7 0.00000000 0 +3626959.6 0.00000000 0 +3656151.5 0.00000000 0 +\end{verbatim} + +For each radius value and for each angular value, a certain temperature will be established. +Once executed, the script will generate a file named \texttt{perturbation\_ascii.txt}. Before running our simulation, we should move our file to the following directory: + +\begin{verbatim} +$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ +\end{verbatim} + +To implement it in our simulation (\texttt{.prm} file), we initialize the temperature model as follows: + +\begin{verbatim} +# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. +subsection Initial temperature model + set List of model names = adiabatic, ascii data + subsection Adiabatic + set Age bottom boundary layer = 1e9 + set Age top boundary layer = 1e9 + + subsection Function + set Function expression = 0 + end + + end + +#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. + subsection Ascii data model + set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ + set Data file name = perturbation_ ascii.txt + end +end +\end{verbatim} + +Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. + +\begin{verbatim} +subsection Material model + set Model name = Steinberger + set Material averaging = harmonic average + + subsection Steinberger model + + set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ + set Lateral viscosity file name = temp-viscosity-prefactor.txt + set Material file names = pyr-ringwood88.txt + set Radial viscosity file name = radial-visc-simple.txt + set Latent heat = false + + # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". + set Maximum lateral viscosity variation = 1e2 + set Maximum viscosity = 5e23 + set Minimum viscosity = 1e19 + set Use lateral average temperature for viscosity = false + set Thermal conductivity formulation = p-T-dependent + #set Thermal conductivity = 4.17 + + set Composition viscosity prefactors = 1 + + + + end +end +\end{verbatim} + +The simulation will take some time to run, but this will be the final result: + +\begin{figure}[h!] +\centering +\includegraphics[width=0.48\textwidth]{ascii_temperature_aspect.png} +\caption{Temperature distribution with aspect ratio adjustment.} +\label{fig:ascii-temperature-aspect} +\end{figure} + +You can see the complete video in the following link: +\url{https://www.youtube.com/watch?v=6KVsunMhpj0} + +\end{document} +``` \ No newline at end of file diff --git a/cookbooks/ascii_perturbation/perturbation.py b/cookbooks/ascii_perturbation/perturbation.py new file mode 100644 index 00000000000..ab5d46a683a --- /dev/null +++ b/cookbooks/ascii_perturbation/perturbation.py @@ -0,0 +1,114 @@ +import matplotlib.pyplot as plt +import numpy as np +import math + +# Parametri +r_inner = 3481000 # Raggio interno in metri +r_outer = 6371000 # Raggio esterno in metri +p_large = 700.0 # Ampiezza delle grandi perturbazioni +p_small = 30.0 # Ampiezza delle piccole perturbazioni +frequency_large = 3 # Frequenza delle grandi perturbazioni +frequency_small = 30 # Frequenza delle piccole perturbazioni +spread_angle_large_degrees = 90 # Angolo di diffusione delle grandi perturbazioni in gradi +start_angle_degrees = 270 # Angolo di partenza per la perturbazione in gradi + +# Funzione di temperatura modificata per utilizzare i gradi e gestire gli array +def temperature_function_degrees_array(r, theta_degrees): + # Aggiusta theta per spostare l'angolo di inizio della perturbazione + adjusted_theta_degrees = theta_degrees + start_angle_degrees + adjusted_theta_degrees = adjusted_theta_degrees % 360 + + # Inizializza l'array della temperatura + temp = np.zeros_like(r) + + # Determina la grande perturbazione usando un approccio a funzione gradino + large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) + temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner) + math.pi) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) + + # Applica piccole perturbazioni dove non si applicano le grandi perturbazioni + small_perturbation_mask = ~large_perturbation_mask + temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) + + return temp + + + + +# Generazione dei dati per la visualizzazione +theta = np.linspace(0, 360, 360) # Angoli da 0 a 360 gradi +radius = np.linspace(r_inner, r_outer, 100) # Raggi da r_inner a r_outer + +# Creazione di una griglia per il plotting +R, Theta = np.meshgrid(radius, theta) +Temp = temperature_function_degrees_array(R, Theta) + +def write_ascii_data(radius, theta_degrees, temperatures, filename): + with open(filename, 'w') as file: + file.write("# Test data for ascii data initial conditions.\n") + file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") + file.write("# POINTS: 100 360 1\n") + file.write("# Columns: r phi temperature [K]\n") + + for j in range(len(theta_degrees)): + for i in range(len(radius)): + r = radius[i] + phi = theta_degrees[j] + temp = temperatures[j, i] + + # Formattazione migliorata + r_str = f"{r:.1f}" + phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" + temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" + + # Allineamento delle colonne con spostamento della seconda colonna + file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") + + +# Conversione delle coordinate polari in coordinate cartesiane per il plotting +X = R * np.cos(np.radians(Theta)) +Y = R * np.sin(np.radians(Theta)) + +# Plotting +plt.figure(figsize=(8, 6)) +contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') +plt.colorbar(contour, label='Temperatura') +plt.title('Distribuzione della Temperatura in Coordinate Polari') +plt.xlabel('Coordinata X (m)') +plt.ylabel('Coordinata Y (m)') +plt.axis('equal') +plt.show() + + +# Uso della funzione write_ascii_data per salvare i dati +write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') + +import math + +def convert_to_radians(degrees): + """Convert degrees to radians.""" + return degrees * (math.pi / 180) + +def convert_file_angles(input_file_path, output_file_path): + """Convert the angles in the second column of the file from degrees to radians.""" + with open(input_file_path, 'r') as file: + content = file.readlines() + + converted_lines = content[:4] # Keep the header lines unchanged + for line in content[4:]: + columns = line.split() + if len(columns) == 3: + radius, angle_deg, temperature = columns + angle_rad = convert_to_radians(float(angle_deg)) + converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" + converted_lines.append(converted_line) + else: + converted_lines.append(line) + + with open(output_file_path, 'w') as file: + file.writelines(converted_lines) + +# Example usage +input_file_path = 'perturbation_ascii.txt' # Replace with your input file path +output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path + +convert_file_angles(input_file_path, output_file_path) diff --git a/cookbooks/ascii_perturbation/perturbation_ascii.txt b/cookbooks/ascii_perturbation/perturbation_ascii.txt new file mode 100644 index 00000000000..d2cfd20bd2f --- /dev/null +++ b/cookbooks/ascii_perturbation/perturbation_ascii.txt @@ -0,0 +1,36004 @@ +# Test data for ascii data initial conditions. +# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" +# POINTS: 100 360 1 +# Columns: r phi temperature [K] +3481000.0 0.00000000 0 +3510191.9 0.00000000 0 +3539383.8 0.00000000 0 +3568575.8 0.00000000 0 +3597767.7 0.00000000 0 +3626959.6 0.00000000 0 +3656151.5 0.00000000 0 +3685343.4 0.00000000 0 +3714535.4 0.00000000 0 +3743727.3 0.00000000 0 +3772919.2 0.00000000 0 +3802111.1 0.00000000 0 +3831303.0 0.00000000 0 +3860494.9 0.00000000 0 +3889686.9 0.00000000 0 +3918878.8 0.00000000 0 +3948070.7 0.00000000 0 +3977262.6 0.00000000 0 +4006454.5 0.00000000 0 +4035646.5 0.00000000 0 +4064838.4 0.00000000 0 +4094030.3 0.00000000 0 +4123222.2 0.00000000 0 +4152414.1 0.00000000 0 +4181606.1 0.00000000 0 +4210798.0 0.00000000 0 +4239989.9 0.00000000 0 +4269181.8 0.00000000 0 +4298373.7 0.00000000 0 +4327565.7 0.00000000 0 +4356757.6 0.00000000 0 +4385949.5 0.00000000 0 +4415141.4 0.00000000 0 +4444333.3 0.00000000 0 +4473525.3 0.00000000 0 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<51544149+Francyrad@users.noreply.github.com> Date: Sat, 13 Jul 2024 17:28:18 +0200 Subject: [PATCH 5/7] Add files via upload --- .../documentation/tutorial_ascii.md | 156 ++---------------- cookbooks/ascii_perturbation/perturbation.py | 87 ++++++---- 2 files changed, 70 insertions(+), 173 deletions(-) diff --git a/cookbooks/ascii_perturbation/documentation/tutorial_ascii.md b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.md index c6099e360f0..31ce924301b 100644 --- a/cookbooks/ascii_perturbation/documentation/tutorial_ascii.md +++ b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.md @@ -83,146 +83,20 @@ The final result will be as following: Temperature distribution in ASCII format. ``` - -Now, let's write a Python script to utilize the function and export it in ASCII format - -``` -# The script imports necessary libraries and sets up parameters for our temperature model. - -import matplotlib.pyplot as plt -import numpy as np -import math - -# Parameters -r_inner = 3481000 # Internal radius in meters -r_outer = 6371000 # External radius in meters -p_large = 400.0 # Amplitude of the large perturbations -p_small = 30.0 # Amplitude of the small perturbations -frequency_large = 3 # Frequency of the large perturbations -frequency_small = 30 # Frequency of the small perturbations -spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees -start_angle_degrees = 330 # Starting angle for the perturbation in degrees - -# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. - -def temperature_function_degrees_array(r, theta_degrees): - # Adjust theta to shift the starting angle of the perturbation - adjusted_theta_degrees = theta_degrees + start_angle_degrees - adjusted_theta_degrees = adjusted_theta_degrees % 360 - - # Initialize the temperature array - temp = np.zeros_like(r) - - # Determine the large perturbation using a step function approach - - large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) - temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) - - # Apply small perturbations where large perturbations are not applied - small_perturbation_mask = ~large_perturbation_mask - temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) - - return temp - -# Here we generate data for visualization -theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees -radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer - -# Here we create a grid for plotting - -R, Theta = np.meshgrid(radius, theta) -Temp = temperature_function_degrees_array(R, Theta) - - -# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. -# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. -# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: -# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. -# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. -# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. -# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. -#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. -# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. -# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). -# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. - - - -def write_ascii_data(radius, theta_degrees, temperatures, filename): - with open(filename, 'w') as file: - file.write("# Test data for ascii data initial conditions.\n") - file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") - file.write("# POINTS: 100 360 1\n") - file.write("# Columns: r phi temperature [K]\n") - - for j in range(len(theta_degrees)): - for i in range(len(radius)): - r = radius[i] - phi = theta_degrees[j] - temp = temperatures[j, i] - - # Improved formatting - r_str = f"{r:.1f}" - phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" - temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" - - # Column alignment with offset for the second column - file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") - - -# Conversion of polar coordinates to Cartesian coordinates for plotting -X = R * np.cos(np.radians(Theta)) -Y = R * np.sin(np.radians(Theta)) - - -# Plotting -plt.figure(figsize=(8, 6)) -contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') -plt.colorbar(contour, label='Temperature') -plt.title('Temperature distribution') -plt.xlabel('Coordinate X (m)') -plt.ylabel('Coordinate Y (m)') -plt.axis('equal') -plt.show() - - -# Use the function write_ascii_data to save data -write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') - -# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. - -import math - -def convert_to_radians(degrees): - """Convert degrees to radians.""" - return degrees * (math.pi / 180) - -def convert_file_angles(input_file_path, output_file_path): - """Convert the angles in the second column of the file from degrees to radians.""" - with open(input_file_path, 'r') as file: - content = file.readlines() - - converted_lines = content[:4] # Keep the header lines unchanged - for line in content[4:]: - columns = line.split() - if len(columns) == 3: - radius, angle_deg, temperature = columns - angle_rad = convert_to_radians(float(angle_deg)) - converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" - converted_lines.append(converted_line) - else: - converted_lines.append(line) - - with open(output_file_path, 'w') as file: - file.writelines(converted_lines) - -# Example usage -input_file_path = 'perturbation_ascii.txt' # Replace with your input file path -output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path - -convert_file_angles(input_file_path, output_file_path) - -``` +Along with this imput file, it's provided a complete python script full of comments and details of how it build our ASCII file. +After importing the libraries and defining our function, the script will plot how our temperature profile will look. The next step is to write the temperature perturbation in an ASCII format that ASPECT can read. +The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. +The function opens a file with the given filename in write mode. All the data that follows will be written to this file. +The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: +100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. +360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. +1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. +The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. +In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. +The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. +For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). +The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. +At the end, we convert degrees to radians, since ASPECT only works with radians. Then it creates the file perturbation.txt If everything has been done correctly, the ASCII file should appear as follows: @@ -242,6 +116,8 @@ If everything has been done correctly, the ASCII file should appear as follows: 3626959.6 0.00000000 0 3656151.5 0.00000000 0 +And many other lines... + ``` diff --git a/cookbooks/ascii_perturbation/perturbation.py b/cookbooks/ascii_perturbation/perturbation.py index ab5d46a683a..a4f7bb45812 100644 --- a/cookbooks/ascii_perturbation/perturbation.py +++ b/cookbooks/ascii_perturbation/perturbation.py @@ -1,47 +1,65 @@ +# The script imports necessary libraries and sets up parameters for our temperature model. + import matplotlib.pyplot as plt import numpy as np import math -# Parametri -r_inner = 3481000 # Raggio interno in metri -r_outer = 6371000 # Raggio esterno in metri -p_large = 700.0 # Ampiezza delle grandi perturbazioni -p_small = 30.0 # Ampiezza delle piccole perturbazioni -frequency_large = 3 # Frequenza delle grandi perturbazioni -frequency_small = 30 # Frequenza delle piccole perturbazioni -spread_angle_large_degrees = 90 # Angolo di diffusione delle grandi perturbazioni in gradi -start_angle_degrees = 270 # Angolo di partenza per la perturbazione in gradi - -# Funzione di temperatura modificata per utilizzare i gradi e gestire gli array +# Parameters +r_inner = 3481000 # Internal radius in meters +r_outer = 6371000 # External radius in meters +p_large = 400.0 # Amplitude of the large perturbations +p_small = 30.0 # Amplitude of the small perturbations +frequency_large = 3 # Frequency of the large perturbations +frequency_small = 30 # Frequency of the small perturbations +spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees +start_angle_degrees = 330 # Starting angle for the perturbation in degrees + +# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. + def temperature_function_degrees_array(r, theta_degrees): - # Aggiusta theta per spostare l'angolo di inizio della perturbazione + # Adjust theta to shift the starting angle of the perturbation adjusted_theta_degrees = theta_degrees + start_angle_degrees adjusted_theta_degrees = adjusted_theta_degrees % 360 - # Inizializza l'array della temperatura + # Initialize the temperature array temp = np.zeros_like(r) - # Determina la grande perturbazione usando un approccio a funzione gradino + # Determine the large perturbation using a step function approach + large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) - temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner) + math.pi) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) + temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) - # Applica piccole perturbazioni dove non si applicano le grandi perturbazioni + # Apply small perturbations where large perturbations are not applied small_perturbation_mask = ~large_perturbation_mask temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) return temp - - - - -# Generazione dei dati per la visualizzazione -theta = np.linspace(0, 360, 360) # Angoli da 0 a 360 gradi -radius = np.linspace(r_inner, r_outer, 100) # Raggi da r_inner a r_outer - -# Creazione di una griglia per il plotting + +# Here we generate data for visualization +theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees +radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer + +# Here we create a grid for plotting + R, Theta = np.meshgrid(radius, theta) Temp = temperature_function_degrees_array(R, Theta) +# After importing the libraries and defining our function, the script will plot how our temperature profile will look. The next step is to write the temperature perturbation in an ASCII format that ASPECT can read. +# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. +# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. +# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: +# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. +# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. +# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. +# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. +#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. +# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. +# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). +# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. +# At the end, we convert degrees to radians, since ASPECT only works with radians. Then it creates the file perturbation.txt + + + def write_ascii_data(radius, theta_degrees, temperatures, filename): with open(filename, 'w') as file: file.write("# Test data for ascii data initial conditions.\n") @@ -55,33 +73,36 @@ def write_ascii_data(radius, theta_degrees, temperatures, filename): phi = theta_degrees[j] temp = temperatures[j, i] - # Formattazione migliorata + # Improved formatting r_str = f"{r:.1f}" phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" - # Allineamento delle colonne con spostamento della seconda colonna + # Column alignment with offset for the second column file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") -# Conversione delle coordinate polari in coordinate cartesiane per il plotting +# Conversion of polar coordinates to Cartesian coordinates for plotting X = R * np.cos(np.radians(Theta)) Y = R * np.sin(np.radians(Theta)) + # Plotting plt.figure(figsize=(8, 6)) contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') -plt.colorbar(contour, label='Temperatura') -plt.title('Distribuzione della Temperatura in Coordinate Polari') -plt.xlabel('Coordinata X (m)') -plt.ylabel('Coordinata Y (m)') +plt.colorbar(contour, label='Temperature') +plt.title('Temperature distribution') +plt.xlabel('Coordinate X (m)') +plt.ylabel('Coordinate Y (m)') plt.axis('equal') plt.show() -# Uso della funzione write_ascii_data per salvare i dati +# Use the function write_ascii_data to save data write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') +# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. + import math def convert_to_radians(degrees): From 35f10982dc7526b9fb2a11e9ce5133ea564256ee Mon Sep 17 00:00:00 2001 From: Francesco Radica <51544149+Francyrad@users.noreply.github.com> Date: Sat, 13 Jul 2024 17:29:13 +0200 Subject: [PATCH 6/7] Delete cookbooks/ascii_perturbation directory --- .../ascii_perturbation/ascii_perturbation.prm | 179 - .../documentation/ascii_temperature.png | Bin 334131 -> 0 bytes .../ascii_temperature_aspect.png | Bin 243837 -> 0 bytes .../documentation/perturbation.txt | 36004 ---------------- .../documentation/temperature.png | Bin 190985 -> 0 bytes .../documentation/tutorial_a.docx | Bin 27089 -> 0 bytes .../documentation/tutorial_ascii.md | 205 - .../documentation/tutorial_ascii.tex | 328 - cookbooks/ascii_perturbation/perturbation.py | 135 - .../ascii_perturbation/perturbation_ascii.txt | 36004 ---------------- 10 files changed, 72855 deletions(-) delete mode 100644 cookbooks/ascii_perturbation/ascii_perturbation.prm delete mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature.png delete mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature_aspect.png delete mode 100644 cookbooks/ascii_perturbation/documentation/perturbation.txt delete mode 100644 cookbooks/ascii_perturbation/documentation/temperature.png delete mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_a.docx delete mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.md delete mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex delete mode 100644 cookbooks/ascii_perturbation/perturbation.py delete mode 100644 cookbooks/ascii_perturbation/perturbation_ascii.txt diff --git a/cookbooks/ascii_perturbation/ascii_perturbation.prm b/cookbooks/ascii_perturbation/ascii_perturbation.prm deleted file mode 100644 index 618deb32f05..00000000000 --- a/cookbooks/ascii_perturbation/ascii_perturbation.prm +++ /dev/null @@ -1,179 +0,0 @@ - -set Dimension = 2 -#set Resume computation = auto -set Start time = 0 -set End time = 5e8 -set Use years in output instead of seconds = true -set Adiabatic surface temperature = 1623 -set Use conduction timestep = true -set Output directory = ascii_perturbation - - -set CFL number = 1 -set Nonlinear solver scheme = single Advection, single Stokes -subsection Solver parameters - subsection Stokes solver parameters - set Linear solver tolerance = 1e-5 - set Number of cheap Stokes solver steps = 2000 # 200 - end -end - -subsection Formulation - set Mass conservation = projected density field - set Temperature equation = real density -end - -subsection Checkpointing - set Steps between checkpoint = 100 -end - - -subsection Geometry model - set Model name = spherical shell - - subsection Spherical shell - set Inner radius = 3481000 - set Outer radius = 6371000 - end -end - - -subsection Boundary temperature model - set Fixed temperature boundary indicators = top, bottom - set List of model names = spherical constant - subsection Spherical constant - set Inner temperature = 3700 - set Outer temperature = 273 - end -end - - -subsection Boundary velocity model - set Tangential velocity boundary indicators = bottom, top -end - - -subsection Gravity model - set Model name = ascii data -end - - -# Here we initialize the temeprature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. - -subsection Initial temperature model - set List of model names = adiabatic, ascii data - subsection Adiabatic - set Age bottom boundary layer = 1e9 - set Age top boundary layer = 1e9 - - subsection Function - set Function expression = 0 - end - - end - -# Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. - - subsection Ascii data model - set Data directory = $ASPECT_SOURCE_DIR/data/cookbooks/ascii_perturbation - set Data file name = perturbation_ascii.txt - end -end - - -subsection Material model - set Model name = Steinberger - set Material averaging = harmonic average - - subsection Steinberger model - - set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ - set Lateral viscosity file name = temp-viscosity-prefactor.txt - set Material file names = pyr-ringwood88.txt - set Radial viscosity file name = radial-visc-simple.txt - set Latent heat = false - - # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". - - set Maximum lateral viscosity variation = 1e2 - set Maximum viscosity = 5e23 - set Minimum viscosity = 1e19 - - - set Use lateral average temperature for viscosity = false - set Thermal conductivity formulation = p-T-dependent - - set Composition viscosity prefactors = 1 - - end -end - - -subsection Heating model - set List of model names = adiabatic heating, shear heating -end - - -# We refine the mesh near the boundaries, and where temperature variations are -# large. In addition, we make sure that in the transition zone, where both the -# viscosity and the density change a lot, we use the highest refinement level. -subsection Mesh refinement - set Initial adaptive refinement = 1 - set Initial global refinement = 5 - set Refinement fraction = 0.95 - set Coarsening fraction = 0.05 - set Strategy = temperature, boundary, minimum refinement function - set Time steps between mesh refinement = 5 - - subsection Boundary - set Boundary refinement indicators = top, bottom - end - - subsection Minimum refinement function - set Coordinate system = depth - set Variable names = depth, phi - set Function expression = if(depth<700000, 6, 5) - end -end - -subsection Boundary temperature model - set Fixed temperature boundary indicators = 0,1 -end - - -subsection Nullspace removal - set Remove nullspace = net rotation -end - -subsection Compositional fields - set Number of fields = 1 - set Names of fields = density_field - set Types of fields = density - set Compositional field methods = prescribed field -end - - - -subsection Initial composition model - set Model name = function - subsection Function - set Variable names = x,y - set Function constants = r_inner=3481000, r_outer=6371000 - set Function expression = if(sqrt(x^2+y^2)NnjvAa1S9saCZ+7+}&+(cZcBa4g&-Y5Fki!cXxLgU~qTYlk2{( z_j&hP&xid3_SBlG9#(hLl$_@wRfH?ZNdVpvyn}&(0Z4xPsssZAZvX=WSA~oS{mIKR zks!2!byAWLfvFfHfP-IOrRC^?z&lT-g7)V=mmkXTuxh!vA{=SM~R@{-6r!yEBAsET8!Yb~tN7+cZreg6gkHLeiJ5g^i6lBWC!r-Ks z%1cU0${OB%0e;n;RDG}8TUB*%@TFqks3&N#w;XQ{HO$`tM)CbC99#lbyW8vfY1xU> zxX-D;?kLkH%QXMx38bQ;w4%aE&TSrYa*!7zQkrL(`@a^0Xe$Hv=u`!i5`zD|R3Vna zs*whj2K;ZOt{}kD{}-j$yiqCQ|5{+xa{ku~O9TG@OaHG1`~Tida}od@-+M4bLhwPc z>3%oUtJG~$47V`n<*L|XFoBZ)tS-IbypM1?*6(Tis#x&(XYqnGL*u9CBQrti;S~DA zfXc`oM!)-E=P~ZRg5SS?yC{0o*Zg;67!aH15*Qo`LFxud16+Ov+_s+jSRDSU2i>gq z5!z)5T*SwgOUKVgR`X_$c`C++C*R%HKYMvDbd#iv@t(GT%J=y8xGmbBZ=}`reO%DJ zZ9X%>pmS~bU!AzMH`Am%+8_PyFA5d7%7dKxy?VjxtH*bv3-a+FD8@?FuevTbVdkZ1 zvn%{ls#4gQno@?#dQ|}`fO2EN2#BB8rtN;0Ux`k)>65PSJ?ZqozIoH$Npta^-&OAC zTW@3mw3PwDD7Zx)m%EyNkvQ~P9*AxT5i|nZif&zZcXwarjm*udN7I-o=yjW%lilg` z+g6;h%r-+pL$O-sof~eJtfo1ZtrK16d9Rz-pDXOr@${bR)*IRB)xrAzK9w!I0-(yJ z>{ZKiwnJ;aV^V@N`_3v<@M#mBlsKUcn<=(!!)6H0rKR|+&_AW);b#C%n{Gu;@~^s5 z=%n1Q45)rBNSqrtb$qs34X*gP7|QLm+Yo0I<|3U%q>YWQ77TP8EF-Pv0e6LID(+uP?V$$$cP#i&K|Mufk=!cK&Sdi^1?kQUka4$JJ@h z_WRKgL@H!-zq{^iPCk|_y{9eQ%pzfhAmIZ&uVYgpcfV7wb$KtrePOv8w&TTdU)QGH z46CJ2{O8h)&ptdC1Nl=e_m{G)cKHYp{THzQl>Y0(JPF?p@5|kG^yMbH&p?fTtk=r+ z)WATPVf+2DU6kJk>B@2B!D09NtLMQbf%nC{hFgR`Z#ARM0N}*)JFj!=kVq6 z)J_LTDEZng_!L;lkD7FM7Ak0cH%OH;Ws;Xz9fY>@cOF0j(7pZ7|E&8yBFYa*ufL4B z5fBG94>L3uplADfY9)i?1n&o9r`H~jwjF_ES?Mu62PMwOb$*AmoTk5zVh%}P@A@lb zBA%f`Twa36;cEt~Tg+u=V?X~%yxz}8r4)LQeb-yrwe=SqQ~&<;OVBOfrLhGaWO5R} z?PbrejaAXlK;Gv-@IJ!!Tl)qA<9>YJC#ERhvp~`kJukvovk1@Y<@y`YZA(8F>GQq> ziicBS)bS~f=_{DgkNL@z(W^04e(lHJ)}G*NqebWT>7cxCL?v0u?RHV7t>sJLUiS0ta%CR(WsRAuz%xXiyLI`b*$wox)6ILiH}2+{<8uSq zEPfUx#*Z#2so~tzTBSj zfobF+M@@$nAr_Jv67XP>jIP&`{FqvXKP#4HV~Hv;L@Ca`&xiViw{fCq9MAmF(Hn!< zm)%YB>V6o^QW6NnBm|jdU$-+Pws6;&xy0~Y42)rnyNA5Q>}NR+(ezET@Lw*!`oj}6 zx$Z=O`rk(els!_#fj z*E9zce{R3#<3FcFrDjo{=jD9RAYEG_{BWS&Zh1GX|Kd1(7Wjh3z4LzfwU4uP@*Wze zYp$H!%@QwUMlADxHf<5Hdj8es^-ao%c!NIarf}c&Sw}r zEabAfJC=EPyA$9g&|!~%oK5<27Rt}YuK0h#DO(5bF2UbC$YBro057Az;Kks5J`u6)SOJx3D86{W zRSoME8kE-JjYB`{ek^W%ecrv#G7~KJ&!Bz!1I!LD={L-#K2`BlHRl+JBj1Sq~~g?+_mp^hZN zx_rPlkWYn$d%xbAVc28~=B!|4m}~w_2979YPklIj}d0IZr+M8#%8} zd$-Bg4~Lbvsjk2tDd;oR;Mi=!|{s{&RLpU_dJfA0n5Qo`Dx9A$`undsHPVAq}7c^0rRP@h;(sw_ziovJdfG zXpUzD4bjE(S@QVtAg1ZG6V{Jl${KOO3N?;YU!&N-N14^>QzL4$<1@LlCeAaOH`1kS|0N(jC{W*Ri+Not0}c=r`KO%WLOpz6AJ?VZn>N0)xs9z9Fh-P(vfmI6we2d+HD&wpsI|Tl>lPKe2TR}0DEvmJE=bX9RPJ}C z9l$yJcGRv{k99PtaQ*4?jUD#K8~JFHezd)Vqc8N@w3=;lGPfpQ@)kR;8pnOc9<3Lo zgJX~zh|C1X-Oc!-_t%GlQkK+1=!o4`91_nKrN3%-@e7T8)E73e+QaazW%bUTaBA0THz z>b`73ae}UXHI*Qk24Z99WA*S0l#OJyzI@fS^B@;lfsXG3cZ#J)^cb8<

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z1Tlch$8r;~`e!w6PcnE_MM)kYy8O?@EcBec(GZC1%?X5x331ecc;_fO*xEU=8rnMi zq2!Pt>i_SZ1Lw|%$d_q`jVJ)@?F-S?1i5UCCuDRFjW^G#m_ZA$1PxI(FyMxC#P^G$HE1} zKw^$Kj8*(qvk*{+zNfGePcF>TOgq}HpJf(NWoAIK&6r}j2;F2Z}aa_0&Q$GA!H!Y6-lFpJlKP@pIKxLgb0u&`Z7*{8IjhV|9IWgNA zoIxI=_3%Kl#GivM+xuOdHm9{8Xt zWgBR1c*Zusq6{x_ff1~*5a@Nrkj0xcD)&`9HNUVK=oC~u9v+ByjQ`CbR!p8|NhSvv z?!8_y0fm1rSM7;m-uEIW?(@q^&zQ;Yl*J!-xB2MX!vQ6pL{rFBL19KHM3GRIc)7cE z@71&Y{*v;m$66G4l3=kY`*$A-H6Ck2&>2AT&aWiqs74g{D3-jfQ&1 zZvE)Jpz2-3xB%#Q^Iu!oS;&+FSpDZvX{=?!|_mAJghL+Z`%{9yEoAE1%J4h*_hHgcaI)5az`qTee&_JJ9sHBSH=X}*_?uPyJO1w$#!oZ=u&NIL o{KMY(9sc(w{#SU0;Vr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) -end -``` - -The given function is defined in a spherical coordinate system and calculates values based on the radial position r and angular position theta. The function behaves differently inside, outside, and between two specified radii, r_inner and r_outer. -The function is defined using conditional statements (if) to determine the value based on r: -Inside the Inner Radius (rr_outer): Like the inner radius case, but here the constant tsurf is added to the sinusoidal perturbation term. -Formula: - -```{math} -t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , -``` - -Otherwise (For r Values Between r_inner and r_outer): Only the sinusoidal perturbation term is calculated. -Formula: - -```{math} -p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , -``` - -This is the result for a quarter of shell: - -```{figure-md} fig:temperature - - -Temperature for the above muparser function. -``` - -However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. -For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. -Therefore, we may use the following mathematical function: - -```{math} -temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , -``` - -And - - -```{math} -temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , -``` - -In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. -The final result will be as following: - -``` - - -Temperature distribution in ASCII format. -``` - -Along with this imput file, it's provided a complete python script full of comments and details of how it build our ASCII file. -After importing the libraries and defining our function, the script will plot how our temperature profile will look. The next step is to write the temperature perturbation in an ASCII format that ASPECT can read. -The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. -The function opens a file with the given filename in write mode. All the data that follows will be written to this file. -The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: -100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. -360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. -1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. -The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. -In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. -The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. -For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). -The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. -At the end, we convert degrees to radians, since ASPECT only works with radians. Then it creates the file perturbation.txt - - -If everything has been done correctly, the ASCII file should appear as follows: - - -``` - -# Test data for ascii data initial conditions. -# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" -# POINTS: 100 360 1 -# Columns: r phi temperature [K] -3481000.0 0.00000000 0 -3510191.9 0.00000000 0 -3539383.8 0.00000000 0 -3568575.8 0.00000000 0 -3597767.7 0.00000000 0 -3626959.6 0.00000000 0 -3656151.5 0.00000000 0 - -And many other lines... - - -``` - -For each radius value and for each angular value, a certain temperature will be established. -Once executed, the script will generate a file named `perturbation_ascii.txt`. Before running our simulation, we should move our file to the following directory: - -``` -`$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/` -``` - - - -To implement it in our simulation (.prm file), we initialize the temperature model as follows: - -``` - -# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. -subsection Initial temperature model - set List of model names = adiabatic, ascii data - subsection Adiabatic - set Age bottom boundary layer = 1e9 - set Age top boundary layer = 1e9 - - subsection Function - set Function expression = 0 - end - - end - -#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. - subsection Ascii data model - set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ - set Data file name = perturbation_ ascii.txt - end -end - -``` - - - -Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. - -``` - -subsection Material model - set Model name = Steinberger - set Material averaging = harmonic average - - subsection Steinberger model - - set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ - set Lateral viscosity file name = temp-viscosity-prefactor.txt - set Material file names = pyr-ringwood88.txt - set Radial viscosity file name = radial-visc-simple.txt - set Latent heat = false - - # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". - set Maximum lateral viscosity variation = 1e2 - set Maximum viscosity = 5e23 - set Minimum viscosity = 1e19 - set Use lateral average temperature for viscosity = false - set Thermal conductivity formulation = p-T-dependent - #set Thermal conductivity = 4.17 - - set Composition viscosity prefactors = 1 - - end -end -``` - -The simulation will take some time to run, but this will be the final result: - -``` - - - -Temperature distribution with aspect ratio adjustment. -``` - - - -You can see the complete video in the following link: - -https://www.youtube.com/watch?v=6KVsunMhpj0 - diff --git a/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex deleted file mode 100644 index 87b58891496..00000000000 --- a/cookbooks/ascii_perturbation/documentation/tutorial_ascii.tex +++ /dev/null @@ -1,328 +0,0 @@ - - -\documentclass{article} -\usepackage{amsmath} -\usepackage{graphicx} -\usepackage{hyperref} - -\begin{document} - -\section*{Using ASCII file to compute a personalized temperature distribution} - -\textit{This section was contributed by Francesco Radica.} - -In this cookbook, we will explore how to implement complex temperature perturbations in a simulation using Steinberger's material model. Specifically, we'll modify a temperature function originally developed for the CITCOM simulation program, designed to initiate mantle convection through an ASCII file. Additionally, we will implement a stagnant lid type subduction, aiming for a viscosity profile that is as realistic as possible. - -ASPECT employs the muparser language for writing mathematical functions, which are useful for describing various features such as temperature perturbation functions. For the simulation program CITCOM, a particular mathematical function is well-known for generating perturbations. We will thus apply this function to our adiabatic temperature profile, to which temperature will be added and subtracted according to the mathematical function: - -\begin{verbatim} -subsection Initial temperature model - set List of model names = adiabatic, function - subsection Adiabatic - set Age bottom boundary layer = 5e8 - set Age top boundary layer = 5e8 - - subsection Function - set Function expression = 0 - end - end - -subsection Function - set Coordinate system = spherical - set Variable names = r,theta - - set Function constants = r_inner=3481000, r_outer=6371000, tcmb=3700, tsurf=300, w=2*pi, p=300.0, frequency=100 - set Function expression = if(rr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) -end -\end{verbatim} - -The given function is defined in a spherical coordinate system and calculates values based on the radial position \(r\) and angular position \(\theta\). The function behaves differently inside, outside, and between two specified radii, \(r_{\text{inner}}\) and \(r_{\text{outer}}\). -The function is defined using conditional statements (if) to determine the value based on \(r\): -Inside the Inner Radius (\(r < r_{\text{inner}}\)): The function calculates a value by adding the constant \(t_{\text{cmb}}\) to a sinusoidal perturbation term. This perturbation term depends on the radial position \(r\), the angular position \(\theta\), and the constants \(p\) and frequency. -Formula: - -\begin{equation} -t_\text{cmb} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , -\end{equation} - -Outside the Outer Radius (\(r > r_{\text{outer}}\)): Like the inner radius case, but here the constant \(t_{\text{surf}}\) is added to the sinusoidal perturbation term. -Formula: - -\begin{equation} -t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , -\end{equation} - -Otherwise (For \(r\) Values Between \(r_{\text{inner}}\) and \(r_{\text{outer}}\)): Only the sinusoidal perturbation term is calculated. -Formula: - -\begin{equation} -p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , -\end{equation} - -This is the result for a quarter of shell: - -\begin{figure}[h!] -\centering -\includegraphics[width=0.48\textwidth]{temperature.png} -\caption{Temperature for the above muparser function.} -\label{fig:temperature} -\end{figure} - -However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. -For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. -Therefore, we may use the following mathematical function: - -\begin{equation} -temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , -\end{equation} - -And - -\begin{equation} -temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , -\end{equation} - -In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. -The final result will be as following: - -\begin{figure}[h!] -\centering -\includegraphics[width=0.48\textwidth]{ascii_temperature.png} -\caption{Temperature distribution in ASCII format.} -\label{fig:ascii-temperature} -\end{figure} - -Now, let's write a Python script to utilize the function and export it in ASCII format: - -\begin{verbatim} -# The script imports necessary libraries and sets up parameters for our temperature model. - -import matplotlib.pyplot as plt -import numpy as np -import math - -# Parameters -r_inner = 3481000 # Internal radius in meters -r_outer = 6371000 # External radius in meters -p_large = 400.0 # Amplitude of the large perturbations -p_small = 30.0 # Amplitude of the small perturbations -frequency_large = 3 # Frequency of the large perturbations -frequency_small = 30 # Frequency of the small perturbations -spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees -start_angle_degrees = 330 # Starting angle for the perturbation in degrees - -# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. - -def temperature_function_degrees_array(r, theta_degrees): - # Adjust theta to shift the starting angle of the perturbation - adjusted_theta_degrees = theta_degrees + start_angle_degrees - adjusted_theta_degrees = adjusted_theta_degrees % 360 - - # Initialize the temperature array - temp = np.zeros_like(r) - - # Determine the large perturbation using a step function approach - - large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) - temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) - - # Apply small perturbations where large perturbations are not applied - small_perturbation_mask = ~large_perturbation_mask - temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) - - return temp - -# Here we generate data for visualization -theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees -radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer - -# Here we create a grid for plotting - -R, Theta = np.meshgrid(radius, theta) -Temp = temperature_function_de - -grees_array(R, Theta) - - -# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. -# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. -# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: -# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. -# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. -# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. -# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. -#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. -# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. -# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). -# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. - - - -def write_ascii_data(radius, theta_degrees, temperatures, filename): - with open(filename, 'w') as file: - file.write("# Test data for ascii data initial conditions.\n") - file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") - file.write("# POINTS: 100 360 1\n") - file.write("# Columns: r phi temperature [K]\n") - - for j in range(len(theta_degrees)): - for i in range(len(radius)): - r = radius[i] - phi = theta_degrees[j] - temp = temperatures[j, i] - - # Improved formatting - r_str = f"{r:.1f}" - phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" - temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" - - # Column alignment with offset for the second column - file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") - - -# Conversion of polar coordinates to Cartesian coordinates for plotting -X = R * np.cos(np.radians(Theta)) -Y = R * np.sin(np.radians(Theta)) - - -# Plotting -plt.figure(figsize=(8, 6)) -contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') -plt.colorbar(contour, label='Temperature') -plt.title('Temperature distribution') -plt.xlabel('Coordinate X (m)') -plt.ylabel('Coordinate Y (m)') -plt.axis('equal') -plt.show() - - -# Use the function write_ascii_data to save data -write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') - -# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. - -import math - -def convert_to_radians(degrees): - """Convert degrees to radians.""" - return degrees * (math.pi / 180) - -def convert_file_angles(input_file_path, output_file_path): - """Convert the angles in the second column of the file from degrees to radians.""" - with open(input_file_path, 'r') as file: - content = file.readlines() - - converted_lines = content[:4] # Keep the header lines unchanged - for line in content[4:]: - columns = line.split() - if len(columns) == 3: - radius, angle_deg, temperature = columns - angle_rad = convert_to_radians(float(angle_deg)) - converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" - converted_lines.append(converted_line) - else: - converted_lines.append(line) - - with open(output_file_path, 'w') as file: - file.writelines(converted_lines) - -# Example usage -input_file_path = 'perturbation_ascii.txt' # Replace with your input file path -output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path - -convert_file_angles(input_file_path, output_file_path) - -\end{verbatim} - -If everything has been done correctly, the ASCII file should appear as follows: - -\begin{verbatim} -# Test data for ascii data initial conditions. -# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" -# POINTS: 100 360 1 -# Columns: r phi temperature [K] -3481000.0 0.00000000 0 -3510191.9 0.00000000 0 -3539383.8 0.00000000 0 -3568575.8 0.00000000 0 -3597767.7 0.00000000 0 -3626959.6 0.00000000 0 -3656151.5 0.00000000 0 -\end{verbatim} - -For each radius value and for each angular value, a certain temperature will be established. -Once executed, the script will generate a file named \texttt{perturbation\_ascii.txt}. Before running our simulation, we should move our file to the following directory: - -\begin{verbatim} -$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ -\end{verbatim} - -To implement it in our simulation (\texttt{.prm} file), we initialize the temperature model as follows: - -\begin{verbatim} -# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. -subsection Initial temperature model - set List of model names = adiabatic, ascii data - subsection Adiabatic - set Age bottom boundary layer = 1e9 - set Age top boundary layer = 1e9 - - subsection Function - set Function expression = 0 - end - - end - -#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. - subsection Ascii data model - set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ - set Data file name = perturbation_ ascii.txt - end -end -\end{verbatim} - -Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. - -\begin{verbatim} -subsection Material model - set Model name = Steinberger - set Material averaging = harmonic average - - subsection Steinberger model - - set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ - set Lateral viscosity file name = temp-viscosity-prefactor.txt - set Material file names = pyr-ringwood88.txt - set Radial viscosity file name = radial-visc-simple.txt - set Latent heat = false - - # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". - set Maximum lateral viscosity variation = 1e2 - set Maximum viscosity = 5e23 - set Minimum viscosity = 1e19 - set Use lateral average temperature for viscosity = false - set Thermal conductivity formulation = p-T-dependent - #set Thermal conductivity = 4.17 - - set Composition viscosity prefactors = 1 - - - - end -end -\end{verbatim} - -The simulation will take some time to run, but this will be the final result: - -\begin{figure}[h!] -\centering -\includegraphics[width=0.48\textwidth]{ascii_temperature_aspect.png} -\caption{Temperature distribution with aspect ratio adjustment.} -\label{fig:ascii-temperature-aspect} -\end{figure} - -You can see the complete video in the following link: -\url{https://www.youtube.com/watch?v=6KVsunMhpj0} - -\end{document} -``` \ No newline at end of file diff --git a/cookbooks/ascii_perturbation/perturbation.py b/cookbooks/ascii_perturbation/perturbation.py deleted file mode 100644 index a4f7bb45812..00000000000 --- a/cookbooks/ascii_perturbation/perturbation.py +++ /dev/null @@ -1,135 +0,0 @@ -# The script imports necessary libraries and sets up parameters for our temperature model. - -import matplotlib.pyplot as plt -import numpy as np -import math - -# Parameters -r_inner = 3481000 # Internal radius in meters -r_outer = 6371000 # External radius in meters -p_large = 400.0 # Amplitude of the large perturbations -p_small = 30.0 # Amplitude of the small perturbations -frequency_large = 3 # Frequency of the large perturbations -frequency_small = 30 # Frequency of the small perturbations -spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees -start_angle_degrees = 330 # Starting angle for the perturbation in degrees - -# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. - -def temperature_function_degrees_array(r, theta_degrees): - # Adjust theta to shift the starting angle of the perturbation - adjusted_theta_degrees = theta_degrees + start_angle_degrees - adjusted_theta_degrees = adjusted_theta_degrees % 360 - - # Initialize the temperature array - temp = np.zeros_like(r) - - # Determine the large perturbation using a step function approach - - large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) - temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) - - # Apply small perturbations where large perturbations are not applied - small_perturbation_mask = ~large_perturbation_mask - temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) - - return temp - -# Here we generate data for visualization -theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees -radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer - -# Here we create a grid for plotting - -R, Theta = np.meshgrid(radius, theta) -Temp = temperature_function_degrees_array(R, Theta) - -# After importing the libraries and defining our function, the script will plot how our temperature profile will look. The next step is to write the temperature perturbation in an ASCII format that ASPECT can read. -# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. -# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. -# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: -# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. -# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. -# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. -# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. -#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. -# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. -# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). -# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. -# At the end, we convert degrees to radians, since ASPECT only works with radians. Then it creates the file perturbation.txt - - - -def write_ascii_data(radius, theta_degrees, temperatures, filename): - with open(filename, 'w') as file: - file.write("# Test data for ascii data initial conditions.\n") - file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") - file.write("# POINTS: 100 360 1\n") - file.write("# Columns: r phi temperature [K]\n") - - for j in range(len(theta_degrees)): - for i in range(len(radius)): - r = radius[i] - phi = theta_degrees[j] - temp = temperatures[j, i] - - # Improved formatting - r_str = f"{r:.1f}" - phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" - temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" - - # Column alignment with offset for the second column - file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") - - -# Conversion of polar coordinates to Cartesian coordinates for plotting -X = R * np.cos(np.radians(Theta)) -Y = R * np.sin(np.radians(Theta)) - - -# Plotting -plt.figure(figsize=(8, 6)) -contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') -plt.colorbar(contour, label='Temperature') -plt.title('Temperature distribution') -plt.xlabel('Coordinate X (m)') -plt.ylabel('Coordinate Y (m)') -plt.axis('equal') -plt.show() - - -# Use the function write_ascii_data to save data -write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') - -# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. - -import math - -def convert_to_radians(degrees): - """Convert degrees to radians.""" - return degrees * (math.pi / 180) - -def convert_file_angles(input_file_path, output_file_path): - """Convert the angles in the second column of the file from degrees to radians.""" - with open(input_file_path, 'r') as file: - content = file.readlines() - - converted_lines = content[:4] # Keep the header lines unchanged - for line in content[4:]: - columns = line.split() - if len(columns) == 3: - radius, angle_deg, temperature = columns - angle_rad = convert_to_radians(float(angle_deg)) - converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" - converted_lines.append(converted_line) - else: - converted_lines.append(line) - - with open(output_file_path, 'w') as file: - file.writelines(converted_lines) - -# Example usage -input_file_path = 'perturbation_ascii.txt' # Replace with your input file path -output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path - -convert_file_angles(input_file_path, output_file_path) diff --git a/cookbooks/ascii_perturbation/perturbation_ascii.txt b/cookbooks/ascii_perturbation/perturbation_ascii.txt deleted file mode 100644 index d2cfd20bd2f..00000000000 --- a/cookbooks/ascii_perturbation/perturbation_ascii.txt +++ /dev/null @@ -1,36004 +0,0 @@ -# Test data for ascii data initial conditions. -# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" -# POINTS: 100 360 1 -# Columns: r phi temperature [K] -3481000.0 0.00000000 0 -3510191.9 0.00000000 0 -3539383.8 0.00000000 0 -3568575.8 0.00000000 0 -3597767.7 0.00000000 0 -3626959.6 0.00000000 0 -3656151.5 0.00000000 0 -3685343.4 0.00000000 0 -3714535.4 0.00000000 0 -3743727.3 0.00000000 0 -3772919.2 0.00000000 0 -3802111.1 0.00000000 0 -3831303.0 0.00000000 0 -3860494.9 0.00000000 0 -3889686.9 0.00000000 0 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-6137464.6 6.28318531 -0.0 -6166656.6 6.28318531 -0.0 -6195848.5 6.28318531 -0.0 -6225040.4 6.28318531 -0.0 -6254232.3 6.28318531 -0.0 -6283424.2 6.28318531 -0.0 -6312616.2 6.28318531 -0.0 -6341808.1 6.28318531 -0.0 -6371000.0 6.28318531 -0.0 From 89fd10e3f4b3673612ced52d7f87d6110fd0e35b Mon Sep 17 00:00:00 2001 From: Francesco Radica <51544149+Francyrad@users.noreply.github.com> Date: Sat, 13 Jul 2024 17:30:23 +0200 Subject: [PATCH 7/7] Add files via upload --- .../ascii_perturbation/ascii_perturbation.prm | 179 + .../documentation/ascii_temperature.png | Bin 0 -> 334131 bytes .../ascii_temperature_aspect.png | Bin 0 -> 243837 bytes .../documentation/perturbation.txt | 36004 ++++++++++++++++ .../documentation/temperature.png | Bin 0 -> 190985 bytes .../documentation/tutorial_ascii.md | 205 + cookbooks/ascii_perturbation/perturbation.py | 135 + .../ascii_perturbation/perturbation_ascii.txt | 36004 ++++++++++++++++ 8 files changed, 72527 insertions(+) create mode 100644 cookbooks/ascii_perturbation/ascii_perturbation.prm create mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature.png create mode 100644 cookbooks/ascii_perturbation/documentation/ascii_temperature_aspect.png create mode 100644 cookbooks/ascii_perturbation/documentation/perturbation.txt create mode 100644 cookbooks/ascii_perturbation/documentation/temperature.png create mode 100644 cookbooks/ascii_perturbation/documentation/tutorial_ascii.md create mode 100644 cookbooks/ascii_perturbation/perturbation.py create mode 100644 cookbooks/ascii_perturbation/perturbation_ascii.txt diff --git a/cookbooks/ascii_perturbation/ascii_perturbation.prm b/cookbooks/ascii_perturbation/ascii_perturbation.prm new file mode 100644 index 00000000000..618deb32f05 --- /dev/null +++ b/cookbooks/ascii_perturbation/ascii_perturbation.prm @@ -0,0 +1,179 @@ + +set Dimension = 2 +#set Resume computation = auto +set Start time = 0 +set End time = 5e8 +set Use years in output instead of seconds = true +set Adiabatic surface temperature = 1623 +set Use conduction timestep = true +set Output directory = ascii_perturbation + + +set CFL number = 1 +set Nonlinear solver scheme = single Advection, single Stokes +subsection Solver parameters + subsection Stokes solver parameters + set Linear solver tolerance = 1e-5 + set Number of cheap Stokes solver steps = 2000 # 200 + end +end + +subsection Formulation + set Mass conservation = projected density field + set Temperature equation = real density +end + +subsection Checkpointing + set Steps between checkpoint = 100 +end + + +subsection Geometry model + set Model name = spherical shell + + subsection Spherical shell + set Inner radius = 3481000 + set Outer radius = 6371000 + end +end + + +subsection Boundary temperature model + set Fixed temperature boundary indicators = top, bottom + set List of model names = spherical constant + subsection Spherical constant + set Inner temperature = 3700 + set Outer temperature = 273 + end +end + + +subsection Boundary velocity model + set Tangential velocity boundary indicators = bottom, top +end + + +subsection Gravity model + set Model name = ascii data +end + + +# Here we initialize the temeprature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. + +subsection Initial temperature model + set List of model names = adiabatic, ascii data + subsection Adiabatic + set Age bottom boundary layer = 1e9 + set Age top boundary layer = 1e9 + + subsection Function + set Function expression = 0 + end + + end + +# Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. + + subsection Ascii data model + set Data directory = $ASPECT_SOURCE_DIR/data/cookbooks/ascii_perturbation + set Data file name = perturbation_ascii.txt + end +end + + +subsection Material model + set Model name = Steinberger + set Material averaging = harmonic average + + subsection Steinberger model + + set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ + set Lateral viscosity file name = temp-viscosity-prefactor.txt + set Material file names = pyr-ringwood88.txt + set Radial viscosity file name = radial-visc-simple.txt + set Latent heat = false + + # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". + + set Maximum lateral viscosity variation = 1e2 + set Maximum viscosity = 5e23 + set Minimum viscosity = 1e19 + + + set Use lateral average temperature for viscosity = false + set Thermal conductivity formulation = p-T-dependent + + set Composition viscosity prefactors = 1 + + end +end + + +subsection Heating model + set List of model names = adiabatic heating, shear heating +end + + +# We refine the mesh near the boundaries, and where temperature variations are +# large. In addition, we make sure that in the transition zone, where both the +# viscosity and the density change a lot, we use the highest refinement level. +subsection Mesh refinement + set Initial adaptive refinement = 1 + set Initial global refinement = 5 + set Refinement fraction = 0.95 + set Coarsening fraction = 0.05 + set Strategy = temperature, boundary, minimum refinement function + set Time steps between mesh refinement = 5 + + subsection Boundary + set Boundary refinement indicators = top, bottom + end + + subsection Minimum refinement function + set Coordinate system = depth + set Variable names = depth, phi + set Function expression = if(depth<700000, 6, 5) + end +end + +subsection Boundary temperature model + set Fixed temperature boundary indicators = 0,1 +end + + +subsection Nullspace removal + set Remove nullspace = net rotation +end + +subsection Compositional fields + set Number of fields = 1 + set Names of fields = density_field + set Types of fields = density + set Compositional field methods = prescribed field +end + + + +subsection Initial composition model + set Model name = function + subsection Function + set Variable names = x,y + set Function constants = r_inner=3481000, r_outer=6371000 + set Function expression = if(sqrt(x^2+y^2)NnjvAa1S9saCZ+7+}&+(cZcBa4g&-Y5Fki!cXxLgU~qTYlk2{( z_j&hP&xid3_SBlG9#(hLl$_@wRfH?ZNdVpvyn}&(0Z4xPsssZAZvX=WSA~oS{mIKR zks!2!byAWLfvFfHfP-IOrRC^?z&lT-g7)V=mmkXTuxh!vA{=SM~R@{-6r!yEBAsET8!Yb~tN7+cZreg6gkHLeiJ5g^i6lBWC!r-Ks z%1cU0${OB%0e;n;RDG}8TUB*%@TFqks3&N#w;XQ{HO$`tM)CbC99#lbyW8vfY1xU> zxX-D;?kLkH%QXMx38bQ;w4%aE&TSrYa*!7zQkrL(`@a^0Xe$Hv=u`!i5`zD|R3Vna zs*whj2K;ZOt{}kD{}-j$yiqCQ|5{+xa{ku~O9TG@OaHG1`~Tida}od@-+M4bLhwPc z>3%oUtJG~$47V`n<*L|XFoBZ)tS-IbypM1?*6(Tis#x&(XYqnGL*u9CBQrti;S~DA zfXc`oM!)-E=P~ZRg5SS?yC{0o*Zg;67!aH15*Qo`LFxud16+Ov+_s+jSRDSU2i>gq z5!z)5T*SwgOUKVgR`X_$c`C++C*R%HKYMvDbd#iv@t(GT%J=y8xGmbBZ=}`reO%DJ zZ9X%>pmS~bU!AzMH`Am%+8_PyFA5d7%7dKxy?VjxtH*bv3-a+FD8@?FuevTbVdkZ1 zvn%{ls#4gQno@?#dQ|}`fO2EN2#BB8rtN;0Ux`k)>65PSJ?ZqozIoH$Npta^-&OAC zTW@3mw3PwDD7Zx)m%EyNkvQ~P9*AxT5i|nZif&zZcXwarjm*udN7I-o=yjW%lilg` z+g6;h%r-+pL$O-sof~eJtfo1ZtrK16d9Rz-pDXOr@${bR)*IRB)xrAzK9w!I0-(yJ z>{ZKiwnJ;aV^V@N`_3v<@M#mBlsKUcn<=(!!)6H0rKR|+&_AW);b#C%n{Gu;@~^s5 z=%n1Q45)rBNSqrtb$qs34X*gP7|QLm+Yo0I<|3U%q>YWQ77TP8EF-Pv0e6LID(+uP?V$$$cP#i&K|Mufk=!cK&Sdi^1?kQUka4$JJ@h z_WRKgL@H!-zq{^iPCk|_y{9eQ%pzfhAmIZ&uVYgpcfV7wb$KtrePOv8w&TTdU)QGH z46CJ2{O8h)&ptdC1Nl=e_m{G)cKHYp{THzQl>Y0(JPF?p@5|kG^yMbH&p?fTtk=r+ z)WATPVf+2DU6kJk>B@2B!D09NtLMQbf%nC{hFgR`Z#ARM0N}*)JFj!=kVq6 z)J_LTDEZng_!L;lkD7FM7Ak0cH%OH;Ws;Xz9fY>@cOF0j(7pZ7|E&8yBFYa*ufL4B z5fBG94>L3uplADfY9)i?1n&o9r`H~jwjF_ES?Mu62PMwOb$*AmoTk5zVh%}P@A@lb zBA%f`Twa36;cEt~Tg+u=V?X~%yxz}8r4)LQeb-yrwe=SqQ~&<;OVBOfrLhGaWO5R} z?PbrejaAXlK;Gv-@IJ!!Tl)qA<9>YJC#ERhvp~`kJukvovk1@Y<@y`YZA(8F>GQq> ziicBS)bS~f=_{DgkNL@z(W^04e(lHJ)}G*NqebWT>7cxCL?v0u?RHV7t>sJLUiS0ta%CR(WsRAuz%xXiyLI`b*$wox)6ILiH}2+{<8uSq zEPfUx#*Z#2so~tzTBSj zfobF+M@@$nAr_Jv67XP>jIP&`{FqvXKP#4HV~Hv;L@Ca`&xiViw{fCq9MAmF(Hn!< zm)%YB>V6o^QW6NnBm|jdU$-+Pws6;&xy0~Y42)rnyNA5Q>}NR+(ezET@Lw*!`oj}6 zx$Z=O`rk(els!_#fj z*E9zce{R3#<3FcFrDjo{=jD9RAYEG_{BWS&Zh1GX|Kd1(7Wjh3z4LzfwU4uP@*Wze zYp$H!%@QwUMlADxHf<5Hdj8es^-ao%c!NIarf}c&Sw}r zEabAfJC=EPyA$9g&|!~%oK5<27Rt}YuK0h#DO(5bF2UbC$YBro057Az;Kks5J`u6)SOJx3D86{W zRSoME8kE-JjYB`{ek^W%ecrv#G7~KJ&!Bz!1I!LD={L-#K2`BlHRl+JBj1Sq~~g?+_mp^hZN zx_rPlkWYn$d%xbAVc28~=B!|4m}~w_2979YPklIj}d0IZr+M8#%8} zd$-Bg4~Lbvsjk2tDd;oR;Mi=!|{s{&RLpU_dJfA0n5Qo`Dx9A$`undsHPVAq}7c^0rRP@h;(sw_ziovJdfG zXpUzD4bjE(S@QVtAg1ZG6V{Jl${KOO3N?;YU!&N-N14^>QzL4$<1@LlCeAaOH`1kS|0N(jC{W*Ri+Not0}c=r`KO%WLOpz6AJ?VZn>N0)xs9z9Fh-P(vfmI6we2d+HD&wpsI|Tl>lPKe2TR}0DEvmJE=bX9RPJ}C z9l$yJcGRv{k99PtaQ*4?jUD#K8~JFHezd)Vqc8N@w3=;lGPfpQ@)kR;8pnOc9<3Lo zgJX~zh|C1X-Oc!-_t%GlQkK+1=!o4`91_nKrN3%-@e7T8)E73e+QaazW%bUTaBA0THz z>b`73ae}UXHI*Qk24Z99WA*S0l#OJyzI@fS^B@;lfsXG3cZ#J)^cb8<

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00000000000..31ce924301b --- /dev/null +++ b/cookbooks/ascii_perturbation/documentation/tutorial_ascii.md @@ -0,0 +1,205 @@ +# Using ASCII file to compute a personalized temperature distribution + +*This section was contributed by Francesco Radica.* + +In this cookbook, we will explore how to implement complex temperature perturbations in a simulation using Steinberger's material model. Specifically, we'll modify a temperature function originally developed for the CITCOM simulation program, designed to initiate mantle convection through an ASCII file. Additionally, we will implement a stagnant lid type subduction, aiming for a viscosity profile that is as realistic as possible. + +ASPECT employs the muparser language for writing mathematical functions, which are useful for describing various features such as temperature perturbation functions. For the simulation program CITCOM, a particular mathematical function is well-known for generating perturbations. We will thus apply this function to our adiabatic temperature profile, to which temperature will be added and subtracted according to the mathematical function: + +``` +subsection Initial temperature model + set List of model names = adiabatic, function + subsection Adiabatic + set Age bottom boundary layer = 5e8 + set Age top boundary layer = 5e8 + + subsection Function + set Function expression = 0 + end + end + +subsection Function + set Coordinate system = spherical + set Variable names = r,theta + + set Function constants = r_inner=3481000, r_outer=6371000, tcmb=3700, tsurf=300, w=2*pi, p=300.0, frequency=100 + set Function expression = if(rr_outer, tsurf + (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)), (p*sin(pi*(r-r_inner)/(r_outer-r_inner))*sin(frequency*w*theta)))) +end +``` + +The given function is defined in a spherical coordinate system and calculates values based on the radial position r and angular position theta. The function behaves differently inside, outside, and between two specified radii, r_inner and r_outer. +The function is defined using conditional statements (if) to determine the value based on r: +Inside the Inner Radius (rr_outer): Like the inner radius case, but here the constant tsurf is added to the sinusoidal perturbation term. +Formula: + +```{math} +t_\text{surf} + \left( p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) \right) , +``` + +Otherwise (For r Values Between r_inner and r_outer): Only the sinusoidal perturbation term is calculated. +Formula: + +```{math} +p \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency} \cdot 2\pi \cdot \theta \right) , +``` + +This is the result for a quarter of shell: + +```{figure-md} fig:temperature + + +Temperature for the above muparser function. +``` + +However, there may be a need to implement more complex temperature functions in our simulation that are difficult to reproduce with muparser language but can be easily crafted using the Python programming language. In such cases, it would be convenient to implement our perturbation using an ASCII file rather than a muparser function. +For instance, we can modify the previous function to include numerous small perturbations along with three large perturbations (two cool and one warm, with a broader perturbation value), to induce a mega convection within our planet, while leaving the remainder undisturbed. +Therefore, we may use the following mathematical function: + +```{math} +temp = p_\text{large} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{large} \cdot \theta_\text{radians} \right) , +``` + +And + + +```{math} +temp = p_\text{small} \cdot \sin \left( \frac{\pi \cdot (r - r_\text{inner})}{r_\text{outer} - r_\text{inner}} \right) \cdot \sin \left( \text{frequency}_\text{small} \cdot \theta_\text{radians} \right) , +``` + +In the model, large temperature perturbations are designated to specific angular sections of a planetary ring to simulate intense convective movements. Conversely, the remaining sections are subjected to smaller perturbations. +The final result will be as following: + +``` + + +Temperature distribution in ASCII format. +``` + +Along with this imput file, it's provided a complete python script full of comments and details of how it build our ASCII file. +After importing the libraries and defining our function, the script will plot how our temperature profile will look. The next step is to write the temperature perturbation in an ASCII format that ASPECT can read. +The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. +The function opens a file with the given filename in write mode. All the data that follows will be written to this file. +The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: +100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. +360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. +1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. +The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. +In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. +The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. +For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). +The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. +At the end, we convert degrees to radians, since ASPECT only works with radians. Then it creates the file perturbation.txt + + +If everything has been done correctly, the ASCII file should appear as follows: + + +``` + +# Test data for ascii data initial conditions. +# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" +# POINTS: 100 360 1 +# Columns: r phi temperature [K] +3481000.0 0.00000000 0 +3510191.9 0.00000000 0 +3539383.8 0.00000000 0 +3568575.8 0.00000000 0 +3597767.7 0.00000000 0 +3626959.6 0.00000000 0 +3656151.5 0.00000000 0 + +And many other lines... + + +``` + +For each radius value and for each angular value, a certain temperature will be established. +Once executed, the script will generate a file named `perturbation_ascii.txt`. Before running our simulation, we should move our file to the following directory: + +``` +`$ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/` +``` + + + +To implement it in our simulation (.prm file), we initialize the temperature model as follows: + +``` + +# Here we initialize the temperature model, an adiabatic profile which we will add and subtract temperature according to the ASCII profile. +subsection Initial temperature model + set List of model names = adiabatic, ascii data + subsection Adiabatic + set Age bottom boundary layer = 1e9 + set Age top boundary layer = 1e9 + + subsection Function + set Function expression = 0 + end + + end + +#Here we add the ascii file produced from the python script. Please, be sure to add the file in the path below. + subsection Ascii data model + set Data directory = $ASPECT_SOURCE_DIR/data/initial-temperature/ascii-data/test/ + set Data file name = perturbation_ ascii.txt + end +end + +``` + + + +Let's modify some lines in our Steinberger material model within our script. Specifically, let's limit the lateral viscosity variation to 100. For higher values, we won't achieve a stagnant lid convection regime. + +``` + +subsection Material model + set Model name = Steinberger + set Material averaging = harmonic average + + subsection Steinberger model + + set Data directory = $ASPECT_SOURCE_DIR/data/material-model/steinberger/ + set Lateral viscosity file name = temp-viscosity-prefactor.txt + set Material file names = pyr-ringwood88.txt + set Radial viscosity file name = radial-visc-simple.txt + set Latent heat = false + + # We decrease the Maximum lateral viscosity variation to facilitate stagnant lid subduction. This term has a relation with the "thermal viscosity prefactor". + set Maximum lateral viscosity variation = 1e2 + set Maximum viscosity = 5e23 + set Minimum viscosity = 1e19 + set Use lateral average temperature for viscosity = false + set Thermal conductivity formulation = p-T-dependent + #set Thermal conductivity = 4.17 + + set Composition viscosity prefactors = 1 + + end +end +``` + +The simulation will take some time to run, but this will be the final result: + +``` + + + +Temperature distribution with aspect ratio adjustment. +``` + + + +You can see the complete video in the following link: + +https://www.youtube.com/watch?v=6KVsunMhpj0 + diff --git a/cookbooks/ascii_perturbation/perturbation.py b/cookbooks/ascii_perturbation/perturbation.py new file mode 100644 index 00000000000..a4f7bb45812 --- /dev/null +++ b/cookbooks/ascii_perturbation/perturbation.py @@ -0,0 +1,135 @@ +# The script imports necessary libraries and sets up parameters for our temperature model. + +import matplotlib.pyplot as plt +import numpy as np +import math + +# Parameters +r_inner = 3481000 # Internal radius in meters +r_outer = 6371000 # External radius in meters +p_large = 400.0 # Amplitude of the large perturbations +p_small = 30.0 # Amplitude of the small perturbations +frequency_large = 3 # Frequency of the large perturbations +frequency_small = 30 # Frequency of the small perturbations +spread_angle_large_degrees = 90 # Spread angle of the large perturbations in degrees +start_angle_degrees = 330 # Starting angle for the perturbation in degrees + +# The temperature_function_degrees_array function computes temperature values over a mesh grid of radii and angles, applying the perturbations and returning an array of temperature values. + +def temperature_function_degrees_array(r, theta_degrees): + # Adjust theta to shift the starting angle of the perturbation + adjusted_theta_degrees = theta_degrees + start_angle_degrees + adjusted_theta_degrees = adjusted_theta_degrees % 360 + + # Initialize the temperature array + temp = np.zeros_like(r) + + # Determine the large perturbation using a step function approach + + large_perturbation_mask = (adjusted_theta_degrees < spread_angle_large_degrees) | (adjusted_theta_degrees > 360 - spread_angle_large_degrees) + temp[large_perturbation_mask] = p_large * np.sin(np.pi * (r[large_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_large * np.radians(theta_degrees[large_perturbation_mask])) + + # Apply small perturbations where large perturbations are not applied + small_perturbation_mask = ~large_perturbation_mask + temp[small_perturbation_mask] = p_small * np.sin(np.pi * (r[small_perturbation_mask] - r_inner) / (r_outer - r_inner)) * np.sin(frequency_small * np.radians(theta_degrees[small_perturbation_mask])) + + return temp + +# Here we generate data for visualization +theta = np.linspace(0, 360, 360) # Angles from 0 to 360 degrees +radius = np.linspace(r_inner, r_outer, 100) # Radii from r_inner to r_outer + +# Here we create a grid for plotting + +R, Theta = np.meshgrid(radius, theta) +Temp = temperature_function_degrees_array(R, Theta) + +# After importing the libraries and defining our function, the script will plot how our temperature profile will look. The next step is to write the temperature perturbation in an ASCII format that ASPECT can read. +# The script includes a function, write_ascii_data, which is responsible for writing temperature data into an ASCII file that can be read by the ASPECT. The function takes arrays representing radial distances (radius), angular degrees (theta_degrees), temperature values (temperatures), and a filename (filename) where the data will be saved. +# The function opens a file with the given filename in write mode. All the data that follows will be written to this file. +# The line with the keyword "POINTS:" in the header of the ASCII file is crucial because it defines the dimensions of the data grid for the ASPECT simulation program. The numbers following "POINTS:" represent the size of the grid in each dimension: +# 100 represents the number of points along the radial dimension (nx). In this case, it means there are 100 radial divisions or layers from the inner radius r_inner to the outer radius r_outer. +# 360 represents the number of points along the angular dimension (ny). This indicates that the angular data is divided into 360 segments, corresponding to the degrees in a full circle. +# 1 represents the number of points along the third dimension (nz). In this context, it implies that the data is essentially two-dimensional, with no depth or third dimension to vary over. This would be applicable for a surface or a shell where only the radius and the angle change. +# The structure indicated by "POINTS: 100 360 1" tells ASPECT how to read the subsequent data lines. Each line of data will correspond to a point in this grid, and ASPECT will expect to read 100 x 360 x 1 lines of data following the headers. The arrangement of data points in the file must match this grid layout for ASPECT to interpret the file correctly. +#In the write_ascii_data function, the nested for loops iterate over the angular positions (theta_degrees) and radial positions (radius), writing out the temperature (temp) at each point. The formatting ensures that each value occupies a specific width in the file, aligning the data into neat columns. This formatting is not just for aesthetics; it is essential for ensuring that ASPECT can correctly parse each value, especially when the data is read by automated scripts or tools that expect a consistent column width. Without such structured formatting, there could be parsing errors, leading to incorrect simulation results or program failures. +# The function iterates through the provided arrays of angles and radii to write the temperature data for each grid point. +# For each point, it formats the radius (r), angle (phi), and temperature (temp) with improved formatting to ensure numerical precision and readability. The formatting specifies that radius should have one decimal place, angle should have four decimal places (or be an integer if it is a whole number), and temperature should have one decimal place (or be an integer if it is a whole number). +# The data is written with aligned columns, ensuring that each row lines up correctly for the radius, angle, and temperature values. This is crucial for ASPECT to correctly parse the file. Each value is given a specific column width with left alignment. +# At the end, we convert degrees to radians, since ASPECT only works with radians. Then it creates the file perturbation.txt + + + +def write_ascii_data(radius, theta_degrees, temperatures, filename): + with open(filename, 'w') as file: + file.write("# Test data for ascii data initial conditions.\n") + file.write("# Only next line is parsed in format: [nx] [ny] [nz] because of keyword \"POINTS:\"\n") + file.write("# POINTS: 100 360 1\n") + file.write("# Columns: r phi temperature [K]\n") + + for j in range(len(theta_degrees)): + for i in range(len(radius)): + r = radius[i] + phi = theta_degrees[j] + temp = temperatures[j, i] + + # Improved formatting + r_str = f"{r:.1f}" + phi_str = f"{phi:.4f}" if not phi.is_integer() else f"{int(phi)}" + temp_str = f"{temp:.1f}" if not temp.is_integer() else f"{int(temp)}" + + # Column alignment with offset for the second column + file.write(f"{r_str:<10} {phi_str:<11}{temp_str}\n") + + +# Conversion of polar coordinates to Cartesian coordinates for plotting +X = R * np.cos(np.radians(Theta)) +Y = R * np.sin(np.radians(Theta)) + + +# Plotting +plt.figure(figsize=(8, 6)) +contour = plt.contourf(X, Y, Temp, levels=50, cmap='viridis') +plt.colorbar(contour, label='Temperature') +plt.title('Temperature distribution') +plt.xlabel('Coordinate X (m)') +plt.ylabel('Coordinate Y (m)') +plt.axis('equal') +plt.show() + + +# Use the function write_ascii_data to save data +write_ascii_data(radius, theta, Temp, 'perturbation_ascii.txt') + +# In this step, we will transform the angle measurements from degrees into radians. It's crucial to make this conversion because ASPECT is compatible with ASCII files that contain radian values only, not degrees. + +import math + +def convert_to_radians(degrees): + """Convert degrees to radians.""" + return degrees * (math.pi / 180) + +def convert_file_angles(input_file_path, output_file_path): + """Convert the angles in the second column of the file from degrees to radians.""" + with open(input_file_path, 'r') as file: + content = file.readlines() + + converted_lines = content[:4] # Keep the header lines unchanged + for line in content[4:]: + columns = line.split() + if len(columns) == 3: + radius, angle_deg, temperature = columns + angle_rad = convert_to_radians(float(angle_deg)) + converted_line = f"{radius} {angle_rad:.8f} {temperature}\n" + converted_lines.append(converted_line) + else: + converted_lines.append(line) + + with open(output_file_path, 'w') as file: + file.writelines(converted_lines) + +# Example usage +input_file_path = 'perturbation_ascii.txt' # Replace with your input file path +output_file_path = 'perturbation_ascii.txt' # Replace with your desired output file path + +convert_file_angles(input_file_path, output_file_path) diff --git a/cookbooks/ascii_perturbation/perturbation_ascii.txt b/cookbooks/ascii_perturbation/perturbation_ascii.txt new file mode 100644 index 00000000000..d2cfd20bd2f --- /dev/null +++ b/cookbooks/ascii_perturbation/perturbation_ascii.txt @@ -0,0 +1,36004 @@ +# Test data for ascii data initial conditions. +# Only next line is parsed in format: [nx] [ny] [nz] because of keyword "POINTS:" +# POINTS: 100 360 1 +# Columns: r phi temperature [K] +3481000.0 0.00000000 0 +3510191.9 0.00000000 0 +3539383.8 0.00000000 0 +3568575.8 0.00000000 0 +3597767.7 0.00000000 0 +3626959.6 0.00000000 0 +3656151.5 0.00000000 0 +3685343.4 0.00000000 0 +3714535.4 0.00000000 0 +3743727.3 0.00000000 0 +3772919.2 0.00000000 0 +3802111.1 0.00000000 0 +3831303.0 0.00000000 0 +3860494.9 0.00000000 0 +3889686.9 0.00000000 0 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