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*.mesh | ||
*.bson | ||
*.inp | ||
*.msh | ||
**/Manifest.toml | ||
out*/ | ||
docs/build | ||
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name = "Trixi" | ||
uuid = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb" | ||
authors = ["Michael Schlottke-Lakemper <[email protected]>", "Gregor Gassner <[email protected]>", "Hendrik Ranocha <[email protected]>", "Andrew R. Winters <[email protected]>", "Jesse Chan <[email protected]>"] | ||
version = "0.6.6-pre" | ||
version = "0.6.7-pre" | ||
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[deps] | ||
CodeTracking = "da1fd8a2-8d9e-5ec2-8556-3022fb5608a2" | ||
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examples/structured_2d_dgsem/elixir_euler_warm_bubble.jl
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using OrdinaryDiffEq | ||
using Trixi | ||
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# Warm bubble test case from | ||
# - Wicker, L. J., and Skamarock, W. C. (1998) | ||
# A time-splitting scheme for the elastic equations incorporating | ||
# second-order Runge–Kutta time differencing | ||
# [DOI: 10.1175/1520-0493(1998)126%3C1992:ATSSFT%3E2.0.CO;2](https://doi.org/10.1175/1520-0493(1998)126%3C1992:ATSSFT%3E2.0.CO;2) | ||
# See also | ||
# - Bryan and Fritsch (2002) | ||
# A Benchmark Simulation for Moist Nonhydrostatic Numerical Models | ||
# [DOI: 10.1175/1520-0493(2002)130<2917:ABSFMN>2.0.CO;2](https://doi.org/10.1175/1520-0493(2002)130<2917:ABSFMN>2.0.CO;2) | ||
# - Carpenter, Droegemeier, Woodward, Hane (1990) | ||
# Application of the Piecewise Parabolic Method (PPM) to | ||
# Meteorological Modeling | ||
# [DOI: 10.1175/1520-0493(1990)118<0586:AOTPPM>2.0.CO;2](https://doi.org/10.1175/1520-0493(1990)118<0586:AOTPPM>2.0.CO;2) | ||
struct WarmBubbleSetup | ||
# Physical constants | ||
g::Float64 # gravity of earth | ||
c_p::Float64 # heat capacity for constant pressure (dry air) | ||
c_v::Float64 # heat capacity for constant volume (dry air) | ||
gamma::Float64 # heat capacity ratio (dry air) | ||
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function WarmBubbleSetup(; g = 9.81, c_p = 1004.0, c_v = 717.0, gamma = c_p / c_v) | ||
new(g, c_p, c_v, gamma) | ||
end | ||
end | ||
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# Initial condition | ||
function (setup::WarmBubbleSetup)(x, t, equations::CompressibleEulerEquations2D) | ||
@unpack g, c_p, c_v = setup | ||
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# center of perturbation | ||
center_x = 10000.0 | ||
center_z = 2000.0 | ||
# radius of perturbation | ||
radius = 2000.0 | ||
# distance of current x to center of perturbation | ||
r = sqrt((x[1] - center_x)^2 + (x[2] - center_z)^2) | ||
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# perturbation in potential temperature | ||
potential_temperature_ref = 300.0 | ||
potential_temperature_perturbation = 0.0 | ||
if r <= radius | ||
potential_temperature_perturbation = 2 * cospi(0.5 * r / radius)^2 | ||
end | ||
potential_temperature = potential_temperature_ref + potential_temperature_perturbation | ||
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# Exner pressure, solves hydrostatic equation for x[2] | ||
exner = 1 - g / (c_p * potential_temperature) * x[2] | ||
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# pressure | ||
p_0 = 100_000.0 # reference pressure | ||
R = c_p - c_v # gas constant (dry air) | ||
p = p_0 * exner^(c_p / R) | ||
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# temperature | ||
T = potential_temperature * exner | ||
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# density | ||
rho = p / (R * T) | ||
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v1 = 20.0 | ||
v2 = 0.0 | ||
E = c_v * T + 0.5 * (v1^2 + v2^2) | ||
return SVector(rho, rho * v1, rho * v2, rho * E) | ||
end | ||
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# Source terms | ||
@inline function (setup::WarmBubbleSetup)(u, x, t, equations::CompressibleEulerEquations2D) | ||
@unpack g = setup | ||
rho, _, rho_v2, _ = u | ||
return SVector(zero(eltype(u)), zero(eltype(u)), -g * rho, -g * rho_v2) | ||
end | ||
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############################################################################### | ||
# semidiscretization of the compressible Euler equations | ||
warm_bubble_setup = WarmBubbleSetup() | ||
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equations = CompressibleEulerEquations2D(warm_bubble_setup.gamma) | ||
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boundary_conditions = (x_neg = boundary_condition_periodic, | ||
x_pos = boundary_condition_periodic, | ||
y_neg = boundary_condition_slip_wall, | ||
y_pos = boundary_condition_slip_wall) | ||
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polydeg = 3 | ||
basis = LobattoLegendreBasis(polydeg) | ||
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# This is a good estimate for the speed of sound in this example. | ||
# Other values between 300 and 400 should work as well. | ||
surface_flux = FluxLMARS(340.0) | ||
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volume_flux = flux_kennedy_gruber | ||
volume_integral = VolumeIntegralFluxDifferencing(volume_flux) | ||
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solver = DGSEM(basis, surface_flux, volume_integral) | ||
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coordinates_min = (0.0, 0.0) | ||
coordinates_max = (20_000.0, 10_000.0) | ||
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cells_per_dimension = (64, 32) | ||
mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max) | ||
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semi = SemidiscretizationHyperbolic(mesh, equations, warm_bubble_setup, solver, | ||
source_terms = warm_bubble_setup, | ||
boundary_conditions = boundary_conditions) | ||
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############################################################################### | ||
# ODE solvers, callbacks etc. | ||
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tspan = (0.0, 1000.0) # 1000 seconds final time | ||
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ode = semidiscretize(semi, tspan) | ||
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summary_callback = SummaryCallback() | ||
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analysis_interval = 1000 | ||
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analysis_callback = AnalysisCallback(semi, interval = analysis_interval, | ||
extra_analysis_errors = (:entropy_conservation_error,)) | ||
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alive_callback = AliveCallback(analysis_interval = analysis_interval) | ||
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save_solution = SaveSolutionCallback(interval = analysis_interval, | ||
save_initial_solution = true, | ||
save_final_solution = true, | ||
output_directory = "out", | ||
solution_variables = cons2prim) | ||
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stepsize_callback = StepsizeCallback(cfl = 1.0) | ||
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callbacks = CallbackSet(summary_callback, | ||
analysis_callback, | ||
alive_callback, | ||
save_solution, | ||
stepsize_callback) | ||
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############################################################################### | ||
# run the simulation | ||
sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), | ||
maxiters = 1.0e7, | ||
dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback | ||
save_everystep = false, callback = callbacks); | ||
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summary_callback() |
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