LinearizedEuler3D (#1903)

* LinearizedEuler3D

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Co-authored-by: Lars Christmann <[email protected]>

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* unit tests for full coverage

---------

Co-authored-by: Lars Christmann <[email protected]>

examples/p4est_3d_dgsem/elixir_linearizedeuler_convergence.jl

@@ -0,0 +1,64 @@
+using OrdinaryDiffEq
+using Trixi
+
+###############################################################################
+# semidiscretization of the linearized Euler equations
+
+equations = LinearizedEulerEquations3D(v_mean_global = (0.0, 0.0, 0.0), c_mean_global = 1.0,
+                                       rho_mean_global = 1.0)
+
+initial_condition = initial_condition_convergence_test
+
+solver = DGSEM(polydeg = 3, surface_flux = flux_hll)
+
+coordinates_min = (-1.0, -1.0, -1.0) # minimum coordinates (min(x), min(y), min(z))
+coordinates_max = (1.0, 1.0, 1.0) # maximum coordinates (max(x), max(y), max(z))
+
+# `initial_refinement_level` is provided here to allow for a 
+# convenient convergence test, see
+# https://trixi-framework.github.io/Trixi.jl/stable/#Performing-a-convergence-analysis
+trees_per_dimension = (4, 4, 4)
+mesh = P4estMesh(trees_per_dimension, polydeg = 3,
+                 coordinates_min = coordinates_min,
+                 coordinates_max = coordinates_max,
+                 initial_refinement_level = 0)
+
+# A semidiscretization collects data structures and functions for the spatial discretization
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+# Create ODE problem with time span from 0.0 to 0.2
+tspan = (0.0, 0.2)
+ode = semidiscretize(semi, tspan)
+
+# At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup
+# and resets the timers
+summary_callback = SummaryCallback()
+
+analysis_interval = 100
+
+# The AnalysisCallback allows to analyse the solution in regular intervals and prints the results
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
+
+# The AliveCallback prints short status information in regular intervals
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
+
+# The StepsizeCallback handles the re-calculation of the maximum Δt after each time step
+stepsize_callback = StepsizeCallback(cfl = 0.8)
+
+# Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver
+callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+# OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks
+sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false),
+            dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
+            save_everystep = false, callback = callbacks);
+
+# print the timer summary
+summary_callback() # print the timer summary

examples/tree_3d_dgsem/elixir_linearizedeuler_gauss_wall.jl

@@ -0,0 +1,65 @@
+using OrdinaryDiffEq
+using Trixi
+
+###############################################################################
+# semidiscretization of the linearized Euler equations
+
+equations = LinearizedEulerEquations3D(v_mean_global = (0.5, 0.5, 0.5), c_mean_global = 1.0,
+                                       rho_mean_global = 1.0)
+
+solver = DGSEM(polydeg = 5, surface_flux = flux_lax_friedrichs)
+
+coordinates_min = (0.0, 0.0, 0.0)
+coordinates_max = (90.0, 90.0, 90.0)
+
+mesh = TreeMesh(coordinates_min, coordinates_max,
+                initial_refinement_level = 4,
+                n_cells_max = 100_000,
+                periodicity = false)
+
+# Initialize density and pressure perturbation with a Gaussian bump
+# that splits into radial waves which are advected with v - c and v + c.
+function initial_condition_gauss_wall(x, t, equations::LinearizedEulerEquations3D)
+    v1_prime = 0.0
+    v2_prime = 0.0
+    v3_prime = 0.0
+    rho_prime = p_prime = 2 * exp(-((x[1] - 45)^2 + (x[2] - 45)^2) / 25)
+    return SVector(rho_prime, v1_prime, v2_prime, v3_prime, p_prime)
+end
+initial_condition = initial_condition_gauss_wall
+
+# A semidiscretization collects data structures and functions for the spatial discretization
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
+                                    boundary_conditions = boundary_condition_wall)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+# At t = 30, the wave moving with v + c crashes into the wall
+tspan = (0.0, 30.0)
+ode = semidiscretize(semi, tspan)
+
+# At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup
+# and resets the timers
+summary_callback = SummaryCallback()
+
+# The AnalysisCallback allows to analyse the solution in regular intervals and prints the results
+analysis_callback = AnalysisCallback(semi, interval = 100)
+
+# The StepsizeCallback handles the re-calculation of the maximum Δt after each time step
+stepsize_callback = StepsizeCallback(cfl = 0.9)
+
+# Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver
+callbacks = CallbackSet(summary_callback, analysis_callback,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+# OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks
+sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false),
+            dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
+            save_everystep = false, callback = callbacks)
+
+# Print the timer summary
+summary_callback()

src/Trixi.jl

@@ -160,7 +160,7 @@ export AcousticPerturbationEquations2D,
        LatticeBoltzmannEquations2D, LatticeBoltzmannEquations3D,
        ShallowWaterEquations1D, ShallowWaterEquations2D,
        ShallowWaterEquationsQuasi1D,
-       LinearizedEulerEquations1D, LinearizedEulerEquations2D,
+       LinearizedEulerEquations1D, LinearizedEulerEquations2D, LinearizedEulerEquations3D,
        PolytropicEulerEquations2D,
        TrafficFlowLWREquations1D
 

src/equations/equations.jl

@@ -503,6 +503,7 @@ abstract type AbstractLinearizedEulerEquations{NDIMS, NVARS} <:
               AbstractEquations{NDIMS, NVARS} end
 include("linearized_euler_1d.jl")
 include("linearized_euler_2d.jl")
+include("linearized_euler_3d.jl")
 
 abstract type AbstractEquationsParabolic{NDIMS, NVARS, GradientVariables} <:
               AbstractEquations{NDIMS, NVARS} end

src/equations/linearized_euler_1d.jl

@@ -8,7 +8,7 @@
 @doc raw"""
     LinearizedEulerEquations1D(v_mean_global, c_mean_global, rho_mean_global)
 
-Linearized euler equations in one space dimension. The equations are given by
+Linearized Euler equations in one space dimension. The equations are given by
 ```math
 \partial_t
 \begin{pmatrix}

src/equations/linearized_euler_2d.jl

@@ -8,7 +8,7 @@
 @doc raw"""
     LinearizedEulerEquations2D(v_mean_global, c_mean_global, rho_mean_global)
 
-Linearized euler equations in two space dimensions. The equations are given by
+Linearized Euler equations in two space dimensions. The equations are given by
 ```math
 \partial_t
 \begin{pmatrix}