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| runs-on: ubuntu-latest | ||
| steps: | ||
| - name: Checkout Actions Repository | ||
| uses: actions/checkout@v3 | ||
| uses: actions/checkout@v4 | ||
| - name: Check spelling | ||
| uses: crate-ci/[email protected].9 | ||
| uses: crate-ci/[email protected].15 | ||
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| @@ -1,7 +1,7 @@ | ||
| 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 = "0.5.45-pre" | ||
| version = "0.5.46-pre" | ||
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| [deps] | ||
| CodeTracking = "da1fd8a2-8d9e-5ec2-8556-3022fb5608a2" | ||
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215 changes: 215 additions & 0 deletions
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examples/p4est_2d_dgsem/elixir_navierstokes_convergence_nonperiodic.jl
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| using OrdinaryDiffEq | ||
| using Trixi | ||
|
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| ############################################################################### | ||
| # semidiscretization of the ideal compressible Navier-Stokes equations | ||
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| prandtl_number() = 0.72 | ||
| mu() = 0.01 | ||
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| equations = CompressibleEulerEquations2D(1.4) | ||
| equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu=mu(), Prandtl=prandtl_number(), | ||
| gradient_variables=GradientVariablesPrimitive()) | ||
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| # Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux | ||
| solver = DGSEM(polydeg=3, surface_flux=flux_lax_friedrichs, | ||
| volume_integral=VolumeIntegralWeakForm()) | ||
|
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| coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) | ||
| coordinates_max = ( 1.0, 1.0) # maximum coordinates (max(x), max(y)) | ||
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| trees_per_dimension = (4, 4) | ||
| mesh = P4estMesh(trees_per_dimension, | ||
| polydeg=3, initial_refinement_level=2, | ||
| coordinates_min=coordinates_min, coordinates_max=coordinates_max, | ||
| periodicity=(false, false)) | ||
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| # Note: the initial condition cannot be specialized to `CompressibleNavierStokesDiffusion2D` | ||
| # since it is called by both the parabolic solver (which passes in `CompressibleNavierStokesDiffusion2D`) | ||
| # and by the initial condition (which passes in `CompressibleEulerEquations2D`). | ||
| # This convergence test setup was originally derived by Andrew Winters (@andrewwinters5000) | ||
| function initial_condition_navier_stokes_convergence_test(x, t, equations) | ||
| # Amplitude and shift | ||
| A = 0.5 | ||
| c = 2.0 | ||
|
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| # convenience values for trig. functions | ||
| pi_x = pi * x[1] | ||
| pi_y = pi * x[2] | ||
| pi_t = pi * t | ||
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| rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) | ||
| v1 = sin(pi_x) * log(x[2] + 2.0) * (1.0 - exp(-A * (x[2] - 1.0)) ) * cos(pi_t) | ||
| v2 = v1 | ||
| p = rho^2 | ||
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| return prim2cons(SVector(rho, v1, v2, p), equations) | ||
| end | ||
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| @inline function source_terms_navier_stokes_convergence_test(u, x, t, equations) | ||
| y = x[2] | ||
|
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| # TODO: parabolic | ||
| # we currently need to hardcode these parameters until we fix the "combined equation" issue | ||
| # see also https://github.com/trixi-framework/Trixi.jl/pull/1160 | ||
| inv_gamma_minus_one = inv(equations.gamma - 1) | ||
| Pr = prandtl_number() | ||
| mu_ = mu() | ||
|
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| # Same settings as in `initial_condition` | ||
| # Amplitude and shift | ||
| A = 0.5 | ||
| c = 2.0 | ||
|
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| # convenience values for trig. functions | ||
| pi_x = pi * x[1] | ||
| pi_y = pi * x[2] | ||
| pi_t = pi * t | ||
|
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| # compute the manufactured solution and all necessary derivatives | ||
| rho = c + A * sin(pi_x) * cos(pi_y) * cos(pi_t) | ||
| rho_t = -pi * A * sin(pi_x) * cos(pi_y) * sin(pi_t) | ||
| rho_x = pi * A * cos(pi_x) * cos(pi_y) * cos(pi_t) | ||
| rho_y = -pi * A * sin(pi_x) * sin(pi_y) * cos(pi_t) | ||
| rho_xx = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) | ||
| rho_yy = -pi * pi * A * sin(pi_x) * cos(pi_y) * cos(pi_t) | ||
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| v1 = sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) | ||
| v1_t = -pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * sin(pi_t) | ||
| v1_x = pi * cos(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) | ||
| v1_y = sin(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) | ||
| v1_xx = -pi * pi * sin(pi_x) * log(y + 2.0) * (1.0 - exp(-A * (y - 1.0))) * cos(pi_t) | ||
| v1_xy = pi * cos(pi_x) * (A * log(y + 2.0) * exp(-A * (y - 1.0)) + (1.0 - exp(-A * (y - 1.0))) / (y + 2.0)) * cos(pi_t) | ||
| v1_yy = (sin(pi_x) * ( 2.0 * A * exp(-A * (y - 1.0)) / (y + 2.0) | ||
| - A * A * log(y + 2.0) * exp(-A * (y - 1.0)) | ||
| - (1.0 - exp(-A * (y - 1.0))) / ((y + 2.0) * (y + 2.0))) * cos(pi_t)) | ||
| v2 = v1 | ||
| v2_t = v1_t | ||
| v2_x = v1_x | ||
| v2_y = v1_y | ||
| v2_xx = v1_xx | ||
| v2_xy = v1_xy | ||
| v2_yy = v1_yy | ||
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| p = rho * rho | ||
| p_t = 2.0 * rho * rho_t | ||
| p_x = 2.0 * rho * rho_x | ||
| p_y = 2.0 * rho * rho_y | ||
| p_xx = 2.0 * rho * rho_xx + 2.0 * rho_x * rho_x | ||
| p_yy = 2.0 * rho * rho_yy + 2.0 * rho_y * rho_y | ||
|
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| # Note this simplifies slightly because the ansatz assumes that v1 = v2 | ||
| E = p * inv_gamma_minus_one + 0.5 * rho * (v1^2 + v2^2) | ||
| E_t = p_t * inv_gamma_minus_one + rho_t * v1^2 + 2.0 * rho * v1 * v1_t | ||
| E_x = p_x * inv_gamma_minus_one + rho_x * v1^2 + 2.0 * rho * v1 * v1_x | ||
| E_y = p_y * inv_gamma_minus_one + rho_y * v1^2 + 2.0 * rho * v1 * v1_y | ||
|
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| # Some convenience constants | ||
| T_const = equations.gamma * inv_gamma_minus_one / Pr | ||
| inv_rho_cubed = 1.0 / (rho^3) | ||
|
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| # compute the source terms | ||
| # density equation | ||
| du1 = rho_t + rho_x * v1 + rho * v1_x + rho_y * v2 + rho * v2_y | ||
|
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| # x-momentum equation | ||
| du2 = ( rho_t * v1 + rho * v1_t + p_x + rho_x * v1^2 | ||
| + 2.0 * rho * v1 * v1_x | ||
| + rho_y * v1 * v2 | ||
| + rho * v1_y * v2 | ||
| + rho * v1 * v2_y | ||
| # stress tensor from x-direction | ||
| - 4.0 / 3.0 * v1_xx * mu_ | ||
| + 2.0 / 3.0 * v2_xy * mu_ | ||
| - v1_yy * mu_ | ||
| - v2_xy * mu_ ) | ||
| # y-momentum equation | ||
| du3 = ( rho_t * v2 + rho * v2_t + p_y + rho_x * v1 * v2 | ||
| + rho * v1_x * v2 | ||
| + rho * v1 * v2_x | ||
| + rho_y * v2^2 | ||
| + 2.0 * rho * v2 * v2_y | ||
| # stress tensor from y-direction | ||
| - v1_xy * mu_ | ||
| - v2_xx * mu_ | ||
| - 4.0 / 3.0 * v2_yy * mu_ | ||
| + 2.0 / 3.0 * v1_xy * mu_ ) | ||
| # total energy equation | ||
| du4 = ( E_t + v1_x * (E + p) + v1 * (E_x + p_x) | ||
| + v2_y * (E + p) + v2 * (E_y + p_y) | ||
| # stress tensor and temperature gradient terms from x-direction | ||
| - 4.0 / 3.0 * v1_xx * v1 * mu_ | ||
| + 2.0 / 3.0 * v2_xy * v1 * mu_ | ||
| - 4.0 / 3.0 * v1_x * v1_x * mu_ | ||
| + 2.0 / 3.0 * v2_y * v1_x * mu_ | ||
| - v1_xy * v2 * mu_ | ||
| - v2_xx * v2 * mu_ | ||
| - v1_y * v2_x * mu_ | ||
| - v2_x * v2_x * mu_ | ||
| - T_const * inv_rho_cubed * ( p_xx * rho * rho | ||
| - 2.0 * p_x * rho * rho_x | ||
| + 2.0 * p * rho_x * rho_x | ||
| - p * rho * rho_xx ) * mu_ | ||
| # stress tensor and temperature gradient terms from y-direction | ||
| - v1_yy * v1 * mu_ | ||
| - v2_xy * v1 * mu_ | ||
| - v1_y * v1_y * mu_ | ||
| - v2_x * v1_y * mu_ | ||
| - 4.0 / 3.0 * v2_yy * v2 * mu_ | ||
| + 2.0 / 3.0 * v1_xy * v2 * mu_ | ||
| - 4.0 / 3.0 * v2_y * v2_y * mu_ | ||
| + 2.0 / 3.0 * v1_x * v2_y * mu_ | ||
| - T_const * inv_rho_cubed * ( p_yy * rho * rho | ||
| - 2.0 * p_y * rho * rho_y | ||
| + 2.0 * p * rho_y * rho_y | ||
| - p * rho * rho_yy ) * mu_ ) | ||
|
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| return SVector(du1, du2, du3, du4) | ||
| end | ||
|
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| initial_condition = initial_condition_navier_stokes_convergence_test | ||
|
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| # BC types | ||
| velocity_bc_top_bottom = NoSlip((x, t, equations) -> initial_condition_navier_stokes_convergence_test(x, t, equations)[2:3]) | ||
| heat_bc_top_bottom = Adiabatic((x, t, equations) -> 0.0) | ||
| boundary_condition_top_bottom = BoundaryConditionNavierStokesWall(velocity_bc_top_bottom, heat_bc_top_bottom) | ||
|
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| boundary_condition_left_right = BoundaryConditionDirichlet(initial_condition_navier_stokes_convergence_test) | ||
|
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| # define inviscid boundary conditions | ||
| boundary_conditions = Dict(:x_neg => boundary_condition_left_right, | ||
| :x_pos => boundary_condition_left_right, | ||
| :y_neg => boundary_condition_slip_wall, | ||
| :y_pos => boundary_condition_slip_wall) | ||
|
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| # define viscous boundary conditions | ||
| boundary_conditions_parabolic = Dict(:x_neg => boundary_condition_left_right, | ||
| :x_pos => boundary_condition_left_right, | ||
| :y_neg => boundary_condition_top_bottom, | ||
| :y_pos => boundary_condition_top_bottom) | ||
|
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| semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), initial_condition, solver; | ||
| boundary_conditions=(boundary_conditions, boundary_conditions_parabolic), | ||
| source_terms=source_terms_navier_stokes_convergence_test) | ||
|
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| # ############################################################################### | ||
| # # ODE solvers, callbacks etc. | ||
|
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| # Create ODE problem with time span `tspan` | ||
| tspan = (0.0, 0.5) | ||
| ode = semidiscretize(semi, tspan) | ||
|
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| summary_callback = SummaryCallback() | ||
| alive_callback = AliveCallback(alive_interval=10) | ||
| analysis_interval = 100 | ||
| analysis_callback = AnalysisCallback(semi, interval=analysis_interval) | ||
| callbacks = CallbackSet(summary_callback, alive_callback, analysis_callback) | ||
|
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| ############################################################################### | ||
| # run the simulation | ||
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| time_int_tol = 1e-8 | ||
| sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5, | ||
| ode_default_options()..., callback=callbacks) | ||
| summary_callback() # print the timer summary | ||
|
|
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