Added Shu-Osher initialization for 1D compressible Euler with Gauss nodes

examples/dgmulti_1d/elixir_euler_shu_osher_gauss_shock_capturing.jl

@@ -0,0 +1,93 @@
+using Trixi
+using OrdinaryDiffEq
+
+gamma_gas = 1.4
+equations = CompressibleEulerEquations1D(gamma_gas)
+
+###############################################################################
+# setup the GSBP DG discretization that uses the Gauss operators from 
+# Chan, Del Rey Fernandez, Carpenter (2019). 
+# [https://doi.org/10.1137/18M1209234](https://doi.org/10.1137/18M1209234)
+
+# Shu-Osher initial condition for 1D compressible Euler equations
+# Example 8 from Shu, Osher (1989).
+# [https://doi.org/10.1016/0021-9991(89)90222-2](https://doi.org/10.1016/0021-9991(89)90222-2)
+function initial_condition_shu_osher(x, t, equations::CompressibleEulerEquations1D)
+    x0 = -4
+
+    rho_left = 27 / 7
+    v_left = 4 * sqrt(35) / 9
+    p_left = 31 / 3
+
+    # Replaced v_right = 0 to v_right = 0.1 to avoid positivity issues.
+    v_right = 0.1
+    p_right = 1.0
+
+    rho = ifelse(x[1] > x0, 1 + 1 / 5 * sin(5 * x[1]), rho_left)
+    v = ifelse(x[1] > x0, v_right, v_left)
+    p = ifelse(x[1] > x0, p_right, p_left)
+
+    return prim2cons(SVector(rho + 0.1 * rand(), v + 0.1 * rand(), p + 0.1 * rand()),
+                     equations)
+end
+
+initial_condition = initial_condition_shu_osher
+
+surface_flux = flux_lax_friedrichs
+volume_flux = flux_ranocha
+
+polydeg = 3
+basis = DGMultiBasis(Line(), polydeg, approximation_type = GaussSBP())
+
+indicator_sc = IndicatorHennemannGassner(equations, basis,
+                                         alpha_max = 0.5,
+                                         alpha_min = 0.001,
+                                         alpha_smooth = true,
+                                         variable = density_pressure)
+volume_integral = VolumeIntegralShockCapturingHG(indicator_sc;
+                                                 volume_flux_dg = volume_flux,
+                                                 volume_flux_fv = surface_flux)
+
+dg = DGMulti(basis,
+             surface_integral = SurfaceIntegralWeakForm(surface_flux),
+             volume_integral = volume_integral)
+
+boundary_condition = BoundaryConditionDirichlet(initial_condition)
+boundary_conditions = (; :entire_boundary => boundary_condition)
+
+###############################################################################
+#  setup the 1D mesh
+
+cells_per_dimension = (64,)
+mesh = DGMultiMesh(dg, cells_per_dimension,
+                   coordinates_min = (-5.0,), coordinates_max = (5.0,),
+                   periodicity = false)
+
+###############################################################################
+#  setup the semidiscretization and ODE problem
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition,
+                                    dg, boundary_conditions = boundary_conditions)
+
+tspan = (0.0, 1.0)
+ode = semidiscretize(semi, tspan)
+
+###############################################################################
+#  setup the callbacks
+
+# prints a summary of the simulation setup and resets the timers
+summary_callback = SummaryCallback()
+
+# analyse the solution in regular intervals and prints the results
+analysis_callback = AnalysisCallback(semi, interval = 100, uEltype = real(dg))
+
+# handles the re-calculation of the maximum Δt after each time step
+stepsize_callback = StepsizeCallback(cfl = 0.1)
+
+# collect all callbacks such that they can be passed to the ODE solver
+callbacks = CallbackSet(summary_callback, analysis_callback, stepsize_callback)
+
+# ###############################################################################
+# # run the simulation
+
+sol = solve(ode, SSPRK43(), adaptive = true, callback = callbacks, save_everystep = false)

test/test_dgmulti_1d.jl

@@ -52,12 +52,37 @@ end
                         l2=[
                             7.853842541289665e-7,
                             9.609905503440606e-7,
-                            2.832322219966481e-6,
+                            2.832322219966481e-6
                         ] ./ sqrt(2.0),
                         linf=[
                             1.5003758788711963e-6,
                             1.802998748523521e-6,
-                            4.83599270806323e-6,
+                            4.83599270806323e-6
+                        ])
+    # Ensure that we do not have excessive memory allocations
+    # (e.g., from type instabilities)
+    let
+        t = sol.t[end]
+        u_ode = sol.u[end]
+        du_ode = similar(u_ode)
+        @test (@allocated Trixi.rhs!(du_ode, u_ode, semi, t)) < 1000
+    end
+end
+
+@trixi_testset "elixir_euler_shu_osher_gauss_shock_capturing.jl " begin
+    @test_trixi_include(joinpath(EXAMPLES_DIR,
+                                 "elixir_euler_shu_osher_gauss_shock_capturing.jl"),
+                        cells_per_dimension=(64,), tspan=(0.0, 1.0),
+                        # division by sqrt(2.0) corresponds to normalization by the square root of the size of the domain
+                        l2=[
+                            1.7177729727131328,
+                            6.191308529732632,
+                            22.281999765458117
+                        ],
+                        linf=[
+                            3.228727516356452,
+                            10.989654948503484,
+                            38.65258452259893
                         ])
     # Ensure that we do not have excessive memory allocations
     # (e.g., from type instabilities)
@@ -93,12 +118,12 @@ end
                         l2=[
                             6.437827414849647e-6,
                             2.1840558851820947e-6,
-                            1.3245669629438228e-5,
+                            1.3245669629438228e-5
                         ],
                         linf=[
                             2.0715843751295537e-5,
                             8.519520630301258e-6,
-                            4.2642194098885255e-5,
+                            4.2642194098885255e-5
                         ])
     # Ensure that we do not have excessive memory allocations
     # (e.g., from type instabilities)
@@ -122,12 +147,12 @@ end
                         l2=[
                             1.8684509287853788e-5,
                             1.0641411823379635e-5,
-                            5.178010291876143e-5,
+                            5.178010291876143e-5
                         ],
                         linf=[
                             6.933493585936645e-5,
                             3.0277366229292113e-5,
-                            0.0002220020568932668,
+                            0.0002220020568932668
                         ])
     show(stdout, semi.solver.basis)
     show(stdout, MIME"text/plain"(), semi.solver.basis)
@@ -145,11 +170,11 @@ end
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_fdsbp_periodic.jl"),
                         l2=[
                             9.146929178341782e-7, 1.8997616876521201e-6,
-                            3.991417701005622e-6,
+                            3.991417701005622e-6
                         ],
                         linf=[
                             1.7321089882393892e-6, 3.3252888869128583e-6,
-                            6.525278767988141e-6,
+                            6.525278767988141e-6
                         ])
     show(stdout, semi.solver.basis)
     show(stdout, MIME"text/plain"(), semi.solver.basis)
@@ -186,13 +211,13 @@ end
                             3.03001101100507e-6,
                             1.692177335948727e-5,
                             3.002634351734614e-16,
-                            1.1636653574178203e-15,
+                            1.1636653574178203e-15
                         ],
                         linf=[
                             1.2043401988570679e-5,
                             5.346847010329059e-5,
                             9.43689570931383e-16,
-                            2.220446049250313e-15,
+                            2.220446049250313e-15
                         ])
     # Ensure that we do not have excessive memory allocations
     # (e.g., from type instabilities)
@@ -212,13 +237,13 @@ end
                             1.633271343738687e-5,
                             9.575385661756332e-6,
                             1.2700331443128421e-5,
-                            0.0,
+                            0.0
                         ],
                         linf=[
                             7.304984704381567e-5,
                             5.2365944135601694e-5,
                             6.469559594934893e-5,
-                            0.0,
+                            0.0
                         ])
     # Ensure that we do not have excessive memory allocations
     # (e.g., from type instabilities)