Compressible Euler Quasi-1D

examples/tree_1d_dgsem/elixir_euler_quasi_1d_discontinuous.jl

@@ -0,0 +1,85 @@
+using OrdinaryDiffEq
+using Trixi
+
+###############################################################################
+# Semidiscretization of the quasi 1d compressible Euler equations
+# See Chan et al.  https://doi.org/10.48550/arXiv.2307.12089 for details
+
+equations = CompressibleEulerEquationsQuasi1D(1.4)
+
+"""
+    initial_condition_discontinuity(x, t, equations::CompressibleEulerEquations1D)
+
+A discontinuous initial condition taken from
+- Jesse Chan, Khemraj Shukla, Xinhui Wu, Ruofeng Liu, Prani Nalluri (2023)
+    High order entropy stable schemes for the quasi-one-dimensional
+    shallow water and compressible Euler equations
+    [DOI: 10.48550/arXiv.2307.12089](https://doi.org/10.48550/arXiv.2307.12089)   
+"""
+function initial_condition_discontinuity(x, t,
+                                         equations::CompressibleEulerEquationsQuasi1D)
+    rho = (x[1] < 0) ? 3.4718 : 2.0
+    v1 = (x[1] < 0) ? -2.5923 : -3.0
+    p = (x[1] < 0) ? 5.7118 : 2.639
+    a = (x[1] < 0) ? 1.0 : 1.5
+
+    return prim2cons(SVector(rho, v1, p, a), equations)
+end
+
+initial_condition = initial_condition_discontinuity
+
+volume_flux = (flux_chan_etal, flux_nonconservative_chan_etal)
+surface_flux = (flux_lax_friedrichs, flux_nonconservative_chan_etal)
+
+basis = LobattoLegendreBasis(3)
+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)
+solver = DGSEM(basis, surface_flux, volume_integral)
+
+coordinates_min = (-1.0,)
+coordinates_max = (1.0,)
+mesh = TreeMesh(coordinates_min, coordinates_max,
+                initial_refinement_level = 6,
+                n_cells_max = 10_000)
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 2.0)
+ode = semidiscretize(semi, tspan)
+
+summary_callback = SummaryCallback()
+
+analysis_interval = 100
+
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
+
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
+
+save_solution = SaveSolutionCallback(interval = 100,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     solution_variables = cons2prim)
+
+stepsize_callback = StepsizeCallback(cfl = 0.5)
+
+callbacks = CallbackSet(summary_callback,
+                        analysis_callback, alive_callback,
+                        save_solution,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+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);
+summary_callback() # print the timer summary

examples/tree_1d_dgsem/elixir_euler_quasi_1d_ec.jl

@@ -0,0 +1,73 @@
+using OrdinaryDiffEq
+using Trixi
+
+###############################################################################
+# Semidiscretization of the quasi 1d compressible Euler equations with a discontinuous nozzle width function.
+# See Chan et al.  https://doi.org/10.48550/arXiv.2307.12089 for details
+
+equations = CompressibleEulerEquationsQuasi1D(1.4)
+
+# Setup a truly discontinuous density function and nozzle width for
+# this academic testcase of entropy conservation. The errors from the analysis
+# callback are not important but the entropy error for this test case
+# `∑∂S/∂U ⋅ Uₜ` should be around machine roundoff.
+# Works as intended for TreeMesh1D with `initial_refinement_level=6`. If the mesh
+# refinement level is changed the initial condition below may need changed as well to
+# ensure that the discontinuities lie on an element interface.
+function initial_condition_ec(x, t, equations::CompressibleEulerEquationsQuasi1D)
+    v1 = 0.1
+    rho = 2.0 + 0.1 * x[1]
+    p = 3.0
+    a = 2.0 + x[1]
+
+    return prim2cons(SVector(rho, v1, p, a), equations)
+end
+
+initial_condition = initial_condition_ec
+
+volume_flux = (flux_chan_etal, flux_nonconservative_chan_etal)
+surface_flux = volume_flux
+solver = DGSEM(polydeg = 4, surface_flux = surface_flux,
+               volume_integral = VolumeIntegralFluxDifferencing(volume_flux))
+
+coordinates_min = (-1.0,)
+coordinates_max = (1.0,)
+mesh = TreeMesh(coordinates_min, coordinates_max,
+                initial_refinement_level = 6,
+                n_cells_max = 10_000)
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 0.4)
+ode = semidiscretize(semi, tspan)
+
+summary_callback = SummaryCallback()
+
+analysis_interval = 100
+
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
+
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
+
+save_solution = SaveSolutionCallback(interval = 100,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     solution_variables = cons2prim)
+
+stepsize_callback = StepsizeCallback(cfl = 0.8)
+
+callbacks = CallbackSet(summary_callback,
+                        analysis_callback, alive_callback,
+                        save_solution,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+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);
+summary_callback() # print the timer summary

examples/tree_1d_dgsem/elixir_euler_quasi_1d_source_terms.jl

@@ -0,0 +1,60 @@
+using OrdinaryDiffEq
+using Trixi
+using ForwardDiff
+
+###############################################################################
+# Semidiscretization of the quasi 1d compressible Euler equations
+# See Chan et al.  https://doi.org/10.48550/arXiv.2307.12089 for details
+
+equations = CompressibleEulerEquationsQuasi1D(1.4)
+
+initial_condition = initial_condition_convergence_test
+
+volume_flux = (flux_chan_etal, flux_nonconservative_chan_etal)
+surface_flux = volume_flux
+solver = DGSEM(polydeg = 4, surface_flux = surface_flux,
+               volume_integral = VolumeIntegralFluxDifferencing(volume_flux))
+
+coordinates_min = -1.0
+coordinates_max = 1.0
+mesh = TreeMesh(coordinates_min, coordinates_max,
+                initial_refinement_level = 4,
+                n_cells_max = 10_000)
+
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
+                                    source_terms = source_terms_convergence_test)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+tspan = (0.0, 2.0)
+ode = semidiscretize(semi, tspan)
+
+summary_callback = SummaryCallback()
+
+analysis_interval = 100
+analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
+                                     extra_analysis_errors = (:l2_error_primitive,
+                                                              :linf_error_primitive))
+
+alive_callback = AliveCallback(analysis_interval = analysis_interval)
+
+save_solution = SaveSolutionCallback(interval = 100,
+                                     save_initial_solution = true,
+                                     save_final_solution = true,
+                                     solution_variables = cons2prim)
+
+stepsize_callback = StepsizeCallback(cfl = 0.8)
+
+callbacks = CallbackSet(summary_callback,
+                        analysis_callback, alive_callback,
+                        save_solution,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+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);
+summary_callback() # print the timer summary

src/Trixi.jl

@@ -139,6 +139,7 @@ export AcousticPerturbationEquations2D,
        CompressibleEulerEquations3D,
        CompressibleEulerMulticomponentEquations1D,
        CompressibleEulerMulticomponentEquations2D,
+       CompressibleEulerEquationsQuasi1D,
        IdealGlmMhdEquations1D, IdealGlmMhdEquations2D, IdealGlmMhdEquations3D,
        IdealGlmMhdMulticomponentEquations1D, IdealGlmMhdMulticomponentEquations2D,
        HyperbolicDiffusionEquations1D, HyperbolicDiffusionEquations2D,