added entropy conservative test

examples/tree_1d_dgsem/elixir_euler_quasi_1d_ec.jl

@@ -0,0 +1,68 @@
+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)
+
+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
+
+basis = LobattoLegendreBasis(3)
+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, 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