change dt_opt to be that of b_opt and add a new example

examples/structured_1d_dgsem/elixir_euler_source_terms_embedded_perk3.jl

@@ -0,0 +1,66 @@
+# The same setup as tree_1d_dgsem/elixir_euler_source_terms.jl
+# to verify the StructuredMesh implementation against TreeMesh
+using Convex, ECOS, Clarabel
+using OrdinaryDiffEq
+using Trixi
+
+###############################################################################
+# semidiscretization of the compressible Euler equations
+
+equations = CompressibleEulerEquations1D(1.4)
+
+initial_condition = initial_condition_convergence_test
+
+# Note that the expected EOC of 5 is not reached with this flux.
+# Using flux_hll instead yields the expected EOC.
+solver = DGSEM(polydeg = 4, surface_flux = flux_lax_friedrichs)
+
+coordinates_min = (0.0,)
+coordinates_max = (2.0,)
+cells_per_dimension = (16,)
+
+mesh = StructuredMesh(cells_per_dimension, coordinates_min, coordinates_max)
+
+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)
+
+
+ode_algorithm = Trixi.EmbeddedPairedRK3(10, 7, tspan, semi)
+cfl_number = Trixi.calculate_cfl(ode_algorithm, ode)
+
+stepsize_callback = StepsizeCallback(cfl = 0.5)
+
+callbacks = CallbackSet(summary_callback,
+                        alive_callback,
+                        save_solution,
+                        analysis_callback,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+sol = Trixi.solve(ode, ode_algorithm,
+            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
+println("cfl_number = ", cfl_number)

examples/tree_1d_dgsem/elixir_advection_embedded_perk3.jl

@@ -43,7 +43,7 @@ analysis_interval = 100
 analysis_callback = AnalysisCallback(semi, interval = analysis_interval)
 
 # The StepsizeCallback handles the re-calculation of the maximum Δt after each time step
-stepsize_callback = StepsizeCallback(cfl = 1.5)
+
 
 alive_callback = AliveCallback(alive_interval = analysis_interval)
 
@@ -53,11 +53,7 @@ save_solution = SaveSolutionCallback(dt = 0.1,
                                      solution_variables = cons2prim)
 
 # Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver
-callbacks = CallbackSet(summary_callback,
-                        alive_callback,
-                        save_solution,
-                        analysis_callback,
-                        stepsize_callback)
+
 
 ###############################################################################
 # run the simulation
@@ -66,6 +62,14 @@ callbacks = CallbackSet(summary_callback,
 # Pass `tspan` to calculate maximum time step allowed for the bisection algorithm used 
 # in calculating the polynomial coefficients in the ODE algorithm.
 ode_algorithm = Trixi.EmbeddedPairedRK3(10, 7, tspan, semi)
+cfl_number = Trixi.calculate_cfl(ode_algorithm, ode)
+stepsize_callback = StepsizeCallback(cfl = cfl_number)
+
+callbacks = CallbackSet(summary_callback,
+                        alive_callback,
+                        save_solution,
+                        analysis_callback,
+                        stepsize_callback)
 
 sol = Trixi.solve(ode, ode_algorithm,
                   dt = 1.0, # Manual time step value, will be overwritten by the stepsize_callback when it is specified.

src/time_integration/paired_explicit_runge_kutta/methods_embedded_PERK3.jl

@@ -52,14 +52,14 @@ function compute_EmbeddedPairedRK3_butcher_tableau(num_stages, num_stage_evals,
 
 
     #TODO: something wrong when s = e
-    b, _ = solve_b_butcher_coeffs_unknown(num_eig_vals, eig_vals,
+    b, dt_opt_b = solve_b_butcher_coeffs_unknown(num_eig_vals, eig_vals,
                                            num_stages, num_stage_evals,
                                            num_stages - 1, # num_stages_embedded = num_stages - 1	
                                            num_stage_evals - 1, # num_stage_evals_embedded = num_stage_evals - 1
                                            a_unknown, c, dtmax, dteps)
 
 
-    return a_matrix, b, c, dt_opt
+    return a_matrix, b, c, dt_opt_b
 end
 
 # Compute the Butcher tableau for a paired explicit Runge-Kutta method order 3