PERK p2

Project.toml

@@ -6,10 +6,13 @@ version = "0.7.4-pre"
 [deps]
 CodeTracking = "da1fd8a2-8d9e-5ec2-8556-3022fb5608a2"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
+Convex = "f65535da-76fb-5f13-bab9-19810c17039a"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def"
 Downloads = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
+ECOS = "e2685f51-7e38-5353-a97d-a921fd2c8199"
 EllipsisNotation = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -20,6 +23,7 @@ LinearMaps = "7a12625a-238d-50fd-b39a-03d52299707e"
 LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890"
 MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"
 MuladdMacro = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
+NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 Octavian = "6fd5a793-0b7e-452c-907f-f8bfe9c57db4"
 OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 P4est = "7d669430-f675-4ae7-b43e-fab78ec5a902"

examples/tree_1d_dgsem/elixir_advection_PERK2.jl

@@ -0,0 +1,61 @@
+
+using OrdinaryDiffEq
+using Trixi
+
+###############################################################################
+# semidiscretization of the linear advection equation
+
+advection_velocity = 1.0
+equations = LinearScalarAdvectionEquation1D(advection_velocity)
+
+# 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)
+
+coordinates_min = -1.0 # minimum coordinate
+coordinates_max = 1.0 # maximum coordinate
+
+# Create a uniformly refined mesh with periodic boundaries
+mesh = TreeMesh(coordinates_min, coordinates_max,
+                initial_refinement_level = 4,
+                n_cells_max = 30_000) # set maximum capacity of tree data structure
+
+# A semidiscretization collects data structures and functions for the spatial discretization
+semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition_convergence_test,
+                                    solver)
+
+###############################################################################
+# ODE solvers, callbacks etc.
+
+# Create ODE problem with time span from 0.0 to 1.0
+ode = semidiscretize(semi, (0.0, 1.0));
+
+# At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup
+# and resets the timers
+summary_callback = SummaryCallback()
+
+# The AnalysisCallback allows to analyse the solution in regular intervals and prints the results
+analysis_callback = AnalysisCallback(semi, interval = 100)
+
+# The StepsizeCallback handles the re-calculation of the maximum Δt after each time step
+stepsize_callback = StepsizeCallback(cfl = 2.5)
+
+# Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver
+callbacks = CallbackSet(summary_callback, analysis_callback,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+# Define tspan to calculate maximum time step allowed for the bisection algorithm used in calculate polynomial coefficients in ODE algorithm
+tspan = (0.0, 1.0)
+
+# Construct second order PERK method with 6 stages for 
+# given simulation setup
+ode_algorithm = PERK2(6, tspan, semi)
+
+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);
+
+# Print the timer summary
+summary_callback()

src/Trixi.jl

@@ -277,6 +277,8 @@ export trixi_include, examples_dir, get_examples, default_example,
 
 export ode_norm, ode_unstable_check
 
+export PERK2
+
 export convergence_test, jacobian_fd, jacobian_ad_forward, linear_structure
 
 export DGMulti, DGMultiBasis, estimate_dt, DGMultiMesh, GaussSBP