PERK p2

.github/workflows/Downgrade.yml

@@ -72,7 +72,7 @@ jobs:
       - uses: julia-actions/cache@v1
       - uses: julia-actions/julia-downgrade-compat@v1
         with:
-          skip: LinearAlgebra,Printf,SparseArrays,UUIDs,DiffEqBase
+          skip: LinearAlgebra,Printf,SparseArrays,UUIDs,DiffEqBase,DelimitedFiles
           projects: ., test
       - uses: julia-actions/julia-buildpkg@v1
         env:

Project.toml

@@ -6,10 +6,13 @@ version = "0.7.5-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"
@@ -57,10 +60,13 @@ TrixiMakieExt = "Makie"
 [compat]
 CodeTracking = "1.0.5"
 ConstructionBase = "1.3"
+Convex = "0.15.4"
 DataStructures = "0.18.15"
+DelimitedFiles = "1"
 DiffEqBase = "6 - 6.143"
 DiffEqCallbacks = "2.25"
 Downloads = "1.6"
+ECOS = "1.1.2"
 EllipsisNotation = "1.0"
 FillArrays = "0.13.2, 1"
 ForwardDiff = "0.10.24"

examples/tree_1d_dgsem/elixir_advection_PERK2.jl

@@ -0,0 +1,64 @@
+
+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
+tspan = (0.0, 1.0)
+ode = semidiscretize(semi, tspan);
+
+# 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)
+
+alive_callback = AliveCallback(alive_interval = 1)
+
+# Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver
+callbacks = CallbackSet(summary_callback,
+                        alive_callback,
+                        analysis_callback,
+                        stepsize_callback)
+
+###############################################################################
+# run the simulation
+
+# Construct second order PERK method with 6 stages for given simulation setup.
+# Pass `tspan` to calculate maximum time step allowed for the bisection algorithm used 
+# in calculating the polynomial coefficients in the ODE algorithm.
+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

@@ -276,6 +276,8 @@ 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