Time integration methods

Trixi.jl is compatible with the SciML ecosystem for ordinary differential equations. In particular, explicit Runge-Kutta methods from OrdinaryDiffEq.jl are tested extensively. Interesting classes of time integration schemes are

• Explicit low-storage Runge-Kutta methods
• Strong stability preserving methods

Some common options for solve from OrdinaryDiffEq.jl are the following. Further documentation can be found in the SciML docs.

• If you use a fixed time step method like CarpenterKennedy2N54, you need to pass a time step as dt=.... If you use a StepsizeCallback, the value passed as dt=... is irrelevant since it will be overwritten by the StepsizeCallback. If you want to use an adaptive time step method such as SSPRK43 or RDPK3SpFSAL49 and still want to use CFL-based step size control via the StepsizeCallback, you need to pass the keyword argument adaptive=false to solve.
• You should usually set save_everystep=false. Otherwise, OrdinaryDiffEq.jl will (try to) save the numerical solution after every time step in RAM (until you run out of memory or start to swap).
• You can set the maximal number of time steps via maxiters=....
• SSP methods and many low-storage methods from OrdinaryDiffEq.jl support stage_limiter!s and step_limiter!s, e.g., PositivityPreservingLimiterZhangShu from Trixi.jl.
• If you start Julia with multiple threads and want to use them also in the time integration method from OrdinaryDiffEq.jl, you need to pass the keyword argument thread=OrdinaryDiffEq.True() to the algorithm, e.g., RDPK3SpFSAL49(thread=OrdinaryDiffEq.True()) or CarpenterKennedy2N54(thread=OrdinaryDiffEq.True(), williamson_condition=false). For more information on using thread-based parallelism in Trixi.jl, please refer to Shared-memory parallelization with threads.
• If you use error-based step size control (see also the section on error-based adaptive step sizes together with MPI, you need to pass internalnorm=ode_norm and you should pass unstable_check=ode_unstable_check to OrdinaryDiffEq's solve, which are both included in ode_default_options.