User defined RHS Splitting for IMEX

[MarcoArtiano]

The following PR implements a way for the user to define a splitting for the RHS by calling SemidiscretizationHyperbolicSplit and defining two solver (implicit and explicit). The semidiscretize object returns a SplitODEProblem, which can be solved via an IMEX method.

See: https://docs.sciml.ai/OrdinaryDiffEq/stable/imex/IMEXBDF/, for a list of some semi-implicit solvers.

See: IMEX example for a test case example. (The example is actually not ideal, see the point below)

• Add a better rhs splitting example
• Check compatibility with AMR

Features:

• Define explicit and implicit solvers ( mixed weak and flux differencing form solvers are supported)
• Define boundary conditions for the implicit and explicit part
• Define source terms for the implicit and explicit part
• The splitting has to be defined as $$y_t = f_1(y) + f_2(y)$$

[github-actions]

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Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

❌ Patch coverage is 0% with 191 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (main@531ee91). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
src/semidiscretization/semidiscretization_split.jl	0.00%	93 Missing ⚠️
src/callbacks_step/amr.jl	0.00%	38 Missing ⚠️
...es/p4est_2d_dgsem/elixir_euler_imex_warm_bubble.jl	0.00%	37 Missing ⚠️
...est_3d_dgsem/elixir_mhd_imex_shockcapturing_amr.jl	0.00%	23 Missing ⚠️

Additional details and impacted files

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