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.

Features:

• Define explicit and implicit solvers (only flux differencing, to avoid incorrect definition of the rhs of the implicit or explicit part due to analytical flux being used in the weak form)
• 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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[codecov]

Codecov Report

❌ Patch coverage is 99.34641% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 96.86%. Comparing base (01dfdb3) to head (de1d471).

Files with missing lines	Patch %	Lines
src/semidiscretization/semidiscretization_split.jl	98.51%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2518      +/-   ##
==========================================
+ Coverage   96.85%   96.86%   +0.01%     
==========================================
  Files         546      548       +2     
  Lines       43246    43399     +153     
==========================================
+ Hits        41885    42038     +153     
  Misses       1361     1361              

Flag	Coverage Δ
unittests	96.86% <99.35%> (+0.01%)	⬆️

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[DanielDoehring]

@MarcoArtiano you can ping me for review when you feel this is ready - I have recently more or less familiarized myself with the splitfunction/splitproblem business

[MarcoArtiano]

@DanielDoehring this is ready for a review. I've changed the splitting to have something a bit more meaningful.

[MarcoArtiano]

Based on See comment, I reverted the constructor of the semidiscretization, by keeping the the two of them.

[DanielDoehring]

Based on See comment, I reverted the constructor of the semidiscretization, by keeping the the two of them.

Hm we should agree on something to have this consistent to avoid artificial confusion. For SemidiscretizationEulerGravity and SemidiscretizationEulerAcoustics we have two constructors, while SemidiscretizationHyperbolic and SemidiscretizationCoupled have only one.

I am very much in favor of having only one (the documented one) and let anyone who does not use this and is not knowing what they are doing crash.

[DanielDoehring]

see the thread