NaN check callback

[DanielDoehring]

Having merged #1781 we have return now by default NaN if there are negative arguments to sqrt and log . Opposed to the integrators from OrdinaryDiffEq.jl which come with an unstable_check that is effectively a NaN-check using the built-in any function the custom integrators in Trixi do not check by default for NaN and thus a simulation continues although it is already corrupted.

This PR adds a NaN callback which is recommended to use when using Trixi.solve.

I am not sure if we want to use @trixi_timeit timer() as the cb should be really cheap assuming an effective divide & conquer implementation of any.

[github-actions]

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[codecov]

Codecov Report

Attention: Patch coverage is 78.57143% with 6 lines in your changes are missing coverage. Please review.

Project coverage is 89.38%. Comparing base (27d91b3) to head (a7cb1ea).
Report is 1 commits behind head on main.

Files	Patch %	Lines
src/callbacks_step/nan.jl	76.92%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1854      +/-   ##
==========================================
- Coverage   96.28%   89.38%   -6.90%     
==========================================
  Files         438      439       +1     
  Lines       35386    35401      +15     
==========================================
- Hits        34071    31643    -2428     
- Misses       1315     3758    +2443     

Flag	Coverage Δ
unittests	89.38% <78.57%> (-6.90%)	⬇️

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[ranocha]

Shall we really use another callback for this? I think it may be better to use the same approach as OrdinaryDiffEq.jl and allow more arguments to solve - in particular an unstable_check that could just be our ode_unstable_check. See

Trixi.jl/src/auxiliary/auxiliary.jl

Lines 152 to 167 in 4ee60e7

	"""
	ode_default_options()
	Return the default options for OrdinaryDiffEq's `solve`. Pass `ode_default_options()...` to `solve`
	to only return the solution at the final time and enable **MPI aware** error-based step size control,
	whenever MPI is used.
	For example, use `solve(ode, alg; ode_default_options()...)`.
	"""
	function ode_default_options()
	if mpi_isparallel()
	return (; save_everystep = false, internalnorm = ode_norm,
	unstable_check = ode_unstable_check)
	else
	return (; save_everystep = false)
	end
	end

and

Trixi.jl/src/auxiliary/mpi.jl

Lines 115 to 130 in 4ee60e7

	"""
	ode_unstable_check(dt, u, semi, t)
	Implementation of the basic check for instability used in OrdinaryDiffEq.jl.
	Instead of checking something like `any(isnan, u)`, this function just checks
	`isnan(dt)`. This helps when using MPI parallelization, since no additional
	global communication is required and all ranks will return the same result.
	You should pass this function as a keyword argument
	`unstable_check=ode_unstable_check`
	to OrdinaryDiffEq.jl's `solve` when using error-based step size control with MPI
	parallel execution of Trixi.jl.
	See the "Miscellaneous" section of the [documentation](https://docs.sciml.ai/DiffEqDocs/stable/basics/common_solver_opts/).
	"""
	ode_unstable_check(dt, u, semi, t) = isnan(dt)

[DanielDoehring]

Shall we really use another callback for this? I think it may be better to use the same approach as OrdinaryDiffEq.jl and allow more arguments to solve - in particular an unstable_check that could just be our ode_unstable_check. See

Trixi.jl/src/auxiliary/auxiliary.jl

Lines 152 to 167 in 4ee60e7

	"""
	ode_default_options()
	Return the default options for OrdinaryDiffEq's `solve`. Pass `ode_default_options()...` to `solve`
	to only return the solution at the final time and enable **MPI aware** error-based step size control,
	whenever MPI is used.
	For example, use `solve(ode, alg; ode_default_options()...)`.
	"""
	function ode_default_options()
	if mpi_isparallel()
	return (; save_everystep = false, internalnorm = ode_norm,
	unstable_check = ode_unstable_check)
	else
	return (; save_everystep = false)
	end
	end

and

Trixi.jl/src/auxiliary/mpi.jl

Lines 115 to 130 in 4ee60e7

	"""
	ode_unstable_check(dt, u, semi, t)
	Implementation of the basic check for instability used in OrdinaryDiffEq.jl.
	Instead of checking something like `any(isnan, u)`, this function just checks
	`isnan(dt)`. This helps when using MPI parallelization, since no additional
	global communication is required and all ranks will return the same result.
	You should pass this function as a keyword argument
	`unstable_check=ode_unstable_check`
	to OrdinaryDiffEq.jl's `solve` when using error-based step size control with MPI
	parallel execution of Trixi.jl.
	See the "Miscellaneous" section of the [documentation](https://docs.sciml.ai/DiffEqDocs/stable/basics/common_solver_opts/).
	"""
	ode_unstable_check(dt, u, semi, t) = isnan(dt)

I briefly looked into this, but I personally find this approach less intuitive than using a callback.
Plus, I think overall more code changes would be necessary.