Implement max_abs_speed for real maximum speed

[DanielDoehring]

The current implementation of the LLF flux uses max_abs_speed_naive

Trixi.jl/src/equations/numerical_fluxes.jl

Lines 209 to 222 in e93de2a

	function FluxLaxFriedrichs(max_abs_speed = max_abs_speed_naive)
	FluxPlusDissipation(flux_central, DissipationLocalLaxFriedrichs(max_abs_speed))
	end
	function Base.show(io::IO, f::FluxLaxFriedrichs)
	print(io, "FluxLaxFriedrichs(", f.dissipation.max_abs_speed, ")")
	end
	"""
	flux_lax_friedrichs
	See [`FluxLaxFriedrichs`](@ref).
	"""
	const flux_lax_friedrichs = FluxLaxFriedrichs()

which is somewhat too conservative/over-diffusive:

Trixi.jl/src/equations/compressible_euler_2d.jl

Line 1413 in e93de2a

λ_max = max(abs(v_ll), abs(v_rr)) + max(c_ll, c_rr)

In particular, this is actually different compared to the values used in the StepsizeCallback:

Trixi.jl/src/callbacks_step/stepsize_dg2d.jl

Line 18 in e93de2a

lambda1, lambda2 = max_abs_speeds(u_node, equations)

which uses the actual (sharp) true eigenvalues of the flux Jacobian:

Trixi.jl/src/equations/compressible_euler_2d.jl

Lines 1863 to 1868 in e93de2a

	@inline function max_abs_speeds(u, equations::CompressibleEulerEquations2D)
	rho, v1, v2, p = cons2prim(u, equations)
	c = sqrt(equations.gamma * p / rho)
	return abs(v1) + c, abs(v2) + c
	end

This PR adds the sharper functions + tests.

Whether we want to change the default used wave speed estimate remains for discussion for a separate PR.

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.44%. Comparing base (fafa540) to head (db0569d).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2233      +/-   ##
==========================================
+ Coverage   96.42%   96.44%   +0.03%     
==========================================
  Files         487      487              
  Lines       39352    39636     +284     
==========================================
+ Hits        37942    38226     +284     
  Misses       1410     1410              

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[ranocha]

Thanks a lot! I think this is a good idea and we should likely update the default estimate as well. The only concern I have is as follows: In general, this is not a perfect estimate of the fastest wave speed in the solution of a Riemann problem but more a David-type estimate. Shall we rename it accordingly to max_abd_speed_davis?

[DanielDoehring]

In general, this is not a perfect estimate of the fastest wave speed in the solution of a Riemann problem but more a David-type estimate. Shall we rename it accordingly to max_abd_speed_davis?

Hm true. The thing is, though, that this then somewhat indicates a different notion compared to max_abs_speeds which we use for the CFl condition, which might seem confusing.
I guess things boil down to some extent what we mean with "speed".

[ranocha]

That's true. For max_abs_speeds, we just have single-point information. In this case, we have two points.