HLLE CEE 2D3D NonCartesian Meshes

[DanielDoehring]

This is an intermediate step towards HLLC on noncartesian meshes and is helpful for e.g. showcasing how to do the Roe averages right.
Essentially we have this already for e.g. SWE:

Trixi.jl/src/equations/shallow_water_2d.jl

Lines 1078 to 1098 in dc0dc1d

	@inline function min_max_speed_einfeldt(u_ll, u_rr, normal_direction::AbstractVector,
	equations::ShallowWaterEquations2D)
	h_ll = waterheight(u_ll, equations)
	v1_ll, v2_ll = velocity(u_ll, equations)
	h_rr = waterheight(u_rr, equations)
	v1_rr, v2_rr = velocity(u_rr, equations)
	norm_ = norm(normal_direction)
	c_ll = sqrt(equations.gravity * h_ll) * norm_
	c_rr = sqrt(equations.gravity * h_rr) * norm_
	v_normal_ll = (v1_ll * normal_direction[1] + v2_ll * normal_direction[2])
	v_normal_rr = (v1_rr * normal_direction[1] + v2_rr * normal_direction[2])
	v_roe, c_roe = calc_wavespeed_roe(u_ll, u_rr, normal_direction, equations)
	λ_min = min(v_normal_ll - c_ll, v_roe - c_roe)
	λ_max = max(v_normal_rr + c_rr, v_roe + c_roe)
	return λ_min, λ_max
	end

Trixi.jl/src/equations/shallow_water_2d.jl

Lines 1209 to 1230 in dc0dc1d

	@inline function calc_wavespeed_roe(u_ll, u_rr, normal_direction::AbstractVector,
	equations::ShallowWaterEquations2D)
	h_ll = waterheight(u_ll, equations)
	v1_ll, v2_ll = velocity(u_ll, equations)
	h_rr = waterheight(u_rr, equations)
	v1_rr, v2_rr = velocity(u_rr, equations)
	norm_ = norm(normal_direction)
	h_roe = 0.5 * (h_ll + h_rr)
	c_roe = sqrt(equations.gravity * h_roe) * norm_
	h_ll_sqrt = sqrt(h_ll)
	h_rr_sqrt = sqrt(h_rr)
	v1_roe = (h_ll_sqrt * v1_ll + h_rr_sqrt * v1_rr) / (h_ll_sqrt + h_rr_sqrt)
	v2_roe = (h_ll_sqrt * v2_ll + h_rr_sqrt * v2_rr) / (h_ll_sqrt + h_rr_sqrt)
	v_roe = (v1_roe * normal_direction[1] + v2_roe * normal_direction[2])
	return v_roe, c_roe
	end

and I generalized from there.

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (61c33b0) 94.25% compared to head (c34dc6e) 83.59%.

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #1692       +/-   ##
===========================================
- Coverage   94.25%   83.59%   -10.66%     
===========================================
  Files         431      431               
  Lines       34690    34668       -22     
===========================================
- Hits        32694    28979     -3715     
- Misses       1996     5689     +3693     

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unittests	83.59% <100.00%> (-10.66%)	⬇️

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Files	Coverage Δ
src/Trixi.jl	43.48% <ø> (ø)
src/equations/compressible_euler_1d.jl	52.24% <100.00%> (-45.12%)	⬇️
src/equations/compressible_euler_2d.jl	97.54% <100.00%> (+0.46%)	⬆️
src/equations/compressible_euler_3d.jl	97.95% <100.00%> (+0.91%)	⬆️

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[ranocha]

Thanks for the contribution! Is this technically an HLL flux such that we basically only need to provide an min_max_speed_einfeldt similar to min_max_speed_davis?

[DanielDoehring]

Yes exactly, it is a HLL-type 2 wave solver. See #1545 and #1525 for a discussion on that.

[ranocha]

Can't we use the same approach as with the Davis estimates to just provide the wave speed estimates in a new function and let the generic FluxHLL implementation handle the construction of the fluxes based thereon?

[DanielDoehring]

Can't we use the same approach as with the Davis estimates to just provide the wave speed estimates in a new function and let the generic FluxHLL implementation handle the construction of the fluxes based thereon?

Absolutely, I think this would a good idea in terms of Code consistency, made the concept clearer and also shorten the code.

Since no elixirs use hlle this would also be no breaking change.

[ranocha]

I guess we should also use the same pattern we use for flux_hll - define a flux_hlle based on the FluxHLL with the appropriate wave speed estimates. That would be fully backwards compatible and allows re-using the wave speed estimates elsewhere.

[ranocha]

Thanks a lot! I think we are close to the last iteration.