Resolve CFL magic

[ranocha]

I've marked the cfl-magic examples as resolved. For most of them, I just switched to the more robust CFL number. The Euler+gravity examples are also sensitive to the choice of resid_tol, but I didn't change that.

[sloede]

LGTM, thanks!

There is one more thing I was hoping you could check: In an earlier commit, 168bd5d, the CFL number for elixir_euler_sedov_blast_wave_shockcapturing_amr.jl (and the corresponding Taam setup) were already reduced. However, I am not sure if the same "metric" you used to determine a proper new CFL number was employed. Could you thus maybe have a look at this case and see if it matches the modified CFL that you also used in similar cases?

[ranocha]

I've checked examples/2d/parameters_euler_sedov_blast_wave_shockcapturing_amr.toml using the same code as yesterday:

julia> function verify_taam(toml_file; amplitude, t_end=nothing, kwargs...)
         taam = Trixi.run(toml_file; t_end=t_end, kwargs...)
         
         Trixi.init_parameters(toml_file; t_end=t_end, kwargs...)
         mesh, solver, time_parameters, time_integration_function = Trixi.init_simulation()
         solver.elements.u .+= 2*amplitude .* (rand(Float64, size(solver.elements.u)) .- 0.5)
         taam_noise = Trixi.run_simulation(mesh, solver, time_parameters, time_integration_function)
         
         diff_l2 = taam.l2 - taam_noise.l2
         diff_linf = taam.linf - taam_noise.linf
         
         
         # Show results
         println("="^80)
         println("L2 (Taam - noise):")
         display(diff_l2)
         println("="^80)
         println("Linf (Taam - noise):")
         display(diff_linf)
         println("="^80)
       end

julia> verify_taam("examples/2d/parameters_euler_sedov_blast_wave_shockcapturing_amr.toml", amplitude=1.0e-15, t_end=12.5, cfl=0.4)
[...]
================================================================================
L2 (Taam - noise):
4-element StaticArrays.SArray{Tuple{4},Float64,1,4} with indices SOneTo(4):
 1.9273471707492718e-13
 1.1102230246251565e-15
 1.3322676295501878e-15
 1.1102230246251565e-16
================================================================================
Linf (Taam - noise):
4-element StaticArrays.SArray{Tuple{4},Float64,1,4} with indices SOneTo(4):
  1.8349766151004587e-12
 -1.6298074001497298e-13
 -1.624256285026604e-13
  8.881784197001252e-15
================================================================================

julia> verify_taam("examples/2d/parameters_euler_sedov_blast_wave_shockcapturing_amr.toml", amplitude=1.0e-15, t_end=12.5, cfl=0.5)
[...]
================================================================================
L2 (Taam - noise):
4-element StaticArrays.SArray{Tuple{4},Float64,1,4} with indices SOneTo(4):
  2.8209323765793215e-10
 -1.1736125959949106e-11
 -1.4230255862557328e-11
  2.9320990080350384e-12
================================================================================
Linf (Taam - noise):
4-element StaticArrays.SArray{Tuple{4},Float64,1,4} with indices SOneTo(4):
 -4.86261697574264e-10
 -1.177855146750062e-9
 -1.5639797235067476e-9
  4.525535501898048e-11
================================================================================

Hence, our metric from yesterday states that the current value cfl=0.4 is okay there.

[sloede]

Sounds OK. A difference of 1e-13 in the L2 norm for density feels a bit high to me. However, I also checked the difference to Taam and with t_end=2 and >400 steps the solutions are within 1e-16, so let's leave it as it is.

[sloede]

Thanks for checking, though, @ranocha!

[ranocha]

For t_end = 12.5, we're running for more than 1000 time steps. Yesterday, our rough metric was "number of time steps times machine precision is an acceptable deviation".