Sc/polytropic

[SimonCan]

Polytropic compressible Euler equations in 2d. Can be used to simulate compressible isothermal Euler equations. No viscosity is involved here.

TODO:

• Write tests.
• Add examples.

Convergence tests using examples/structured_2d_dgsem/elixir_eulerpolytropic_convergence.jl:

####################################################################################################
l2
rho                 rho_v1              rho_v2
error     EOC       error     EOC       error     EOC
1.67e-03  -         2.59e-03  -         3.28e-03  -
1.32e-04  3.66      1.34e-04  4.27      2.06e-04  3.99
1.02e-05  3.70      8.57e-06  3.97      1.24e-05  4.06
6.56e-07  3.96      5.26e-07  4.03      7.26e-07  4.09
3.58e-08  4.20      3.09e-08  4.09      4.52e-08  4.01

mean      3.88      mean      4.09      mean      4.04
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2
error     EOC       error     EOC       error     EOC
1.10e-02  -         1.33e-02  -         2.01e-02  -
1.13e-03  3.28      9.13e-04  3.87      1.90e-03  3.40
1.09e-04  3.38      8.65e-05  3.40      1.27e-04  3.90
7.76e-06  3.82      5.84e-06  3.89      7.93e-06  4.00
4.50e-07  4.11      3.45e-07  4.08      4.92e-07  4.01

mean      3.64      mean      3.81      mean      3.83
----------------------------------------------------------------------------------------------------
Dict{Symbol, Any} with 3 entries:
  :variables => ("rho", "rho_v1", "rho_v2")
  :l2        => [3.87748, 4.08884, 4.03706]
  :linf      => [3.64439, 3.80898, 3.82941]

Entropy conservation test using examples/structured_2d_dgsem/elixir_eulerpolytropic_ec_shockcapturing.jl:

∂S/∂U ⋅ Uₜ :   2.02384406e-17

[codecov]

Codecov Report

All modified lines are covered by tests ✅

Comparison is base (dfdaef5) 87.95% compared to head (462bf61) 96.09%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1526      +/-   ##
==========================================
+ Coverage   87.95%   96.09%   +8.14%     
==========================================
  Files         419      423       +4     
  Lines       34159    34335     +176     
==========================================
+ Hits        30043    32992    +2949     
+ Misses       4116     1343    -2773     

Flag	Coverage Δ
unittests	96.09% <100.00%> (+8.14%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files	Coverage Δ
...s/structured_2d_dgsem/elixir_eulerpolytropic_ec.jl	100.00% <100.00%> (ø)
...2d_dgsem/elixir_eulerpolytropic_isothermal_wave.jl	100.00% <100.00%> (ø)
...structured_2d_dgsem/elixir_eulerpolytropic_wave.jl	100.00% <100.00%> (ø)
src/Trixi.jl	43.48% <ø> (-9.15%)	⬇️
src/auxiliary/math.jl	100.00% <100.00%> (ø)
src/equations/equations.jl	98.04% <ø> (ø)
src/equations/polytropic_euler_2d.jl	100.00% <100.00%> (ø)

... and 57 files with indirect coverage changes

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[sloede]

overall this looks already very good to me. I have a left only a few minor comments. once resolved, could you please also apply the formatter?

[sloede]

Review part 1/2. Second part will follow

[sloede]

Second part of the review 🙂

[andrewwinters5000]

Just a comment on the naming convention used for the new system. I think it is misleading to call this new system PolytropicEuler.

From what I can tell the goal here is to implement the isothermal Euler equations where gamma = 1 and p(rho) = kappa * rho, then we use it in some kind of coupled simulation. Along the way, assuming isothermal Euler, the internal energy is e(rho) = kappa * log(rho) and the flux from Hendrik should work directly for EC/ES by removing the total energy equation contributions.

Generalizing to polytropic Euler, we take gamma > 1 and p(rho) = kappa * rho^gamma so this part is still valid in the isothermal limit because the correct pressure equation is recovered. However, the internal energy for the polytropic Euler changes to be e(rho) = kappa * rho^(gamma-1)/(gamma-1), which necessitates a new form of the EC flux.

[SimonCan]

All tests pass now. We might be ready for merging.

[sloede]

Very last comment (sorry, this was an oversight by me earlier 🙈), then ready to merge!

[sloede]

LGTM!

[andrewwinters5000]

LGTM! I just left one small suggestion on a comment in one of the new elixirs.