WIP: Add non-conservative 2D Euler equations with gravity potential

[amrueda]

This set of equations extends the CompressibleEulerEquations2D by incorporating geopotential energy into the total energy rho_e. This ensures that the energy equation remains a conservation law, even in the presence of gravitational effects. Additionally, the source terms in the momentum equations are treated as non-conservative terms rather than point-wise source terms, following:

• Souza, A. N., He, J., Bischoff, T., Waruszewski, M., Novak, L., Barra, V., ... & Schneider, T. (2023). The flux‐differencing discontinuous galerkin method applied to an idealized fully compressible nonhydrostatic dry atmosphere. Journal of Advances in Modeling Earth Systems, 15(4), e2022MS003527. https://doi.org/10.1029/2022MS003527.
• Waruszewski, M., Kozdon, J. E., Wilcox, L. C., Gibson, T. H., & Giraldo, F. X. (2022). Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: Applications to the Euler equations with gravity. Journal of Computational Physics, 468, 111507. https://doi.org/10.1016/j.jcp.2022.111507.

We implement the non-conservative term flux_nonconservative_waruszewski, which provides well-balancedness (to machine precision accuracy) for isothermal hydrostatic equilibria:

Other standard benchmark tests are provided as well:

RisingBubble_afterBugFix_lmars.mp4

[codecov]

Codecov Report

Attention: Patch coverage is 33.54430% with 315 lines in your changes missing coverage. Please review.

Project coverage is 80.51%. Comparing base (dcc9c9a) to head (d0789a0).

Files with missing lines	Patch %	Lines
src/equations/compressible_euler_gravity_2d.jl	33.54%	315 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main      #79       +/-   ##
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- Coverage   90.68%   80.51%   -10.17%     
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  Files          22       23        +1     
  Lines        2189     2663      +474     
===========================================
+ Hits         1985     2144      +159     
- Misses        204      519      +315     

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[tristanmontoya]

@amrueda What still needs to be done for this PR to be ready?