EC mortars: Tree 2D

[DanielDoehring]

I tried to port #247 to Trixi's current state. Does currently not work - not sure if I did a mistake or if the original draft was flawed.

@amrueda

[github-actions]

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[codecov]

Codecov Report

Attention: Patch coverage is 97.29730% with 4 lines in your changes missing coverage. Please review.

Project coverage is 96.91%. Comparing base (dc8cd7e) to head (d3085f0).

Files with missing lines	Patch %	Lines
src/solvers/dgsem/basis_lobatto_legendre.jl	83.33%	3 Missing ⚠️
src/solvers/dgsem_tree/dg_2d.jl	98.97%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2302      +/-   ##
==========================================
- Coverage   96.91%   96.91%   -0.00%     
==========================================
  Files         496      497       +1     
  Lines       41140    41267     +127     
==========================================
+ Hits        39870    39993     +123     
- Misses       1270     1274       +4     

Flag	Coverage Δ
unittests	96.91% <97.30%> (-<0.01%)	⬇️

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[sloede]

Does currently not work - not sure if I did a mistake or if the original draft was flawed.

What exactly does not work? IIRC (though that's from >4 years ago), the final version of the original PR was fully functional for at least one test setup and did show proper convergence behavior as well as EC properties.

[DanielDoehring]

What exactly does not work? IIRC (though that's from >4 years ago), the final version of the original PR was fully functional for at least one test setup and did show proper convergence behavior as well as EC properties.

Not sure, the current version seems to be correct - (although there are some allocations that need to be removed). My first try did not work, this is why I have not touched this for a long time. I believe #2134 resolved this.

[DanielDoehring]

This is the only true difference to the L2 mortar.

[DanielDoehring]

Maybe this can be made more efficient using multiply_dimensionwise!?

[DanielDoehring]

Convergence test:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       
6.13e-04  -         2.49e-02  -         2.64e-02  -         5.80e-02  -         
8.40e-05  2.87      3.43e-03  2.86      3.74e-03  2.82      8.20e-03  2.82      
2.98e-06  4.82      1.58e-04  4.44      1.52e-04  4.62      3.19e-04  4.68      
7.15e-08  5.38      4.71e-06  5.06      3.94e-06  5.27      7.94e-06  5.33      

mean      4.35      mean      4.12      mean      4.24      mean      4.28      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       
1.15e-02  -         3.02e-01  -         2.88e-01  -         1.04e+00  -         
1.68e-03  2.77      4.73e-02  2.67      5.28e-02  2.45      1.69e-01  2.63      
7.23e-05  4.54      2.67e-03  4.15      2.42e-03  4.45      7.14e-03  4.57      
2.35e-06  4.95      1.28e-04  4.38      1.21e-04  4.32      2.61e-04  4.78      

mean      4.08      mean      3.73      mean      3.74      mean      3.99      
----------------------------------------------------------------------------------------------------

I suspect that the superconvergence is due to the refinement patch.

For the standard L2 mortar:

####################################################################################################
l2
rho                 rho_v1              rho_v2              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       
6.11e-04  -         2.48e-02  -         2.61e-02  -         5.78e-02  -         
8.47e-05  2.85      3.49e-03  2.83      3.75e-03  2.80      8.30e-03  2.80      
2.86e-06  4.89      1.52e-04  4.52      1.46e-04  4.68      3.03e-04  4.78      
5.60e-08  5.68      3.57e-06  5.41      3.19e-06  5.52      6.13e-06  5.63      

mean      4.47      mean      4.25      mean      4.33      mean      4.40      
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_e               
error     EOC       error     EOC       error     EOC       error     EOC       
1.14e-02  -         3.02e-01  -         2.85e-01  -         1.04e+00  -         
1.70e-03  2.75      4.86e-02  2.64      5.22e-02  2.45      1.70e-01  2.61      
7.21e-05  4.56      2.67e-03  4.19      2.33e-03  4.48      6.95e-03  4.62      
1.89e-06  5.25      7.37e-05  5.18      6.75e-05  5.11      1.62e-04  5.42      

mean      4.19      mean      4.00      mean      4.01      mean      4.22      
----------------------------------------------------------------------------------------------------

To test the entropy-conservation property I probably need to run this with an EC integrator.

[ranocha]

Thanks! This is just a quick first review. I leave reviewing the details of the algorithm to the others.

[jlchan]

Thanks for adding this! This is a very initial pass through; I'll take a closer look (in particular at the 3d and p4est parts) afterwards.

A broader question - why are the parabolic routines modified? the mortars should only impact the hyperbolic interface flux computations?

[sloede]

To test the entropy-conservation property I probably need to run this with an EC integrator.

Yes, but an arguably easier test would be to have a refined mesh and use it with an entropy-generating setup, and to then verify that a call to rhs! will produce an EC update.

For example, the weak blast wave is usually such a test, since it does want to produce entropy. Another option for an initial condition is to just randomly initialize the conservative variables (in a physically valid state of course) such that you get small jumps - that would ordinarily produce entropy - everywhere.

[DanielDoehring]

A broader question - why are the parabolic routines modified? the mortars should only impact the hyperbolic interface flux computations?

Yeah that looks a bit odd. The reason is that the p4est mesh reuses the rhs! from the TreeMesh, which now passes also the u vector as an argument. As the parabolic p4est implementation re-uses some functions of the hyperbolic p4est implementation we have now the observed changes.

[DanielDoehring]

So something is not quite working yet. I do not yet get entropy conservation, but more importantly, conservation of cons. variables is violated.

[DanielDoehring]

The current implementation of the mortars has primary and secondary fluxes, while the implementation had only one (probably primary) . Maybe the bug is somewhere there.