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Covariant solver in DGMulti#140

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tristanmontoya merged 15 commits intotrixi-framework:mainfrom
PhilBaa:covariant-dgmulti-solver
Mar 16, 2026
Merged

Covariant solver in DGMulti#140
tristanmontoya merged 15 commits intotrixi-framework:mainfrom
PhilBaa:covariant-dgmulti-solver

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@PhilBaa
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@PhilBaa PhilBaa commented Jan 26, 2026

This PR adds a covariant solver for the spherical advection and shallow water equations in DGMulti and elixirs for both of them on an icosahedral grid.

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PhilBaa commented Jan 26, 2026

Right now the EoC is capped at 2. For example with polydeg = 3 I get

l2
h                   vcon1               vcon2               
error     EOC       error     EOC       error     EOC       
1.61e+02  -         8.03e-11  -         6.43e-11  -         
4.68e+01  1.79      8.19e-12  3.29      7.39e-12  3.12      
1.17e+01  1.99      9.05e-13  3.18      8.77e-13  3.08      
2.93e+00  2.00      1.09e-13  3.06      1.08e-13  3.02      

mean      1.93      mean      3.18      mean      3.07      
----------------------------------------------------------------------------------------------------
linf
h                   vcon1               vcon2               
error     EOC       error     EOC       error     EOC       
8.23e+02  -         2.36e-10  -         2.13e-10  -         
2.51e+02  1.72      3.25e-11  2.86      2.91e-11  2.87      
6.37e+01  1.98      4.13e-12  2.97      3.98e-12  2.87      
1.59e+01  2.00      5.19e-13  2.99      5.14e-13  2.95      

mean      1.90      mean      2.94      mean      2.90      
----------------------------------------------------------------------------------------------------

and polydeg = 4 yields

l2
h                   vcon1               vcon2               
error     EOC       error     EOC       error     EOC       
1.64e+02  -         2.55e-11  -         2.69e-11  -         
4.79e+01  1.78      8.12e-13  4.98      8.56e-13  4.97      
1.20e+01  1.99      2.59e-14  4.97      2.65e-14  5.01      
3.01e+00  2.00      8.15e-16  4.99      8.23e-16  5.01      

mean      1.92      mean      4.98      mean      5.00      
----------------------------------------------------------------------------------------------------
linf
h                   vcon1               vcon2               
error     EOC       error     EOC       error     EOC       
8.53e+02  -         9.19e-11  -         9.19e-11  -         
2.56e+02  1.74      3.03e-12  4.92      3.25e-12  4.82      
6.53e+01  1.97      1.05e-13  4.85      1.04e-13  4.96      
1.64e+01  2.00      3.30e-15  4.99      3.32e-15  4.98      

mean      1.90      mean      4.92      mean      4.92      
----------------------------------------------------------------------------------------------------

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PhilBaa commented Mar 9, 2026

polydeg = 3 and upwinding now yields:

####################################################################################################
l2
h                   vcon1               vcon2               
error     EOC       error     EOC       error     EOC       
1.04e-01  -         8.01e-12  -         7.40e-12  -         
6.33e-03  4.04      8.99e-13  3.16      8.74e-13  3.08      
3.76e-04  4.07      1.09e-13  3.05      1.08e-13  3.02      
2.35e-05  4.00      1.34e-14  3.01      1.34e-14  3.00      

mean      4.04      mean      3.07      mean      3.04      
----------------------------------------------------------------------------------------------------
linf
h                   vcon1               vcon2               
error     EOC       error     EOC       error     EOC       
1.18e+00  -         3.19e-11  -         2.94e-11  -         
1.18e-01  3.32      4.11e-12  2.96      3.96e-12  2.89      
9.92e-03  3.58      5.18e-13  2.99      5.13e-13  2.95      
6.76e-04  3.88      6.50e-14  2.99      6.47e-14  2.99      

mean      3.59      mean      2.98      mean      2.94      
----------------------------------------------------------------------------------------------------
Dict{Symbol, Any} with 3 entries:
  :variables => ("h", "vcon1", "vcon2")
  :l2        => [4.03828, 3.07332, 3.03639]
  :linf      => [3.59165, 2.98015, 2.94321]

@PhilBaa PhilBaa marked this pull request as ready for review March 9, 2026 16:03
@tristanmontoya tristanmontoya merged commit c621a12 into trixi-framework:main Mar 16, 2026
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2 participants