Manufactured solution for Svärd-Kalisch equations with variable bathymetry

[JoshuaLampert]

I finally found a working version for a manufactured solution for the Svärd-Kalisch equations with a variable bathymetry, see also #65.

Convergence test:

p = 2:

julia> convergence_test("examples/svaerd_kalisch_1d/svaerd_kalisch_1d_manufactured.jl", 3, N = 32, accuracy_order = 2, tspan = (0.0, 0.01))
[...]
####################################################################################################
l2
η                        v                        D                        
N    error     EOC       N    error     EOC       N    error     EOC       
32   5.00e-03  -         32   2.40e-04  -         32   0.00e+00  -         
64   1.26e-03  1.99      64   5.90e-05  2.02      64   0.00e+00  NaN       
128  3.15e-04  2.00      128  1.47e-05  2.01      128  0.00e+00  NaN       

mean      2.00      mean      2.02      mean      NaN       
----------------------------------------------------------------------------------------------------
linf
η                        v                        D                        
N    error     EOC       N    error     EOC       N    error     EOC       
32   9.48e-03  -         32   4.11e-04  -         32   0.00e+00  -         
64   2.35e-03  2.01      64   1.02e-04  2.00      64   0.00e+00  NaN       
128  5.89e-04  2.00      128  2.56e-05  2.00      128  0.00e+00  NaN       

mean      2.00      mean      2.00      mean      NaN       
----------------------------------------------------------------------------------------------------

p = 4:

julia> convergence_test("examples/svaerd_kalisch_1d/svaerd_kalisch_1d_manufactured.jl", 3, N = 32, accuracy_order = 4, tspan = (0.0, 0.01))
[...]
####################################################################################################
l2
η                        v                        D                        
N    error     EOC       N    error     EOC       N    error     EOC       
32   1.50e-04  -         32   3.55e-06  -         32   0.00e+00  -         
64   9.54e-06  3.98      64   2.24e-07  3.98      64   0.00e+00  NaN       
128  5.99e-07  3.99      128  1.41e-08  3.99      128  0.00e+00  NaN       

mean      3.99      mean      3.99      mean      NaN       
----------------------------------------------------------------------------------------------------
linf
η                        v                        D                        
N    error     EOC       N    error     EOC       N    error     EOC       
32   2.64e-04  -         32   7.32e-06  -         32   0.00e+00  -         
64   1.69e-05  3.97      64   4.73e-07  3.95      64   0.00e+00  NaN       
128  1.06e-06  3.99      128  2.96e-08  4.00      128  0.00e+00  NaN       

mean      3.98      mean      3.97      mean      NaN       
----------------------------------------------------------------------------------------------------

p = 6:

julia> convergence_test("examples/svaerd_kalisch_1d/svaerd_kalisch_1d_manufactured.jl", 3, N = 32, accuracy_order = 6, tspan = (0.0, 0.01))
[...]
####################################################################################################
l2
η                        v                        D                        
N    error     EOC       N    error     EOC       N    error     EOC       
32   6.37e-06  -         32   2.18e-07  -         32   0.00e+00  -         
64   1.03e-07  5.95      64   3.54e-09  5.95      64   0.00e+00  NaN       
128  1.97e-09  5.71      128  5.58e-11  5.99      128  0.00e+00  NaN       

mean      5.83      mean      5.97      mean      NaN       
----------------------------------------------------------------------------------------------------
linf
η                        v                        D                        
N    error     EOC       N    error     EOC       N    error     EOC       
32   1.09e-05  -         32   3.78e-07  -         32   0.00e+00  -         
64   1.80e-07  5.92      64   6.10e-09  5.95      64   0.00e+00  NaN       
128  7.40e-09  4.61      128  9.65e-11  5.98      128  0.00e+00  NaN       

mean      5.26      mean      5.97      mean      NaN       
----------------------------------------------------------------------------------------------------

[JoshuaLampert]

This is breaking because I change the behavior of initial_condition_manufactured and source_terms_manufactured for the Svärd-Kalisch equations, but I think having a breaking change isn't too much of a trouble at this stage. We could also keep the old manufactured solution (for a constant bathymetry) and introduce a new for the variable bathymetry, but I don't think this is so useful.

[ranocha]

Thanks a lot! This looks good to me - nice work 👍

[ranocha]

CI failed in the last run. Do you have an idea why - do we need to increase the test tolerances?

[JoshuaLampert]

CI failed in the last run. Do you have an idea why - do we need to increase the test tolerances?

Yes, the tolerances need to be increased. I just did that in 9c94fa3. Let's hope CI passes now.

[ranocha]

Thanks a lot!

[JoshuaLampert]

I put the tolerance at the wrong place - stupid me. 🙄

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (6fb0978) 96.07% compared to head (529413a) 96.12%.
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #84      +/-   ##
==========================================
+ Coverage   96.07%   96.12%   +0.05%     
==========================================
  Files          17       17              
  Lines        1095     1110      +15     
==========================================
+ Hits         1052     1067      +15     
  Misses         43       43              

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[JoshuaLampert]

To avoid massive clutter of the terminal, I increased the interval of the AnalysisCallback for those elixirs with a very strict time step restriction.