Subcell positivity IDP limiting for conservative variables

[bennibolm]

This PR provides the very basic subcell positivity limiting feature using the IDP limiting.
Conservative variables can be limited with a one-sided Zalesak-type limiter. We pass these in positivity_variables_cons.
Only the mesh type TreeMesh2D is supported.

TODOs:

• Use number of conservative variables Implement positivty limiter with numbers for conservative variables bennibolm/Trixi.jl#113

There are more PRs to come. All implemented features can be found in the branch subcell-limiting and PR #1502.

[codecov]

Codecov Report

Merging #1476 (0fca290) into main (a4283e1) will decrease coverage by 1.53%.
The diff coverage is 93.90%.

@@            Coverage Diff             @@
##             main    #1476      +/-   ##
==========================================
- Coverage   96.17%   94.64%   -1.53%     
==========================================
  Files         406      414       +8     
  Lines       33532    33942     +410     
==========================================
- Hits        32248    32123     -125     
- Misses       1284     1819     +535     

Flag	Coverage Δ
unittests	94.64% <93.90%> (-1.53%)	⬇️

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

Files Changed	Coverage Δ
src/Trixi.jl	43.48% <ø> (ø)
src/solvers/dgsem_tree/dg.jl	94.12% <ø> (ø)
src/time_integration/time_integration.jl	100.00% <ø> (ø)
src/solvers/dgsem_tree/subcell_limiters.jl	83.87% <83.87%> (ø)
src/time_integration/methods_SSP.jl	84.62% <84.62%> (ø)
src/solvers/dg.jl	91.63% <92.31%> (+0.05%)	⬆️
...llbacks_stage/subcell_limiter_idp_correction_2d.jl	94.12% <94.12%> (ø)
src/solvers/dgsem_tree/subcell_limiters_2d.jl	94.44% <94.44%> (ø)
src/solvers/dgsem_tree/dg_2d_subcell_limiters.jl	98.85% <98.85%> (ø)
...ee_2d_dgsem/elixir_euler_shockcapturing_subcell.jl	100.00% <100.00%> (ø)
... and 3 more

... and 2 files with indirect coverage changes

[bennibolm]

In my opinion, this PR is now ready so far. I have still noted a few small things.

[sloede]

Overall this LGTM! I've looked at most of the PR and left some comments. Most of them are suggestions, but especially the consistent variable name formatting (snake_case) would be great if it were addressed.

[sloede]

In my opinion, this PR is now ready so far.

Then please mark this PR as "Ready for review" - this will let us know that a) it can and should get a reivew and b) once a reviewer is happy, this can be merged immediately

[sloede]

Do you have any allocations? E.g, can you post the output of the final timer summary?

[ranocha]

Feel free to request a review when you're ready for it

[bennibolm]

Do you have any allocations? E.g, can you post the output of the final timer summary?

It does not look like it. (This is the output of elixir_euler_shockcapturing_subcell.)

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                340                run time:       3.63036940e+00 s
 Δt:             2.26626523e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      1.00000000e+00                time/DOF/rhs!:  2.16431976e-07 s
                                               PID:            2.40560150e-07 s
 #DOF:                    16384                alloc'd memory:       1359.705 MiB
 #elements:                1024

 Variable:       rho              rho_v1           rho_v2           rho_e
 L2 error:       8.50814791e-02   4.51029902e-02   4.51030198e-02   6.93070434e-01
 Linf error:     3.11235465e-01   5.61627487e-01   5.61969271e-01   2.88670199e+00
 ∑∂S/∂U ⋅ Uₜ :  -3.04430445e-01
────────────────────────────────────────────────────────────────────────────────────────────────────

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 1.0  Time steps: 340 (accepted), 340 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

 ───────────────────────────────────────────────────────────────────────────────────────
               Trixi.jl                        Time                    Allocations
                                      ───────────────────────   ────────────────────────
           Tot / % measured:               4.00s /  91.0%           30.0MiB /  26.9%

 Section                      ncalls     time    %tot     avg     alloc    %tot      avg
 ───────────────────────────────────────────────────────────────────────────────────────
 main loop                         1    3.63s   99.7%   3.63s   6.43MiB   79.9%  6.43MiB
   Runge-Kutta stage           1.02k    3.21s   88.2%  3.15ms   10.1KiB    0.1%    10.1B
     rhs!                      1.02k    3.20s   87.9%  3.14ms   9.33KiB    0.1%    9.36B
       volume integral         1.02k    2.83s   77.8%  2.78ms     0.00B    0.0%    0.00B
       interface flux          1.02k    176ms    4.8%   172μs     0.00B    0.0%    0.00B
       prolong2interfaces      1.02k    121ms    3.3%   119μs     0.00B    0.0%    0.00B
       surface integral        1.02k   53.5ms    1.5%  52.5μs     0.00B    0.0%    0.00B
       Jacobian                1.02k   7.92ms    0.2%  7.76μs     0.00B    0.0%    0.00B
       reset ∂u/∂t             1.02k   6.90ms    0.2%  6.77μs     0.00B    0.0%    0.00B
       ~rhs!~                  1.02k   1.70ms    0.0%  1.66μs   9.33KiB    0.1%    9.36B
       prolong2boundaries      1.02k   78.8μs    0.0%  77.3ns     0.00B    0.0%    0.00B
       prolong2mortars         1.02k   75.0μs    0.0%  73.5ns     0.00B    0.0%    0.00B
       mortar flux             1.02k   70.2μs    0.0%  68.8ns     0.00B    0.0%    0.00B
       boundary flux           1.02k   32.2μs    0.0%  31.6ns     0.00B    0.0%    0.00B
       source terms            1.02k   30.8μs    0.0%  30.2ns     0.00B    0.0%    0.00B
     ~Runge-Kutta stage~       1.02k   11.0ms    0.3%  10.8μs      752B    0.0%    0.74B
   antidiffusive_stage!        1.02k    326ms    8.9%   319μs   1.47KiB    0.0%    1.47B
     alpha calculation         1.02k    188ms    5.2%   185μs      752B    0.0%    0.74B
       positivity              1.02k    141ms    3.9%   138μs     0.00B    0.0%    0.00B
       ~alpha calculation~     1.02k   47.5ms    1.3%  46.6μs      752B    0.0%    0.74B
     ~antidiffusive_stage!~    1.02k    137ms    3.8%   135μs      752B    0.0%    0.74B
   analyze solution                4   29.7ms    0.8%  7.42ms   70.3KiB    0.9%  17.6KiB
   ~main loop~                     1   28.0ms    0.8%  28.0ms    285KiB    3.5%   285KiB
   calculate dt                  340   27.1ms    0.7%  79.7μs     0.00B    0.0%    0.00B
   I/O                             4   9.23ms    0.3%  2.31ms   6.08MiB   75.4%  1.52MiB
     save solution                 4   9.19ms    0.3%  2.30ms   6.06MiB   75.2%  1.52MiB
     get element variables         4   30.8μs    0.0%  7.70μs   10.8KiB    0.1%  2.69KiB
     ~I/O~                         4   10.5μs    0.0%  2.62μs   4.20KiB    0.1%  1.05KiB
     save mesh                     4    600ns    0.0%   150ns     0.00B    0.0%    0.00B
 analyze solution                  1   6.75ms    0.2%  6.75ms   17.6KiB    0.2%  17.6KiB
 I/O                               2   3.17ms    0.1%  1.58ms   1.60MiB   19.9%   822KiB
   save solution                   1   1.81ms    0.0%  1.81ms   1.52MiB   18.8%  1.52MiB
   ~I/O~                           2   1.35ms    0.0%   676μs   88.5KiB    1.1%  44.2KiB
   get element variables           1   10.9μs    0.0%  10.9μs   2.69KiB    0.0%  2.69KiB
   save mesh                       1   0.00ns    0.0%  0.00ns     0.00B    0.0%    0.00B
 calculate dt                      1   80.8μs    0.0%  80.8μs     0.00B    0.0%    0.00B
 ───────────────────────────────────────────────────────────────────────────────────────

But this becomes more interesting later with all the analysis routines.

[ranocha]

Thanks

[bennibolm]

This PR is now ready so far.

[ranocha]

Thanks a lot! I just have a few minor comments. I guess you just need to resolve conflicts and we can merge this soon

[ranocha]

Thanks!

[ranocha]

If CI passes, this should be merged automatically. If not, we need to watch out for #1590 etc.

[sloede]

LGTM! I noticed a few things/questions but nothing that would stop a merge once the tests have passed. Great work!

[sloede]

IMHO it would be good to add a NEWS.md item for this addition (just for our own record)