Add two-sided Zalesak-type IDP subcell limiting

[bennibolm]

Right now, only the positivity IDP limiter for conservative variables was merged into main. This PR adds the two-sided local IDP limiting for conservative variables.
It is a Zalesak-type limiter which uses the low-order FV solution to calculate the local bounds.

Since the bound calculation requires boundary values, we introduce the routine get_boundary_outer_state. Since yet we only use this in one elixir, it is only implemented for BoundaryConditionDirichlet.

TODO:

• Add comment/warning in docstring of limiter to clarify functionality and problems of non-conforming meshes (e.g. with AMR) with subcell limiting (see here).
• Add comment in News.md

[github-actions]

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[codecov]

Codecov Report

Attention: 16 lines in your changes are missing coverage. Please review.

Comparison is base (1b75f5e) 96.23% compared to head (f7b8d0a) 86.65%.
Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1648      +/-   ##
==========================================
- Coverage   96.23%   86.65%   -9.58%     
==========================================
  Files         425      428       +3     
  Lines       34253    34482     +229     
==========================================
- Hits        32960    29878    -3082     
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Flag	Coverage Δ
unittests	86.65% <93.60%> (-9.58%)	⬇️

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

Files	Coverage Δ
.../elixir_euler_blast_wave_sc_subcell_nonperiodic.jl	100.00% <100.00%> (ø)
..._dgsem/elixir_euler_sedov_blast_wave_sc_subcell.jl	100.00% <100.00%> (ø)
...ee_2d_dgsem/elixir_euler_shockcapturing_subcell.jl	100.00% <ø> (ø)
...ulti_shock_bubble_shockcapturing_subcell_minmax.jl	100.00% <100.00%> (ø)
..._shock_bubble_shockcapturing_subcell_positivity.jl	100.00% <ø> (ø)
...tree_2d_dgsem/elixir_mhd_shockcapturing_subcell.jl	100.00% <ø> (ø)
src/solvers/dg.jl	91.87% <ø> (ø)
src/solvers/dgsem_tree/dg_2d_subcell_limiters.jl	99.57% <100.00%> (+0.01%)	⬆️
src/solvers/dgsem_tree/subcell_limiters.jl	90.20% <100.00%> (+4.90%)	⬆️
src/equations/equations.jl	96.55% <80.00%> (-1.56%)	⬇️
... and 3 more

... and 84 files with indirect coverage changes

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[bennibolm]

The runtime analysis (1 thread and with --check-bounds=no) looks good to me.
Sedov blast example (local limiting of density) with initial_refinement_level=5 and cfl=0.5:

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                513                run time:       2.20128571e+00 s
 Δt:             4.71011779e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      3.00000000e+00 (100.000%)     time/DOF/rhs!:  7.25639782e-08 s
                                               PID:            8.72189755e-08 s
 #DOFs per field:         16384                alloc'd memory:        427.290 MiB
 #elements:                1024

 Variable:       rho              rho_v1           rho_v2           rho_e         
 L2 error:       9.58103097e-01   1.87127221e-01   1.87127744e-01   6.35166241e-01
 Linf error:     3.23308655e+00   9.21537372e-01   9.21545552e-01   6.58655521e+00
 ∑∂S/∂U ⋅ Uₜ :  -1.06783168e+02
────────────────────────────────────────────────────────────────────────────────────────────────────

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 3.0  Time steps: 513 (accepted), 513 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

 ───────────────────────────────────────────────────────────────────────────────────────
               Trixi.jl                        Time                    Allocations      
                                      ───────────────────────   ────────────────────────
           Tot / % measured:               2.44s /  87.1%           40.1MiB /   8.7%    

 Section                      ncalls     time    %tot     avg     alloc    %tot      avg
 ───────────────────────────────────────────────────────────────────────────────────────
 rhs!                          1.54k    1.83s   86.1%  1.19ms   9.33KiB    0.3%    6.21B
   volume integral             1.54k    1.62s   76.2%  1.05ms     0.00B    0.0%    0.00B
   interface flux              1.54k    119ms    5.6%  77.3μs     0.00B    0.0%    0.00B
   prolong2interfaces          1.54k   32.1ms    1.5%  20.9μs     0.00B    0.0%    0.00B
   surface integral            1.54k   31.7ms    1.5%  20.6μs     0.00B    0.0%    0.00B
   reset ∂u/∂t                 1.54k   14.4ms    0.7%  9.35μs     0.00B    0.0%    0.00B
   Jacobian                    1.54k   11.0ms    0.5%  7.13μs     0.00B    0.0%    0.00B
   ~rhs!~                      1.54k   2.09ms    0.1%  1.36μs   9.33KiB    0.3%    6.21B
   prolong2boundaries          1.54k   97.4μs    0.0%  63.3ns     0.00B    0.0%    0.00B
   prolong2mortars             1.54k   81.1μs    0.0%  52.7ns     0.00B    0.0%    0.00B
   mortar flux                 1.54k   43.4μs    0.0%  28.2ns     0.00B    0.0%    0.00B
   boundary flux               1.54k   25.3μs    0.0%  16.5ns     0.00B    0.0%    0.00B
   source terms                1.54k   24.9μs    0.0%  16.2ns     0.00B    0.0%    0.00B
 a posteriori limiter          1.54k    258ms   12.2%   168μs    338KiB    9.4%     225B
   blending factors            1.54k    198ms    9.3%   129μs    337KiB    9.4%     224B
     local min/max limiting    1.54k    174ms    8.2%   113μs    337KiB    9.4%     224B
     ~blending factors~        1.54k   24.4ms    1.1%  15.8μs      752B    0.0%    0.49B
   ~a posteriori limiter~      1.54k   60.0ms    2.8%  39.0μs      752B    0.0%    0.49B
 calculate dt                    514   29.7ms    1.4%  57.8μs     0.00B    0.0%    0.00B
 I/O                               3   4.11ms    0.2%  1.37ms   3.13MiB   89.3%  1.04MiB
   save solution                   2   3.31ms    0.2%  1.65ms   3.03MiB   86.5%  1.52MiB
   ~I/O~                           3    742μs    0.0%   247μs   87.8KiB    2.4%  29.3KiB
   get element variables           2   56.1μs    0.0%  28.1μs   14.6KiB    0.4%  7.30KiB
   save mesh                       2    132ns    0.0%  66.0ns     0.00B    0.0%    0.00B
 analyze solution                  2   4.05ms    0.2%  2.03ms   36.0KiB    1.0%  18.0KiB
 ───────────────────────────────────────────────────────────────────────────────────────

The same example with IndicatorHennemannGassner (with cfl=0.5 although cfl=0.6 is also possible here -> In that case it takes ~1.57s) gives this:

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerEquations2D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                495                run time:       1.57175039e+00 s
 Δt:             6.26367957e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      3.00000000e+00 (100.000%)     time/DOF/rhs!:  6.01968891e-08 s
                                               PID:            6.45347957e-08 s
 #DOFs per field:         16384                alloc'd memory:        510.093 MiB
 #elements:                1024

 Variable:       rho              rho_v1           rho_v2           rho_e         
 L2 error:       8.43149239e-01   1.68693912e-01   1.68693912e-01   6.35026581e-01
 Linf error:     2.52459483e+00   7.10378224e-01   7.10378224e-01   6.58830417e+00
 ∑∂S/∂U ⋅ Uₜ :  -3.29792691e+00
────────────────────────────────────────────────────────────────────────────────────────────────────

────────────────────────────────────────────────────────────────────────────────────────────────────
Trixi.jl simulation finished.  Final time: 3.0  Time steps: 495 (accepted), 495 (total)
────────────────────────────────────────────────────────────────────────────────────────────────────

 ────────────────────────────────────────────────────────────────────────────────────
              Trixi.jl                      Time                    Allocations      
                                   ───────────────────────   ────────────────────────
         Tot / % measured:              1.82s /  82.4%           39.8MiB /   8.1%    

 Section                   ncalls     time    %tot     avg     alloc    %tot      avg
 ────────────────────────────────────────────────────────────────────────────────────
 rhs!                       1.49k    1.46s   97.7%   986μs   18.6KiB    0.6%    12.8B
   volume integral          1.49k    1.28s   85.1%   859μs   9.28KiB    0.3%    6.40B
     blended DG-FV          1.49k    632ms   42.2%   425μs     0.00B    0.0%    0.00B
     pure DG                1.49k    527ms   35.2%   355μs     0.00B    0.0%    0.00B
     blending factors       1.49k    109ms    7.3%  73.6μs     0.00B    0.0%    0.00B
     ~volume integral~      1.49k   7.47ms    0.5%  5.03μs   9.28KiB    0.3%    6.40B
   interface flux           1.49k    107ms    7.2%  72.2μs     0.00B    0.0%    0.00B
   surface integral         1.49k   29.6ms    2.0%  19.9μs     0.00B    0.0%    0.00B
   prolong2interfaces       1.49k   25.7ms    1.7%  17.3μs     0.00B    0.0%    0.00B
   reset ∂u/∂t              1.49k   14.3ms    1.0%  9.61μs     0.00B    0.0%    0.00B
   Jacobian                 1.49k   10.1ms    0.7%  6.78μs     0.00B    0.0%    0.00B
   ~rhs!~                   1.49k   1.67ms    0.1%  1.12μs   9.33KiB    0.3%    6.43B
   prolong2mortars          1.49k   90.0μs    0.0%  60.6ns     0.00B    0.0%    0.00B
   prolong2boundaries       1.49k   87.4μs    0.0%  58.9ns     0.00B    0.0%    0.00B
   mortar flux              1.49k   47.8μs    0.0%  32.2ns     0.00B    0.0%    0.00B
   boundary flux            1.49k   38.0μs    0.0%  25.6ns     0.00B    0.0%    0.00B
   source terms             1.49k   23.7μs    0.0%  15.9ns     0.00B    0.0%    0.00B
 calculate dt                 496   26.4ms    1.8%  53.3μs     0.00B    0.0%    0.00B
 I/O                            3   4.19ms    0.3%  1.40ms   3.13MiB   97.2%  1.04MiB
   save solution                2   3.37ms    0.2%  1.68ms   3.03MiB   94.1%  1.52MiB
   ~I/O~                        3    621μs    0.0%   207μs   87.8KiB    2.7%  29.3KiB
   get element variables        2    198μs    0.0%  99.1μs   14.6KiB    0.4%  7.30KiB
   save mesh                    2    137ns    0.0%  68.5ns     0.00B    0.0%    0.00B
 analyze solution               2   3.50ms    0.2%  1.75ms   74.3KiB    2.3%  37.1KiB
 ────────────────────────────────────────────────────────────────────────────────────

[efaulhaber]

Again, just a quick review. I didn't work through the details of the method.

[amrueda]

LGTM!
A couple of comments below.

[sloede]

Some more suggestions 😅

[sloede]

Once the last conversation is resolved, this LGTM

[sloede]

LGTM, thanks!

[sloede]

@amrueda wants to take a final look. the test failures seem unrelated to this PR, so if he's happy with it, we can merge this

[amrueda]

Almost there!
However, I just realized a problem with the bounds check routines 😅 :