L2 Mortars for Parabolic Terms on TreeMeshes

[DanielDoehring]

Following #1147 I looked into mortars for 2D DGSEM on Tree meshes.

While I am relatively confident about the part for the viscous fluxes inserted here

Trixi.jl/src/solvers/dgsem_tree/dg_2d_parabolic.jl

Line 89 in d96514f

@assert nmortars(dg, cache) == 0

I have questions regarding the mortar actions in calc_gradient!

Trixi.jl/src/solvers/dgsem_tree/dg_2d_parabolic.jl

Line 592 in d96514f

# TODO: parabolic; mortars

(See the comments in the files)

[codecov]

Codecov Report

Merging #1571 (28ebfac) into main (ce81702) will decrease coverage by 2.77%.
Report is 1 commits behind head on main.
The diff coverage is 98.50%.

@@            Coverage Diff             @@
##             main    #1571      +/-   ##
==========================================
- Coverage   92.90%   90.13%   -2.77%     
==========================================
  Files         402      402              
  Lines       33034    33327     +293     
==========================================
- Hits        30690    30039     -651     
- Misses       2344     3288     +944     

Flag	Coverage Δ
unittests	90.13% <98.50%> (-2.77%)	⬇️

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

Files Changed	Coverage Δ
src/solvers/dgsem_tree/dg_2d_parabolic.jl	95.90% <97.98%> (+0.73%)	⬆️
src/solvers/dgsem_tree/dg_3d_parabolic.jl	92.58% <98.31%> (+2.19%)	⬆️
src/solvers/dgsem_p4est/dg_2d_parabolic.jl	96.11% <100.00%> (+0.38%)	⬆️
src/solvers/dgsem_p4est/dg_3d_parabolic.jl	97.80% <100.00%> (+0.19%)	⬆️

... and 130 files with indirect coverage changes

[DanielDoehring]

I ran a first small convergence study for the 2D Navier-Stokes Convergence Elixir
for a fixed timestep of dt = 5e-4 by passing adaptive=false to the integrator

Trixi.jl/examples/tree_2d_dgsem/elixir_navierstokes_convergence.jl

Lines 210 to 211 in a12f82d

	sol = solve(ode, RDPK3SpFSAL49(); abstol=time_int_tol, reltol=time_int_tol, dt = 1e-5,
	ode_default_options()..., callback=callbacks)

One quarter of the mesh is refined once, "Ref" denotes the initial refinement of the mesh

Trixi.jl/examples/tree_2d_dgsem/elixir_navierstokes_convergence.jl

Line 23 in a12f82d

initial_refinement_level=4,

Errors

  Ref: 3
  
  L2 error:       2.42970015e-04   2.09325060e-04   5.39057437e-04   2.67516565e-04
  Linf error:     1.62100269e-03   2.59325895e-03   2.95390894e-03   2.07741249e-03
  
  Ref: 4
  
  L2 error:       3.66499309e-06   7.97913777e-06   1.20897192e-05   4.40234164e-06
  Linf error:     2.40483342e-05   1.44484365e-04   7.92111352e-05   5.64718938e-05
  
  Ref: 5
  
  L2 error:       3.13692528e-08   7.87977372e-08   7.40638328e-08   1.25181359e-07
  Linf error:     2.10090485e-07   1.89761591e-06   6.65344699e-07   1.06838605e-06
  
  Ref: 6
  
  L2 error:       1.14216609e-09   9.45032663e-10   8.83707914e-10   5.40570956e-09
  Linf error:     7.52437157e-09   1.25224838e-08   8.08031981e-09   3.55402783e-08

There is clearly some superconvergence (Linf errors should only reduce by a factor 16), probably due to the diffusive nature of the testcase.

[sloede]

I ran a first small convergence study

Great work so far! Note that you can also use the convergence_test function to simplify convergence testing and EOC computation. It's also much easier to process the results of you post them in fixed width font (especially when looking at it on a phone screen).

[DanielDoehring]

I ran a first small convergence study

Great work so far! Note that you can also use the convergence_test function to simplify convergence testing and EOC computation. It's also much easier to process the results of you post them in fixed width font (especially when looking at it on a phone screen).

Yeah, I tried to format that, but I somehow did not manage to get this to work in the spoiler HTML environment.

[sloede]

I ran a first small convergence study

Great work so far! Note that you can also use the convergence_test function to simplify convergence testing and EOC computation. It's also much easier to process the results of you post them in fixed width font (especially when looking at it on a phone screen).

Yeah, I tried to format that, but I somehow did not manage to get this to work in the spoiler HTML environment.

I've updated your post above, I hope that's OK for you.

[DanielDoehring]

Aside the 2D Navier-Stokes Convergence Test I also conducted a small study for the 3D version, this time with fixed timestep dt=1e-3 and base refinement 2, where 1/16th of the entire mesh is refined once.

Convergence with Refinement

l2
rho                 rho_v1              rho_v2              rho_v3              rho_e
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC
3.56e-03  -         6.02e-03  -         5.08e-03  -         5.89e-03  -         1.22e-02  -
3.99e-04  3.15      8.85e-04  2.76      1.07e-03  2.25      8.79e-04  2.74      1.40e-03  3.12
2.33e-05  4.10      5.16e-05  4.10      6.01e-05  4.15      5.15e-05  4.09      9.50e-05  3.89

mean      3.63      mean      3.43      mean      3.20      mean      3.42      mean      3.50
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_v3              rho_e
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC
2.40e-02  -         1.06e-01  -         3.57e-02  -         1.06e-01  -         1.47e-01  -
3.53e-03  2.77      1.51e-02  2.82      8.86e-03  2.01      1.51e-02  2.82      3.04e-02  2.27
2.11e-04  4.07      1.17e-03  3.69      6.45e-04  3.78      1.17e-03  3.69      2.83e-03  3.43

mean      3.42      mean      3.25      mean      2.90      mean      3.25      mean      2.85
----------------------------------------------------------------------------------------------------

Convergence without Refinement

l2
rho                 rho_v1              rho_v2              rho_v3              rho_e
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC
3.71e-03  -         6.50e-03  -         5.26e-03  -         6.50e-03  -         1.31e-02  -
4.15e-04  3.16      9.51e-04  2.77      1.13e-03  2.22      9.51e-04  2.77      1.45e-03  3.17
2.43e-05  4.09      5.56e-05  4.10      6.33e-05  4.15      5.56e-05  4.10      9.83e-05  3.89

mean      3.63      mean      3.43      mean      3.19      mean      3.43      mean      3.53
----------------------------------------------------------------------------------------------------
linf
rho                 rho_v1              rho_v2              rho_v3              rho_e
error     EOC       error     EOC       error     EOC       error     EOC       error     EOC
2.08e-02  -         1.06e-01  -         2.65e-02  -         1.06e-01  -         1.49e-01  -
3.52e-03  2.56      1.51e-02  2.81      8.86e-03  1.58      1.51e-02  2.81      3.04e-02  2.29
2.11e-04  4.06      1.17e-03  3.69      6.45e-04  3.78      1.17e-03  3.69      2.83e-03  3.43

mean      3.31      mean      3.25      mean      2.68      mean      3.25      mean      2.86
----------------------------------------------------------------------------------------------------

[ranocha]

Can you go one (or two) steps further in the convergence study? The first refinement does not seem to be in the asymptotic regime

[andrewwinters5000]

Just a small suggestion to adjust the wording. Also, I have lost track on the new capability. This PR only allows for mortars on TreeMesh but no AMR capability, right? To get the AMR working we (maybe) need to do the prologation / restriction of the gradient variables as well. I am not so familiar with the AMR + TreeMesh infrastructure.

[jlchan]

Just a small suggestion to adjust the wording. Also, I have lost track on the new capability. This PR only allows for mortars on TreeMesh but no AMR capability, right? To get the AMR working we (maybe) need to do the prologation / restriction of the gradient variables as well. I am not so familiar with the AMR + TreeMesh infrastructure.

Yes - I think the reshaping of arrays upon refinement/unrefinement required some changes. I think there is another PR which deals with the technical details of reshaping some of the temporary arrays used in rhs_parabolic!.

[DanielDoehring]

This PR only allows for mortars on TreeMesh but no AMR capability, right? To get the AMR working we (maybe) need to do the prologation / restriction of the gradient variables as well. I am not so familiar with the AMR + TreeMesh infrastructure.

Yes, for AMR more changes are required that I plan to submit once this is merged.

[andrewwinters5000]

LGTM!

[jlchan]

@DanielDoehring I believe you added CI tests - does this mean @ranocha's requested changes are addressed? That's blocking merging at the moment.

[DanielDoehring]

@DanielDoehring I believe you added CI tests - does this mean @ranocha's requested changes are addressed? That's blocking merging at the moment.

Yes, I added some tests with manually refined meshes.

[ranocha]

Thanks a lot!

Yes - I also double checked that there are no allocations due to the mortars.

Could you please add some CI checks for allocations like we do in

Trixi.jl/test/test_tree_2d_advection.jl

Lines 34 to 48 in 6c97c48

	@trixi_testset "elixir_advection_mortar.jl" begin
	@test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_advection_mortar.jl"),
	# Expected errors are exactly the same as in the parallel test!
	l2 = [0.0015188466707237375],
	linf = [0.008446655719187679])
	# Ensure that we do not have excessive memory allocations
	# (e.g., from type instabilities)
	let
	t = sol.t[end]
	u_ode = sol.u[end]
	du_ode = similar(u_ode)
	@test (@allocated Trixi.rhs!(du_ode, u_ode, semi, t)) < 1000
	end
	end

[DanielDoehring]

Could you please add some CI checks for allocations

Done in 1caa657 (except for the Navier-Stokes convergence tests, which are still allocating until #1594 is merged)

[ranocha]

Thanks