Validation tests of numerical convergence

[glwagner]

This PR adds verification tests for numerical convergence of time-stepping and spatial discretization.

One test does not pass (the most complicated one): forced, fixed slip simulation. More detailed analysis of this test is needed.

Below is a summary of the results.

Time stepping convergence tests

Advection and diffusion of a one-dimensional cosine

Advection and diffusion of a one-dimensional Gaussian

Two-dimensional diffusion

Two-dimensional Taylor-Green vortex

Two-dimensional forced flow with free-slip boundary conditions

Two-dimensional forced flow with fixed-slip boundary conditions

This test does not pass

We don't know if there is a bug in the test or a problem in Oceananigans.

[codecov]

Codecov Report

Merging #767 into master will increase coverage by 3.93%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master     #767      +/-   ##
==========================================
+ Coverage   70.97%   74.91%   +3.93%     
==========================================
  Files         124      124              
  Lines        2491     2603     +112     
==========================================
+ Hits         1768     1950     +182     
+ Misses        723      653      -70     

Impacted Files	Coverage Δ
src/Forcing/simple_forcing.jl	81.81% <0.00%> (-18.19%)	⬇️
src/Models/incompressible_model.jl	88.88% <0.00%> (-11.12%)	⬇️
src/TimeSteppers/TimeSteppers.jl	66.66% <0.00%> (-8.34%)	⬇️
src/Utils/launch_config.jl	95.23% <0.00%> (-4.77%)	⬇️
...ntations/rozema_anisotropic_minimum_dissipation.jl	30.00% <0.00%> (-4.10%)	⬇️
src/Solvers/batched_tridiagonal_solver.jl	96.42% <0.00%> (-3.58%)	⬇️
src/Solvers/solve_for_pressure.jl	100.00% <0.00%> (ø)
src/OutputWriters/OutputWriters.jl	100.00% <0.00%> (ø)
src/OutputWriters/netcdf_output_writer.jl	84.90% <0.00%> (+0.29%)	⬆️
src/TurbulenceClosures/TurbulenceClosures.jl	37.93% <0.00%> (+1.08%)	⬆️
... and 14 more

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[ali-ramadhan]

This is awesome. Definitely a warm fuzzies™ PR! cc @sandreza

Resolves #611

[glwagner]

I have run the forced fixed slip test with multiple time-steps. The error does not decrease as the time-step decreases:

The results for different time-steps lie on top of one another.

[glwagner]

At last, I found an algebra mistake in my definition of the forced fixed-slip problem. The forced fixed-slip convergence validation test now passes! This means that the Oceananigans pressure solver produces correct results when the pressure gradient is non-zero on the boundary.

@ali-ramadhan I think we should run these in CI eventually. Should we do that in this PR or save for a future PR?

[christophernhill]

Greg - thats great news. grad(p).n triumphs (again!).

…

On Thu, Jun 18, 2020 at 6:40 AM Gregory L. Wagner ***@***.***> wrote: At last, I found an algebra mistake in my definition of the problem. The forced fixed slip now passes! [image: image] <https://user-images.githubusercontent.com/15271942/85010687-6d626b80-b12e-11ea-9169-6dc0bfc11d59.png> @ali-ramadhan <https://github.com/ali-ramadhan> I think we should run these in CI eventually. Should we do that in this PR or save for a future PR? — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#767 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AA27DYEIZ7ZASCPCFPE3DF3RXHVH7ANCNFSM4NOKYQIQ> .

[ali-ramadhan]

That's awesome! No one can make fun of us for not having convergence tests anymore!

@glwagner I might save it for a future PR just to get these scripts merged ASAP but we should do include them as tests before any numerical changes happen.

Would also be good to document all these tests in the "Verification experiments" section of the docs.

[sandreza]

@glwagner That's really awesome Greg!

[glwagner]

Ok, I will merge this PR and open an issue to write up these tests in the docs, and also to execute the run scripts in tests to ensure they remain runnable as the code is changed.

We could also add one or more of the tests as a regression test. We can discuss in the issue.