TVD slope limiters

[akshaysridhar]

Update flux correction stencils
Update column and deformation flow examples to use TVD limiters.

• Code follows the style guidelines OR N/A.
• Unit tests are included OR N/A.
• Code is exercised in an integration test OR N/A.
• Documentation has been added/updated OR N/A.

[charleskawczynski]

A lot of these limiters don't seem to prevent negative values:

Is this behavior expected? Should we add more granular unit tests?

The RZeroLimiter seems to work well at removing negative values:

[akshaysridhar]

@charleskawczynski These are from a class of slope limiting fluxes which combine low-order (monotone) and high-order (not necessarily monotone) fluxes : the RZero here then corresponds to the low order (first order upwind, likely too dissipative to be useful in our simulations) option, and the RMax returns the third order upwind method (which is the current choice of the high-order flux in this method. RHalf equally weights the low / high order methods). (Zalesak, similarly, is a combination of such low / high order fluxes , with flux corrections through an "anti-diffusive" term). This PR introduces the alternative to flux-corrected transport through total-variation diminishing limiters.

[charleskawczynski]

@charleskawczynski These are from a class of slope limiting fluxes which combine low-order (monotone) and high-order (not necessarily monotone) fluxes : the RZero here then corresponds to the low order (first order upwind, likely too dissipative to be useful in our simulations) option, and the RMax returns the third order upwind method (which is the current choice of the high-order flux in this method. RHalf equally weights the low / high order methods). (Zalesak, similarly, is a combination of such low / high order fluxes , with flux corrections through an "anti-diffusive" term). This PR introduces the alternative to flux-corrected transport through total-variation diminishing limiters.

Ok, could we maybe also plot what the solution looks like without a limiter? That way we can see how each one improves over the baseline.

[charleskawczynski]

Ok, could we maybe also plot what the solution looks like without a limiter? That way we can see how each one improves over the baseline.

Actually, maybe that is unstable? Perhaps this is fine? I just want to make sure that this is working, and I'd like to have some sort of test to confirm it. The plots look suspiciously ineffective.

[szy21]

I'm not the best person to review this. @charleskawczynski @dennisYatunin Could any of you take a look at this PR ASAP? We hope to merge this before the end of tomorrow, thanks!

[charleskawczynski]

Hi @akshaysridhar, just a heads up: I'm going to rebase and push some changes

[akshaysridhar]

Hi @akshaysridhar, just a heads up: I'm going to rebase and push some changes

Noted; I've added some commits addressing the unit test comments (I'll wait for the rebase update to push). Thanks @charleskawczynski

[akshaysridhar]

Hi @akshaysridhar, just a heads up: I'm going to rebase and push some changes

Noted; I've added some commits addressing the unit test comments (I'll wait for the rebase update to push). Thanks @charleskawczynski

I've pushed these changes @charleskawczynski

[akshaysridhar]

https://buildkite.com/clima/climacore-ci/builds/4847#0193e491-227b-43eb-a2a2-7fbb72315844 @charleskawczynski This job passes locally (runs all deformation flow configs with plots generated at the end of the simulation) but fails on buildkite - the assertion error is part of this pr, the convergence warnings are not (those are from the horizontal limiter implementations and are consistent with main branch outcomes)

[charleskawczynski]

Alright, it looks like this worked. The only failure is unrelated, it seems like the fieldvector benchmarks have a 137 error. I'll look into that separately.