Hybrid CG DG

[lindsayad]

@joe61vette I was so intrigued by what you're working on that I had to test it myself.

If we ever want to go with a scheme that doesn’t require Rhie-Chow nor petrov-galerkin stabilization, and allows discontinuous boundary conditions on velocity, the hybrid CG-DG approach appears pretty damn cool. I spun up some kernels today and see second and first order L2 errors for velocity and pressure respectively when using first monomial and first Lagrange for velocity and pressure respectively. And third and second order L2 errors for velocity and pressure if I bump the velocity order to SECOND (keeping pressure at FIRST).

Lid driven result for Re=100 (just using averaging of face values for the advection scheme):

Closes #24055

[joe61vette]

@lindsayad Thanks, I’ll see how it works with what I was testing tomorrow. I agree it looks promising, especially for my two-phase app where I need to make sure face values are bounded by the cell-centered values when interfacial drag dominates the eqs.

[lindsayad]

The preliminary work I did here was only for pressure and velocity and I haven't even added any coefficients yet. So if you think you might want to use/extend what is here, let me know

[lindsayad]

@joe61vette in c74e815 I added a hybrid scheme test for the same skewed mesh that we test our finite volume skew correction methodology on. The hybrid scheme maintains the same orders of accuracy for skewed meshes as for non-skewed meshes, e.g.

velocity polynomial order	pressure polynomial order	velocity L2 error order	pressure L2 error order
1	1	2	1
2	1	3	2

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	750e5c	#23986 360f0d
	Total	Total	+/-	New
Rate	85.69%	85.69%	+0.00%	-
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• contact
• electromagnetics
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• fsi
• functional_expansion_tools
• geochemistry
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• phase_field
• porous_flow
• ray_tracing
• rdg
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• richards
• scalar_transport
• solid_properties
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Job Precheck on 5e6bd52 wanted to post the following:

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Job Conda build (ARM Mac) on 0e53445 : invalidated by @lindsayad

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[roystgnr]

I'm pretty thrilled with the code, and astonished that I'd never seen someone using this formulation before ... but could we get some navier_stokes/doc/content/source/kernels/ entries for the new kernels?

[lindsayad]

but could we get some navier_stokes/doc/content/source/kernels/ entries for the new kernels?

Pretty much all the kernels added in this PR are test objects. The objects used for "production" are very general from the framework. I will make a markdown file though that runs through one of the "production" inputs in detail

[roystgnr]

hcgdgfe.md looks good enough for me. Why'd you have to force push, though?

[lindsayad]

Why'd you have to force push, though?

I rebased as I was trying to figure out what turned out to be unrelated local failures

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Job Conda (Intel Mac) on 360f0d3 : invalidated by @lindsayad

[roystgnr]

I'm happy but give Guillaume a chance to chime in before merging.

[lindsayad]

I will probably merge this by the end of the day if I don't hear anything

[GiudGiud]

Apologies. I will review this again tomorrow. Maybe tonight.

[GiudGiud]

looks good

if this approach keeps being successful (robustness especially), it makes a ton of sense to do "coarse mesh" thermal hydraulics with higher order FE (instead of flat FV requiring us to resolve quite a bit) so it could be another Pgh change of direction :)

[lindsayad]

Thanks for the reviews. I did test this with a porosity jump and similar to a naive finite volume implementation, it struggles, so no easy silver bullet for that problem :-)