Finite Volume vs Discontinuous Galerkin methods for the Navier-Stokes equations

[miguelcoolchips]

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Question

Judging from this post (#17383 (comment)), it looks like the finite volume solver is the way to go for the Navier-Stokes equations. I wonder if the MOOSE developers also tried with a Discontinuous Galerkin approach and it did not succeed either.

Additional information

No response

[GiudGiud]

Hello

I confirm we are investing mostly into the finite volume solver at this point for solving the Navier Stokes equations.
Also, @lindsayad is developing a hybridized discontinuous Galerkin solver as a research activity. See this page https://mooseframework.inl.gov/syntax/HDGKernels/index.html for more info

if the MOOSE developers also tried with a Discontinuous Galerkin approach

there was this effort
https://mooseframework.inl.gov/modules/navier_stokes/hcgdgfe.html

and it did not succeed either.

At this point it's a previous generation of developers that did all this work and remember the pros and cons. It's all in technical reports from the 2010-2020 era if you want to dig deeper.

[miguelcoolchips]

I think I found it https://inldigitallibrary.inl.gov/sites/sti/sti/Sort_3448.pdf#page=17.09

[GiudGiud]

I think that one is somewhat related though RELAP-7 was intented to be a multi-D CFD code, but a systems thermal hydraulics code

@lindsayad might know what report would contain DG vs FV comparisons
@jwpeterson @lingzou @andrsd might know what report would contain DG vs CG comparisons

[lindsayad]

HDG is just a sub-type of DG, so I would say that we still have a lot of knowledge about DG methods for NS. However, @GiudGiud is definitely right when he says we have a lot more money (and hence focus) on our finite volume implementations of NS. I have shown very nice results with (H)DG for straightforward lid driven and channel test cases. But my research funding has run out so I don't have any more money for further investigations. Please feel free to spend some time with the recent HDG developments. I'm happy to point you to resources if you wish.

Over the past two years of research on HDG and my recent involvement with frameworks for GPU computing, I kind of think that vanilla DG is the way to go long term because it's more amenable to matrix-free preconditioning and consequently high order methods where you can really get the benefit of GPU. That's also the regime (high order) in which finite elements can show some differentiation against finite volume methods. Of course near singularities you'll still want to be low-order in p and instead h-refine.

[miguelcoolchips]

Thanks @lindsayad for your reply. Is there a report that compares DG and FV implementations on MOOSE?

[lindsayad]

No there is not. There is some discussion sprinkled through various MOOSE github issues and pull requests that shows fairly equivalent performance for our best solver configurations for finite elements (FE) and finite volumes (FV) for simple test cases like the lid driven cavity with moderate Reynolds numbers.

Fundamentally our finite element implementations (both Taylor-Hood CG and DG) are missing things like turbulence models and near-wall treatments that we have available for finite volume. You really need those if you are going to be modeling realistic flow regimes that we encounter in generation IV nuclear reactors, which are the applications that our team primarily target. Until those are implemented comparisons between FE and FV are limited