Shallow Water Equations and Moose Vector Variables

[DamynChipman]

I am attempting to model the shallow water equations (SWE) with Moose (I'm a PhD student at Boise State University). I've used Moose for a variety of other geophysics, but the SWE are slightly more complicated. I mention that to say that I'm familiar with Moose, having gone through most of the tutorials.

Here's my problem setup. I have the strong form that I use to generate the weak form of the equations. The weak form takes the following form (using inner product notation):

(dqdt, \psi) + <F(q) * n, \psi> - (F(q), \nabla \psi) - (b + s, \psi) = 0

\psi is the test function.
q is the variable vector: [h, hu, hv].
F(q) is the flux tensor: [ [hu, hv], [hu^2 + (1/2)gh^2, huv], [huv, hv^2 + (1/2)gh^2] ].
h is water height.
u and v are velocities.
b and s are bathymetry and (friction) source terms.

These would be my questions:

How do I work with vector valued variables in Moose? What classes can I work with/ derive from?
What about for vectors like q where the entries aren't necessarily physically related (like components of a velocity field)?
Would I be able to use some of the tensor functionality to do this? I have briefly looked over it.

I will continue to pour over tutorials and documentation, but any guidance would be appreciated.

And finally, I read somewhere that a SWE module is in the works. Any word on progress there?

Many thanks!

[GiudGiud]

Hello

First, since you only have 3 components and the equation seems to be writable in a vector-formulation, vector is the right choice and should give you better performance over implementing 3 scalar equations.
I m a little concerned that having h and hu hv, which could be of different orders of magnitude since they have a different unit / physical meaning, will lead to convergence/scaling issues. You won't be able to scale the equations separately if you lump them in a vector

I m not sure if we have documentation specially for implementing vector equations. If you find it please let me know. The process is mostly the same, you create a vector variable, then vector kernels to implement your equation etc. There is a VectorKernel base class you can inherit from for your kernels.
If you have a tensor anisotropic diffusivity for example, you will be able to use the tensor utilities (in utils/) for that.

We support the lagrange variables as vector variables. There are vector versions of kernels, bcs, auxkernels etc.
An example of a vector BC:
https://mooseframework.inl.gov/source/bcs/VectorDirichletBC.html

vector kernel:
https://mooseframework.inl.gov/moose/source/kernels/VectorDiffusion.html

AuxKernel has an example of a vector aux in the text:
https://mooseframework.inl.gov/syntax/AuxKernels/

Where did you read about the SWE? It d be easier to tag the person who was talking about it here

Guillaume

[dschwen]

Resurrecting an old thread here, but I'm very close to have a DG based shallow water module ready for a pull request...

[lindsayad]

I'm stoked to here about this. What project is this for?

[lindsayad]

Related to shallow water equations, we have HDG Navier-Stokes now. You can see a newsletter entry about it at https://mooseframework.inl.gov/newsletter/2025/2025_06.html. I would really like a non-hybridized DG implementation of Navier-Stokes as well

[dschwen]

I'm stoked to here about this. What project is this for?

Its... for the AI pilot program. The module is made using Codex as a trial for how far I can get running on ignorance and a few million API tokens...

And it turns out: pretty far.

I need to clean up some idiosyncrasies in the code, HLLC is just 1D right now, but HLL(E) looks pretty good so far.

[lindsayad]

Have you looked at the HLLC implementation in FV? https://mooseframework.inl.gov/source/fvkernels/CNSFVHLLCBase.html is probably the best doc page