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Add divergence conforming discontinuous Galerkin demo for the Navier-Stokes equations #2390

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merged 54 commits into from Jan 26, 2023

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jpdean
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@jpdean jpdean commented Oct 3, 2022

This PR adds a divergence conforming discontinuous Galerkin demo for the Navier-Stokes equations.

It demonstrates:

  • how to implement DG methods
  • how to use predefined and custom restriction operators
  • how upwinding can be implemented
  • the use of H(div) elements in a non-conforming context

As far as I'm aware, none of the other demos demonstrate the above functionality.

I still need to so some tidying. Any feedback would be much appreciated.

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jpdean commented Oct 3, 2022

If anyone feels this would be better kept outside the main repository, it could be added to the FEniCSx tutorial instead if @jorgensd is happy

Co-authored-by: Nate <34454754+nate-sime@users.noreply.github.com>
# $\Omega \subset \mathbb{R}^d$, $d \in \{2, 3\}$, and time interval
# $(0, \infty)$, given by
# $$
# \partial_t u - \nu \Delta u + (u \cdot \nabla)u + \nabla p = f
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Does \nu actually get used in the discretisation?

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The discretisation uses the dimensionless form, where \nu is incorporated into the Reynolds number. I'll make this clearer

@garth-wells garth-wells merged commit 5d43791 into main Jan 26, 2023
@garth-wells garth-wells deleted the jpdean/div_con_navier_stokes branch January 26, 2023 13:51
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3 participants