[petsc-users] FEM Implementation of NS with SUPG Stabilization

[Jed Brown]

I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice.

https://libceed.org/en/latest/examples/fluids/#equation-eq-peclet

Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure.

Brandon Denton via petsc-users <petsc-users at mcs.anl.gov> writes:

> I was thinking about trying to implement Ben Kirk's approach to Navier-Stokes (see attached paper; Section 5). His approach uses these quantities to align the orientation of the unstructured element/cell with the fluid velocity to apply the stabilization/upwinding and to detect shocks.
>
> If you have an example of the approach you mentioned, could you please send it over so I can review it?
>
> On Oct 11, 2023 6:02 AM, Matthew Knepley <knepley at gmail.com> wrote:
> On Tue, Oct 10, 2023 at 9:34 PM Brandon Denton via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:
> Good Evening,
>
> I am looking to implement a form of Navier-Stokes with SUPG Stabilization and shock capturing using PETSc's FEM infrastructure. In this implementation, I need access to the cell's shape function gradients and natural coordinate gradients for calculations within the point-wise residual calculations. How do I get these quantities at the quadrature points? The signatures for fo and f1 don't seem to contain this information.
>
> Are you sure you need those? Darsh and I implemented SUPG without that. You would need local second derivative information, which you can get using -dm_ds_jet_degree 2. If you check in an example, I can go over it.
>
>   Thanks,
>
>      Matt
>
> Thank you in advance for your time.
> Brandon
>
>
> --
> What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>