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

[Matthew Knepley]

On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <jed at jedbrown.org> wrote:

> 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.
>

I was talking about the usual SUPG where we just penalize the true residual.

  Matt


> 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/>
>


-- 
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/>
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