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

[Matthew Knepley]

On Wed, Oct 11, 2023 at 4:15 PM Brandon Denton <bldenton at buffalo.edu> wrote:

> By natural coordinates, I am referring to the reference element
> coordinates. Usually these are represented as (xi, eta, zeta) in the
> literature.
>
> Yes. I would like to have the Jacobian and the derivatives of the map
> available within PetscDSSetResidual() f0 and f1 functions.
>

Yes, we can get these passed an aux data.


>   I believe DMPlexComputeCellGeometryFEM() function provides this
> information. Is there a way to get the cell, shape functions as well? It
> not, can we talk about this more? I would like to understand how the shape
> functions are addressed within PETSc. Dr. Kirk's approach uses the shape
> function gradients in its SUPG parameter. I'd love to talk with you about
> this is more detail.
>

There should be a way to formulate this in a basis independent way.  I
would much prefer that to
explicit inclusion of the basis.

  Thanks,

     Matt


> *From:* Matthew Knepley <knepley at gmail.com>
> *Sent:* Wednesday, October 11, 2023 3:13 PM
> *To:* Brandon Denton <bldenton at buffalo.edu>
> *Cc:* Jed Brown <jed at jedbrown.org>; petsc-users <petsc-users at mcs.anl.gov>
> *Subject:* Re: [petsc-users] FEM Implementation of NS with SUPG
> Stabilization
>
> On Wed, Oct 11, 2023 at 2:09 PM Brandon Denton <bldenton at buffalo.edu>
> wrote:
>
> Thank you for the discussion.
>
> Are we agreed then that the derivatives of the natural coordinates are
> required for the described approach? If so, is this something PETSc can
> currently do within the point-wise residual functions?
>
>
> I am not sure what natural coordinates are. Do we just mean the Jacobian,
> derivatives of the map between reference and real coordinates? If so, yes
> the Jacobian is available. Right now I do not pass it
> directly, but passing it is easy.
>
>   Thanks,
>
>      Matt
>
>
> Matt - Thank you for the command line option for the 2nd derivatives.
> Those will be needed to implement the discussed approach. Specifically in
> the stabilization and shock capture parameters. (Ref.: B. Kirk's Thesis).
> What is a good reference for the usual SUPG method you are referencing?
> I've been looking through my textbooks but haven't found a good reference.
>
> Jed - Thank you for the link. I will review the information on it.
>
> Sorry about the attachment. I will upload it to this thread later (I'm at
> work right now and I can't do it from here).
> ------------------------------
> *From:* Jed Brown <jed at jedbrown.org>
> *Sent:* Wednesday, October 11, 2023 1:38 PM
> *To:* Matthew Knepley <knepley at gmail.com>
> *Cc:* Brandon Denton <bldenton at buffalo.edu>; petsc-users <
> petsc-users at mcs.anl.gov>
> *Subject:* Re: [petsc-users] FEM Implementation of NS with SUPG
> Stabilization
>
> Matthew Knepley <knepley at gmail.com> writes:
>
> > 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://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flibceed.org%2Fen%2Flatest%2Fexamples%2Ffluids%2F%23equation-eq-peclet&data=05%7C01%7Cbldenton%40buffalo.edu%7Cd9372f934b26455371a708dbca80dc8e%7C96464a8af8ed40b199e25f6b50a20250%7C0%7C0%7C638326427028053956%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=skMsKDmpBxiaXtBSqhsyckvVpTOkGqDsNJIYo22Ywps%3D&reserved=0
> <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.
>
> I think you're focused on computing the strong diffusive flux (which can
> be done using second derivatives or by a projection; the latter produces
> somewhat better results). But you still need a length scale and that's most
> naturally computed using the derivative of reference coordinates with
> respect to physical (or equivalently, the associated metric tensor).
>
>
>
> --
> 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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