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

[Jed Brown]

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://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).