Matthew Knepley <[email protected]> writes:
On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <[email protected]> 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).