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@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 <knep...@gmail.com> wrote: > On Tue, Oct 10, 2023 at 9:34 PM Brandon Denton via petsc-users > <petsc-users@mcs.anl.gov<mailto:petsc-users@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/>
