Dear Jack,
Two-point fluxes are something we have not yet included in deal.II. I
would be very interested if we could realize this feature. I must admit
that I did not yet try to understand the complete formula in the link
you provided, but in fact it should be possible to implement this with
the internal evaluators used by FEEvaluation very efficiently. Would you
be willing to share the FEValues variant, it is enough to provide it in
1D. I did work with the Trixi code before, but did not yet look into the
algorithms, so I would be very curious to learn the details. My initial
approach would be to encode the full D_split matrix to be fed into the
tensor product evaluators in the internal namespace, and then add the
respective boundary fluxes. Once we have a basic version, we can think
about making the interface nicer.
Best,
Martin
Am 23.04.24 um 17:19 schrieb Jack Coughlin:
I am interested in using the deal.ii matrix-free infrastructure to
implement an entropy-stable DG method. The entropy stable family of
methods uses an interesting variation, where the volume flux is
actually a consistent two-point flux function (similar to the
numerical flux).
I've attached a screenshot of the formula in question, which is taken
from this documentation page
<https://trixi-framework.github.io/Trixi.jl/stable/tutorials/DGSEM_FluxDiff/#DGSEM-with-flux-differencing>.
I've also attached a review of the method.
As far as I can tell, to do this you would need to be able to tell a
class like FEEvaluation to integrate a given submission only for one
test function. I think I can see how to do this integration manually
with FEValues, but it would be nice to take advantage of the
matrix-free infrastructure if possible.
Thank you,
-Jack C
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