Computational Mathematics and Scientific Computing Seminar

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Provably entropy stable subcell finite volume shock capturing for high order spectral element discontinuous Galerkin methods

Speaker: Gregor Gassner, University of Cologne

Location: Warren Weaver Hall online

Date: March 26, 2021, 10 a.m.

Synopsis:

In this talk, we explain how to construct a compatible subcell finite volume scheme that can be seemlessly blended with a high order spectral element discontinuous Galerkin method. Our goal applications are the compressible Euler equations and the ideal MHD equations in multiple dimensions.  Starting with an entropy-dissipative split-form discontinuous Galerkin scheme on collocated Legendre-Gauss-Lobatto (LGL) nodes, we show how to carefully design a finite volume type discretization on the LGL subcell grid such that it is (i) still provably entropy-dissipative/stable/conservative and (ii) compatible to the high order DG scheme in the sense for each element, we can seamlessly blend between the low order finite volume and the high order DG discretization. This new hybrid scheme enables us to do shock capturing and preserve positivity of the solution: the straight forward idea is to use the arbitrary blending in the hybrid scheme smartly such that the amount of FV is high in regions that need a lot of stabilization (e.g. shocks), whereas its amount is low in regions where the DG scheme can stay alive without much help.