Numerical Analysis and Scientific Computing Seminar | Gregor Gassner, On Compatible Legendre-Gauss-Lobatto Subcell Low Order Finite Volume Methods (and what we can do with it)

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca  

Speaker

Professor Gregor Gassner, University of Cologne, Division of Mathematics

Title

On Compatible Legendre-Gauss-Lobatto Subcell Low Order Finite Volume Methods (and what we can do with it)

Abstract

In this talk, we explain how to construct a compatible subcell finite volume scheme that can be seamlessly 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. We will present some applications in hydrodynamics and magnetohydrodynamics