Modul: MAT870 Zurich Colloquium in Applied and Computational Mathematics

## Splitform Discontinuous Galerkin for the ideal MHD equations: energy, Lorentz force, entropy and divergence B

Prof. Dr. Gregor Gassner talk

Speaker invited by: Prof. Dr. Rémi Abgrall

**Date:** 04.12.19 **Time:** 16.15 - 17.45 **Room:** ETH HG E 1.2

In this talk, we show how to construct a discontinuous Galerkin type discretisation of the ideal MHD equations based on first principles. By carefully choosing the form of the PDEs (divergence, advective, splitform, etc) it is possible to design a compatible discretisation where e.g. kinetic energy is preserved, with the right Lorentz force behavior, where we recover a discrete entropy evolution and where zero divergence of the B field is satisfied discretely. We will demonstrate these properties for a 3D ideal MHD test case simulated with the open source framework FLUXO (github.com/project-fluxo).