Exactly divergence-free central DG methods for ideal MHD equations
Liwei Xu

Abstract: In this talk, I will report our work on developing high order central discontinuous Galerkin methods for solving ideal magnetohydrodynamic (MHD) equations consisting of a set of nonlinear hyperbolic conservation laws, with a divergence-free constraint on the magnetic eld. The methods are based on the original central discontinuous Galerkin methods designed for hyperbolic conservation laws on overlapping meshes, and use di erent discretization for magnetic induction equations. The resulting schemes carry many features of standard central discontinuous Galerkin methods such as high order accuracy and being free of exact or approximate Riemann solvers. And more importantly, the numerical magnetic eld is exactly divergence-free. Such property is highly desired in reliable simulations of MHD equations. Numerical examples are presented to demonstrate the high order accuracy and the robustness of the schemes. This is a joint work with Prof. Fengyan Li at RPI