Discontinuous galerkin method applied to extended-MHD model in perseus for simulating shocks

Summary form only given. In this poster we report on the application of a discontinuous Galerkin (DG) spatial discretization method to the extended-MHD model used in the PERSEUS^{1, 2} code. The algorithm and its implementation will be briefly introduced. We expect that the DG method will have advantages over the finite volume (FV) method currently used in PERSEUS. In particular, we hope to better simulate shock problems, since the compact form of DG can allow for a detailed local resolution in the neighborhood of a shock. In addition, DG is highly parallelizable, easily adapted to unstructured grids and it has an arbitrary order of accuracy. These features allow DG to potentially improve the simulation accuracy as well as reducing the computational expense. A comparison is carried out between DG-perseus and FV-perseus applied on both MHD and extended-MHD model, focusing on accuracy, stability, convergence and computational expense. Various numerical experiments are performed to validate the analysis and the comparison.