CosmosDG: An hp-Adaptive Discontinuous Galerkin Code for Hyper-Resolved Relativistic MHD

Abstract

We have extended Cosmos++, a multi-dimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for regularization of shocks. High order multi-stage forward Euler and strong stability preserving Runge-Kutta time integration options complement high order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, though we note an equivalent capability currently also exists in CosmosDG for Newtonian systems.