A Curvilinear Discontinuous Galerkin Method for Radiation Hydrodynamics

ABSTRACT In this article, a cell‐centered discontinuous Galerkin (DG) method is presented for solving Lagrangian radiation hydrodynamic equations (RHE). The equations are separated into a hydrodynamic part and a radiation diffusion part. These two parts are written in Lagrangian forms. The hydrodynamic part is discretized by a cell‐centered DG scheme in reference space using Taylor basis functions. An approximate Riemann solver is used for the velocity of vertices, and the radiation diffusion is solved using an interior penalty method. Due to the deformation of the basis functions in physical space, curvilinear mesh is formed. Numerical tests are presented to show its accuracy and robustness.