A High-Order Discontinuous Galerkin Method for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics

In this work, we present a high-order discontinuous Galerkin (DG) method for solving the one-fluid two-temperature Euler equations for non-equilibrium hydrodynamics. In order to achieve optimal order of accuracy as well as suppress potential numerical oscillations behind strong shocks, special jump terms are applied in the DG spatial discretization for the nonconservative equation of electronic internal energy. Moreover, inspired by the solution procedure of Riemann problem, we develop a new HLLC (Harten–Lax–van Leer Contact) approximate Riemann solver for the one-fluid two-temperature Euler equations and use it as a building block for the high-order discontinuous Galerkin method. Several key features of the proposed HLLC approximate Riemann solver are analyzed. Finally, we design typical test cases to numerically verify and demonstrate the performance of the proposed method.