High Order Conservative OEDG Methods with Explicit-Implicit-Null Time Discretizations for Three-Temperature Radiation Hydrodynamics

In this paper, we propose a class of efficient high order accurate conservative oscillation-eliminating discontinuous Galerkin (OEDG) methods combined with explicit-implicit-null (EIN) time discretizations for solving non-equilibrium three-temperature (3-T) radiation hydrodynamics (RHD) equations. The system of 3-T RHD equations consisting of advection, diffusion and energy exchange terms is highly nonlinear, tightly coupled, and expressed in a non-conservative formulation, which poses great difficulties in designing high order accurate conservative numerical algorithms. Besides, when dealing with nonlinear diffusion terms, the explicit time marching always suffers from stringent time step restriction, while the implicit time marching, although it can avoid the constraint of small time step, is very cumbersome because nonlinear iterations are required at each time step. To overcome these challenges, we consider a reformulation of the system of 3-T RHD equations to facilitate the design of high order conservative numerical schemes, and then adopt EIN method to handle nonlinear diffusion terms to improve the efficiency. Namely, we simultaneously add and subtract two equal linear diffusion terms with a uniform constant diffusion coefficient on the right-hand side of the system of 3-T RHD equations, and then utilize implicit-explicit time marching methods to treat the added linear diffusion term implicitly and the other terms explicitly. For the spatial discretization, we employ OEDG methods. By doing so, the proposed methods, referred to as EIN-OEDG methods, not only eliminate spurious oscillations without sacrificing the order of accuracy but also improve the efficiency of dealing with nonlinear diffusion terms. Furthermore, we prove that fully-discrete schemes can keep the conservation of mass, momentum and total energy. Numerical experiments are performed to demonstrate the corresponding orders of accuracy and desired properties of our proposed approaches.