High‐Order Positivity‐Preserving Finite Volume Schemes for Radiation Hydrodynamics Equations in the Equilibrium‐Diffusion Limit

ABSTRACT In this paper, we present the high‐order positivity‐preserving finite volume (PPFV) schemes for radiation hydrodynamics equations (RHE) in the equilibrium‐diffusion limit. The equations are composed of a hyperbolic system of conservation laws and a radiation diffusion term. First, the weighted essentially non‐oscillatory (WENO) reconstruction is applied to the spatial discretization of the hyperbolic system to achieve the high‐order numerical approximation. Subsequently, the adjacent cells are utilized to reconstruct high‐order polynomials for approximating the diffusion flux. Furthermore, the third‐order strong‐stability‐preserving (SSP) Runge‐Kutta scheme is employed for time discretization. Additionally, the positivity‐preserving limiter is implemented to prevent non‐physical numerical results. The positivity‐preserving property of the schemes is also proven. Finally, several numerical examples are presented to show the good performance of the schemes.