Second-order direct Eulerian GRP schemes for radiation hydrodynamical equations

Abstract

The paper proposes second-order accurate direct Eulerian generalized Riemann problem (GRP) schemes for the radiation hydrodynamical equations (RHE) in the zero diffusion limit. The difficulty comes from no explicit expression of the flux in terms of the conservative vector. The characteristic fields and the relations between the left and right states across the elementary-waves are first studied, and the exact solution of the 1D Riemann problem is then gotten. After that, the direct Eulerian GRP scheme is derived by directly using the generalized Riemann invariants and the Rankine–Hugoniot jump conditions to analytically resolve the left and right nonlinear waves of the local GRP in the Eulerian formulation. Several numerical examples show that the GRP schemes can achieve second-order accuracy and high resolution of strong discontinuity.