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The paper proposes a second-order accurate direct Eulerian generalizedRiemann problem (GRP) scheme for the radiation hydrodynamical equations (RHE)in the zero diffusion limit. The difficulty comes from no explicit expressionof the flux in terms of the conservative vector. The characteristic fields andthe relations between the left and right states across the elementary-waves arefirst studied, and then the solution of the one-dimensional Riemann problem isanalyzed and given. Based on those, the direct Eulerian GRP scheme is derivedby directly using the generalized Riemann invariants and the Runkine-Hugoniotjump conditions to analytically resolve the left and right nonlinear waves ofthe local GRP in the Eulerian formulation. Several numerical examples show thatthe GRP scheme can achieve second-order accuracy and high resolution of strongdiscontinuity.

A direct Eulerian GRP scheme for radiation hydrodynamical equations in diffusion limit