We are concerned with efficient numerical simulation of the radiative transfer equations...

In view of radiation hydrodynamics computations, we propose an implicit numerical scheme that captures the diffusion limit of the two moment approximate model for the radiative transfer. We prove by construction the limited flux property. Various test cases show the accuracy and robustness of the scheme. Key words: radiation hydrodynamics, diffusion limit, flux limited and monotone scheme. 1

Abstract. We consider a class of kinetic equations equipped with a single conservation law which generate L 1-contractions. We discuss the hydrodynamic limit to a scalar conservation law and the diffusive limit to a (possibly) degenerate parabolic equation. The limits are obtained in the “dissipative ” sense, equivalent to the notion of entropy solutions for conservation laws, which permits the use of the perturbed test function method and allows for simple proofs. A general compactness framework is obtained for the diffusive scaling in L 1. The radiative transport equations, satisfied by the Wigner function for random acoustic waves, present such a kinetic model that is endowed with conservation of energy. The general theory is used to validate the diffusive approximation of the radiative transport equation. 1.