AN ANALYSIS OF THE HYPERBOLIC NATURE OF THE EQUATIONS OF RADIATION HYDRODYNAMICS

Abstract

In this paper we analyze the equations of radiation hydrodynamics viewed as a system of hyperbolic equations. The purpose is to develop such insights as might be useful in the construction of robust and accurate higher-order Godunov schemes for their numerical solution. As a result we analyze the propagation characteristics of the hyperbolic parts of the equations of radiation hydrodynamics. We show that the system admits the usual sound waves, shear waves and entropy wave familiar from the Euler equations. However, an important point of difference is that these waves make significant contributions to the radiative parts of the full system of equations in ways that were not anticipated. We explain this difference with a view to improving our physical insight. The system also admits a pair of waves that enable the propagation of radiation energy density. They propagate with speeds that can be comparable to the speed of light and as a result they do not produce fluctuations in the hyperbolic parts of the fluid equations. This is physically consistent with the fact that matter cannot move at the speed of light. The system also admits a pair of waves that carry information about the propagation of the transverse radiative fluxes. As a corollary to this work, important new insights have been obtained into the nature of the Eddington factors and their role in radiation hydrodynamics. We have also been able to arrive at some insights into the Cauchy problem for the equations of radiation hydrodynamics.