Hyperbolic character of the angular moment equations of radiative transfer and numerical methods

Abstract

We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and causality preservation lead to mathematical conditions allowing us to establish a useful characterization of the closure relations. We apply numerical methods specifically designed to solve hyperbolic systems of conservation laws (the so-called Godunov-type methods) to calculate numerical solutions of the radiation transport equations in a static background. The feasibility of the method in all regimes, from diffusion to free-streaming, is demonstrated by a number of numerical tests, and the effect of the choice of the closure relation on the results is discussed.