Properties of the implicitly time-differenced equations of thermal radiation transport

Numerical simulations of thermal radiation transport (TRT) use varying levels of implicitness to discretize the time variable t. The degree of implicitness generally depends on the strength of the coupling between the radiation and matter. In this paper we use a contraction mapping method to show that if all terms in the TRT equations except possibly the opacity are discretized implicitly, then for any Δ t > 0 , the time-discretized TRT equations (i) have a unique solution, which (ii) satisfies the maximum principle and (iii) preserves the equilibrium (thick) diffusion limit. No other available time-discretization of the TRT equations has all these desirable properties. Numerical results are included to illustrate the theoretical predictions.