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 Δt>0Δt>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.