  A moving mesh finite difference method based on the moving mesh partial
differential equation is proposed for the numerical solution of the 2T model
for multi-material, non-equilibrium radiation diffusion equations. The model
involves nonlinear diffusion coefficients and its solutions stay positive for
all time when they are positive initially. Nonlinear diffusion and preservation
of solution positivity pose challenges in the numerical solution of the model.
A coefficient-freezing predictor-corrector method is used for nonlinear
diffusion while a cutoff strategy with a positive threshold is used to keep the
solutions positive. Furthermore, a two-level moving mesh strategy and a sparse
matrix solver are used to improve the efficiency of the computation. Numerical
results for a selection of examples of multi-material non-equilibrium radiation
diffusion show that the method is capable of capturing the profiles and local
structures of Marshak waves with adequate mesh concentration. The obtained
numerical solutions are in good agreement with those in the existing
literature. Comparison studies are also made between uniform and adaptive
moving meshes and between one-level and two-level moving meshes.
