Monotone finite point method for non-equilibrium radiation diffusion equations

In this paper, we propose the monotone tailored-finite-point method for solving the non-equilibrium radiation diffusion equations. We first give two tailored finite point schemes for the nonlinear parabolic equation in one-dimensional case, then extend the idea to solve the radiation diffusion problem in 1D as well as 2D. By using variable substitute, our method satisfies the discrete maximum principle automatically, thus preserves the properties of monotonicity and positivity. Numerical results show that our method can capture the sharp front and can be accommodated to discontinues diffusion coefficient.