Semi-implicit and semidiscrete difference schemes for solving a nonstationary kinetic equation of thermal radiative transfer and energy equation

Semi-implicit and semidiscrete difference schemes of higher order accuracy are proposed for solving kinetic equations of thermal radiative transfer and the energy equation by applying a modified splitting method. A feature of the schemes is that thermal radiative transfer is computed using explicit or implicit difference schemes approximating a usual transport equation. The radiation–matter interaction is computed using implicit difference schemes in the semi-implicit case and using analytical solutions of ordinary differential equations in the semidiscrete case. The difference schemes of higher order accuracy are constructed relying on the second-order Runge–Kutta method. Solutions are found without using outer iterations with respect to the collision integral or matrix inversion. The solution algorithms for difference equations are well suited for parallelization. The method can naturally be generalized to multidimensional problems.