A new Monte Carlo method for solving the nonlinear radiative transfer equations is considered. The radiative transfer equations consist of the transfer equation coupled with the energy balance equation. In this article a scheme for calculation particle tracking is presented. This tracking is used to build an energy balance matrix. This leads to an original matrix formulation of the energy balance equation, where the entries of the matrix are computed by the Monte Carlo method.
The energy balance equation is linearized by using Newton’s method. A matrix formulation of the energy balance equation is given. This formulation allows this approach to be easily coupled with the Rosseland diffusion equation, which is needed in optically thick media, via domain decomposition.
A numerical test of the Monte Carlo method for a domain which consists of three media is presented. Numerical tests are shown to prove the efficiency of the presented matrix Monte Carlo method. The author shows, that these results are better than results obtained by the method of J. A. Fleck and J. D. Cummings [J. Comput. Phys. 8, 313-342 (1971; Zbl 0229.65087)].