Stability analysis of a multilevel quasidiffusion method for thermal radiative transfer problems

In this paper we analyze a multilevel quasidiffusion (QD) method for solving time-dependent multigroup nonlinear radiative transfer problems which describe interaction of photons with matter. The multilevel method is formulated by means of the high-order radiative transfer equation and a set of low-order moment equations. The fully implicit scheme is used to discretize equations in time. The stability analysis is applied to the method in semi-continuous and discretized forms. To perform Fourier analysis, the system of equations of the multilevel method is linearized about an equilibrium solution. The effects of discretization with respect to different independent variables are studied. The multilevel method is shown to be stable and fast converging. We also consider a version of the method in which time evolution in the radiative transfer equation is treated by means of the α-approximation. The Fleck-Cummings test problem is used to demonstrate performance of the multilevel QD method and study its iterative stability.