A Coupled Diffusion Synthetic Acceleration for Binary Stochastic Mixture Transport Iterations

Abstract

The standard model for transport through binary stochastic media involves two coupled transport equations. Previous research has shown that several types of source iterations applied to the solution of these equations can converge arbitrarily slowly when one or both of the materials is optically thick and diffusive. In this work, we derive, analyze, and implement an acceleration scheme for binary stochastic mixture transport iterations. The equations are derived using the modified four-step method and take the form of discretized coupled diffusion equations. A Fourier analysis indicates that for a wide variety of physical problems and spatial mesh sizes, the scheme is rapidly convergent. Spectral radii measured during these accelerated iterations compare very well with Fourier analysis predictions.