A Multiple Balance Approach for Differencing the S_n Equations

A new and promising approach for differencing the S_n equations is introduced. This scheme is characterized by the use of the standard balance equation for each discrete phase-space cell together with auxiliary equations that represent approximate balance equations over subregions of the cell. Hence, it is called the “multiple balance” approach. In principle, the multiple balance approach can be applied to the S_n equations in any geometry with general anisotropic scattering. However, the multiple balance approach is applied only to the one-dimensional slab-geometry S_n equations with isotropic scattering. This represents a first step toward applications of this approach in more general contexts. The results are very encouraging. A multiple balance scheme that has several highly desirable properties, which are collectively unique, has been developed. These properties are demonstrated both theoretically and computationally.