The The SK_N Method II: Heterogeneous Problems

The SK_N approximation is slightly altered to solve the integral transport equation for heterogeneous systems. The original formulation of the SK_N approximation has a defect when applied to heterogeneous problems. We propose a correction technique for such problems, which can also be applied to problems with P₁ scattering. Such modified SK_N equations are derived and tested for benchmark problems in one-dimensional geometries, which contain strong heterogeneities. Two-dimensional heterogeneous problems are solved using the unaltered SK_N method with naive boundary conditions to determine how much heterogeneity can be tolerated before the remedy is necessary.