Non-Linear Spatial Multigrid Method For Non-Linear S2 Acceleration

Abstract

A nonlinear spatial multigrid algorithm was developed and explored as a technique to efficiently solve the nonlinear S2 acceleration equations for SN neutron transport calculations in 1-D slabs. Acceleration of the basic source iteration process in SN calculations is necessary in problems with highly diffusive regions. Direct inversion would be a more efficient method in 1-D, but a multigrid method has the potential to be far more efficient than other techniques in 2-D. This work is a first step toward a 2-D multigrid algorithm. The computational results show that this scheme works well for optically-thin cells on the fine mesh, but degrades significantly for optically-thick cells on the fine mesh.