A linear multiple balance method with high order accuracy for discrete ordinates neutron transport equations

A linear multiple balance method (LMB) is developed to provide more accurat e and positive solutions for the discrete ordinates neutron transport equat ions. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation for the angular flux distribution. Fo ur multiple balance equations are used to relate center angular flux with a verage angular flux by Simpson's rule. From the analysis of spatial truncat ion error, the accuracy of the linear multiple balance scheme is O(Delta (4 )) whereas that of diamond differencing is O(Delta (2)). The positivity of the method is also stronger than that of diamond differencing. To accelerat e the linear multiple balance method, we also describe an additive angular dependent rebalance factor scheme which combines a modified boundary projec tion acceleration scheme and the angular dependent rebalance factor acceler ation scheme. It is demonstrated, via Fourier analysis of a simple model pr oblem as well as numerical calculations, that the additive angular dependen t rebalance factor acceleration scheme is unconditionally stable with spect ral radius < 0.2069 c (c being the scattering ratio). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance with additive angular r ebalance acceleration is effective and sufficiently efficient. (C) 2001 Pub lished by Elsevier Science Ltd.