A Rapidly Convergent Generalized Rebalance Method (GRM) for Discrete Ordinates Transport Equations

Recently, there have been some efforts to devise the effective acceleration methods by using the diffusion equation derived without consistency with the transport equation and study theoretically the relation between these methods and the conventional coarse mesh rebalance (CMR) equation. However, to our knowledge, there have been no effective methods giving a satisfied fast convergence for full range of mesh size. In this paper, a generalized rebalance method (GRM) having two parameters (at present, only fine-mesh case is considered) for solving the discrete ordinates transport problems is given. The parameters are related with the coupling coefficient and an interpolation. It is shown that for the step characteristic (SC) and the diamond difference (DD) schemes, this method with a choice of the optimal parameters gives a very fast convergence for full range of mesh size