Effective Use of the Linear Fine Mesh Rebalance for the DSA of S_N Transport Equation with Tetrahedral Meshes

摘要

This paper presents a diffusion synthetic acceleration (DSA) technique coupled with the linear fine mesh rebalance (FMR) method for the S_n transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB). The LDEM-SCB scheme solves the transport equation with discrete ordinates method by using the subcell balances and discontinuous linear expansion of flux . The DSA equations are derived by consistently discretizing the continuous diffusion transport equation with LDEM-SCB(l) in our previous work . Our previous work showed that the DSA is very efficient in reducing the number of transport sweeps but the method to effectively solve the diffusion equation was not suggested. In this paper, we suggest the use of a linear FMR method to effectively solve the discretized diffusion equations. In particular, the FMR equations are solved with the conjugate gradient (CG) method. The effectiveness of the DSA method is tested for a homogeneous 3D problem having varying total cross sections.