Reserch of stability and efficiency of space rebalance acceleration method for linear transport problems

The Space-Dependent Rebalance (SDR) method [1–3] is considered for acceleration the inner iterations in solution of multigroup transport equations by the discrete ordinates Sn method in Pm approximation of scattering matrix. In this method the fictitious boundary flows was introduced on the mesh, given for the transport equation. The SDR method is described on example three-dimensional X-Y-Z geometry. The stability of this version of the rebalance method was not analyzed earlier. The results of Fourier analyses of stability of the SDR method are given. The stability of this method is proved. Numerical results are shown that the SDR method is converges faster than the consistent P1SA scheme [4] in one-dimensional geometry. The computations of radiation fields of reactor plant SVBR-75/100 [5] in three-dimensional X-Y-Z geometry by the Weighted-Difference scheme (WDIF) [6] showed that there are two factors, affecting on the efficiency of SDR: the choice of iteration number to begin the acceleration and the choice of parameter $\teta$ of WDIF scheme. The recommendations on optimal choice of these parameters are developed.