The Effectiveness ofP2and SimplifiedP2Synthetic Accelerations in the Solutions of Discrete Ordinates Transport Equations

Abstract

Using the operator form of a synthetic acceleration, the P{sub 1} acceleration [diffusion synthetic acceleration (DSA)] and P{sub 2} acceleration schemes for one-dimensional slab and the P{sub 1} and simplified P{sub 2} acceleration schemes for two-dimensional x-y geometry are derived. The convergence rate of each scheme for a simple model problem is compared, and the result is generalized by performing a Fourier analysis. In the one-dimensional case, the new second-moment P{sub 2} acceleration outperforms an earlier third-moment P{sub 2} acceleration developed by Miller and Larsen. However, it is still less efficient than P{sub 1} acceleration. Similar results show that the P{sub 1} acceleration converges faster than the simplified P{sub 2} acceleration in two-dimensional x-y geometry. These results confirm that one cannot simply assume that replacement of the DSA method with a higher order operator will lead to a smaller spectral radius.