THE EFFECTIVENESS OF P-2 AND SIMPLIFIED P-2 SYNTHETIC ACCELERATIONS IN THE SOLUTIONS OF DISCRETE ORDINATES TRANSPORT-EQUATIONS

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