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The Effectiveness of P2 and Simplified P2 Synthetic Accelerations in the Solutions of Discrete Ordinates Transport Equations

Taewan Noh, Warren F. Miller, Jr.

Nuclear Science and Engineering / Volume 124 / Number 1 / September 1996 / Pages 18-30

Technical Paper /

Using the operator form of a synthetic acceleration, the P1 acceleration [diffusion synthetic acceleration (DSA)] and P2 acceleration schemes for one-dimensional slab and the P1 and simplified P2 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 P2 acceleration outperforms an earlier third-moment P2 acceleration developed by Miller and Larsen. However, it is still less efficient than P1 acceleration. Similar results show that the P1 acceleration converges faster than the simplified P2 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.