Theoretical Approach to Synthetic Accelerations for the Solution of Neutron Transport Equation

Abstract

A discrete ordinates neutron transport solution usually consists of solving alternately the transport and the diffusion equation. Here, the diffusion equation which is a P₁ approximation to the transport equation is solved only for an acceleration of transport solution to achieve the computational efficiency. The derivation of various low-order accelerating equations are generalized by using an operator form of acceleration in this paper. The source iteration, P₀, P₁, and P₂ acceleration schemes are derived and their spectral radii are calculated and compared by using Fourier convergent analysis. The result is that the P₁ acceleration outperforms the other schemes in accelerating transport solution. These results confirm that one cannot simply assume that the replacement of P₁ with a higher order equation would enhance the acceleration efficiency.