Nonlinear Weighted Flux Methods for Particle Transport Problems

Abstract

A new parameterized family of iterative methods for the 1‐D slab geometry transport equation is proposed. The new methods are derived by integrating the transport equation over −1≤μ≤0 and 0≤μ≤1 with weight 1+β|μ|α, where α≥0. The asymptotic diffusion analysis enables us to determine a particular method of this family the solution of which satisfies a good approximation of both the diffusion equation and asymptotic boundary condition in the diffusive regions. Note that none of the α‐weighted nonlinear methods possesses this combination of properties. The convergence properties of the proposed method are similar to the properties of the diffusion‐synthetic acceleration (DSA), quasi‐diffusion, and DSA‐like α‐weighted nonlinear methods. Numerical results are presented to demonstrate the performance of the derived method.