Accelerating the solution of the [formula omitted] equations with highly anisotropic scattering using the Fokker-Planck approximation

Abstract

The discrete ordinates method can model forward-peaked transport problems accurately. However, convergence of discrete ordinates solution can become arbitrarily slow upon use of standard iterative procedures like source iteration. Standard zeroth and first moment-based acceleration methods like nonlinear diffusion acceleration and diffusion synthetic acceleration are ineffective in accelerating such problems because these methods do not correct higher order Legendre-moments of angular flux. In this paper, we explore the idea of using the Fokker-Planck approximation as a preconditioner to accelerate the convergence of solution of forward-peaked transport problems. We observe that such preconditioning can successfully reduce the iteration count by up to four orders of magnitude, and solver runtime by up to three orders of magnitude when compared to diffusion synthetic acceleration.