Nonlinear Fokker-Planck Acceleration for Forward-Peaked Transport Problems in Slab Geometry

TL;DR

This paper proposes a nonlinear acceleration method based on a modified Fokker-Planck equation to significantly speed up solutions of forward-peaked transport problems, outperforming traditional methods like DSA.

Contribution

It introduces a novel Fokker-Planck based acceleration scheme that preserves key solution properties and achieves substantial computational speed-ups.

Findings

Achieves 3-4 orders of magnitude speed-up over DSA

Effective for various scattering kernels including Henyey-Greenstein

Preserves angular flux and moments of the transport solution

Abstract

This paper introduces a nonlinear acceleration technique that accelerates the convergence of solution of transport problems with highly forward-peaked scattering. The technique is similar to a conventional high-order/low-order (HOLO) acceleration scheme. The Fokker-Planck equation, which is an asymptotic limit of the transport equation in highly forward-peaked settings, is modified and used for acceleration; this modified equation preserves the angular flux and moments of the (high order) transport equation. We present numerical results using the Screened Rutherford, Exponential, and Henyey-Greenstein scattering kernels and compare them to established acceleration methods such as diffusion synthetic acceleration (DSA). We observe three to four orders of magnitude speed-up in wall-clock time compared to DSA.