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

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.