Abstract

This paper introduces a new acceleration technique for the convergence of the 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.

摘要

本文介绍了一种新的加速技术，用于收敛具有高度前向峰值散射的传输问题的解决方案。该技术类似于传统的高阶/低阶 (HOLO) 加速方案。Fokker-Planck 方程是高度前向峰值设置下输运方程的渐近极限，被修改并用于加速；这个修改后的方程保留了（高阶）输运方程的角通量和力矩。我们使用 Screened Rutherford、Exponential 和 Henyey-Greenstein 散射核呈现数值结果，并将它们与已建立的加速方法（如扩散合成加速 (DSA)）进行比较。与 DSA 相比，我们观察到挂钟时间有三到四个数量级的加速。