Abstract

This paper is devoted to solve the steady monoenergetic Fokker-Planck equation in the 1D slab when the incoming fluxes and the source term are allowed to depend on the azimuth θ. The problem is split into a collection of θ-independent problems for the Fourier coefficients of the full solution. The main difficulty is that, except for the zeroth Fourier coefficient, each of these problems contains an artificial absorption coefficient which is singular at the poles. Two numerical schemes capable of dealing with the singularities are proposed: one that is considered as the main scheme, and a second ‘security’ scheme which is used to verify that the results obtained by means of the first one are reliable. Numerical experiments showing second order of convergence are conducted and discussed.

摘要

当允许入射通量和源项取决于方位角θ时，本文致力于求解一维平板中的稳态单能Fokker-Planck方程。问题被分解为θ的集合解的傅立叶系数的一些独立问题。主要困难在于，除了零阶傅立叶系数之外，这些问题中的每一个都包含一个在极点处为奇异的人工吸收系数。提出了两种能够处理奇异性的数值方案：一种被视为主要方案，另一种用于验证通过第一种方法获得的结果是否可靠的“安全性”方案。进行并讨论了显示二阶收敛性的数值实验。