Numerical Solution of the Azimuth-Dependent Fokker-Planck Equation in 1D Slab Geometry
JOURNAL OF COMPUTATIONAL AND THEORETICAL TRANSPORT(2021)
摘要
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 theta. The problem is split into a collection of theta-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.
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关键词
Transport problem,Fokker–,Planck equation,finite difference method,Fourier expansion,continuous scattering operator,degenerate PDE with singular coefficients,forward–,backward PDE,charged particles,electrons,heavy ions,surface PDEs,Primary,Secondary
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