Numerical solution of the Azimuth-dependent Fokker-Planck equation in 1D slab geometry. (English) Zbl 07476658

Summary: 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.


65-XX Numerical analysis
35K65 Degenerate parabolic equations
35Q84 Fokker-Planck equations
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
78A35 Motion of charged particles
65Z05 Applications to the sciences
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