López Pouso, ÓscarJumaniyazov, Nizomjon2024-12-202024-12-202021-03-16López Pouso, Ó., & Jumaniyazov, N. (2021). Numerical Solution of the Azimuth-Dependent Fokker-Planck Equation in 1D Slab Geometry. Journal of Computational and Theoretical Transport, 50(2), 102-133. https://doi.org/10.1080/23324309.2021.18965542332-4325https://hdl.handle.net/10347/38254This is an original manuscript of an article published by Taylor & Francis in Journal of Computational and Theoretical Transport on 16 Mar 2021, available at: https://doi.org/10.1080/23324309.2021.1896554This 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Transport problemFokker–Planck equationFinite difference methodFourier expansionContinuous scattering operatorDegenerate PDE with singular coefficientsForward–backward PDECharged particlesElectronsHeavy ionsSurface PDEsjournal article10.1080/23324309.2021.1896554open access