A Flexible, Moment-Preserving, and Monotone Discretization of the Multidimensional Angular Fokker–Planck Operator

ABSTRACT: A monotone finite-difference scheme is proposed for the multidimensional angular Fokker–Planck operator in discrete ordinates calculations. It is compatible with nonorthogonal quadrature sets on the unit sphere and preserves the null space, the zeroth, and the first three angular moments of the analytical angular Fokker–Planck operator. Numerical results demonstrate that this discretization, combined with the suitable Galerkin quadrature method, eliminates spurious oscillations in the flux solution related to highly anisotropic scattering.