Numerical Resolution of Fokker-Planck Type Kinetic Equations

Abstract

The Fokker-Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces, as in Brownian motion. The equation can be generalized to other observables as well. The Fokker-Planck equation is often used to approximate the description of particle transport processes with highly forward-peaked scattering, then the Fokker-Planck equation is an asymptotic approximation to the linear Boltzmann equation. In this thesis it is considered a new finite difference method and an iterative method to solve the Fokker-Planck equation when the angular flux depends on spatial, polar and azimuthal variables. Fourier technique is applied to split the problem into a set of azimuthal angle-independent problem.