The Investigation Of Spectral Method On The Numerical Solution Of Fokker-Planck Equation

The numerical solution of Fokker-Planck equation is studied in this paper.In chapterâ… , the Fokker-Planck equation and its theoretical ground is presented. The Fokker-Planck collision operator and its Landau form is deduced. Several methods to the numerical solution of the Fokker-Planck equation are introduced concisely and up-to-date study state of this field is summarized.In chapterâ…¡, spectral method is firstly used to discrete the Landau collision operator. The difficulty involved in the collision operator, which contains both differential and integral, is thus bypassed. This scheme maintains the law of mass conservation strictly. Then, in order to utilize FFT algorithm, the collision operator is separated into a series of discrete convolutions, which can considerably reduce the computational cost. In addition, a brief numerical analysis to the error of this discrete scheme is given.In chapterâ…¢, FFT and its several forms are introduced, three roles it plays in this paper is expounded in detail.In chapterâ…£, three problems in the velocity space are simulated numerically under the basic presumption that the distribution function is homogeneous in configuration space. The results of numerical simulations demonstrate that the conservation laws of momentum and energy are obeyed accurately.