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Fast Spectral Methods for the Fokker–Planck–Landau Collision Operator

✍ Scribed by L. Pareschi; G. Russo; G. Toscani

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
122 KB
Volume
165
Category
Article
ISSN
0021-9991

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✦ Synopsis

In this paper we present a new spectral method for the fast evaluation of the Fokker-Planck-Landau (FPL) collision operator. The method allows us to obtain spectrally accurate numerical solutions with simply O(n log 2 n) operations in contrast with the usual O(n 2 ) cost of a deterministic scheme. We show that the method preserves the total mass whereas momentum and energy are approximated with spectral accuracy. Numerical results for the FPL equation for Maxwell molecules and for Coulomb interactions in two and three dimensions in velocity space are also given.

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We present fast numerical algorithms to solve the nonlinear Fokker-Planck-Landau equation in 3D velocity space. The discretization of the collision operator preserves the properties required by the physical nature of the Fokker-Planck-Landau equation, such as the conservation of mass, momentum, an

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A new approach for the accurate numerical solution of the Fokker-Planck-Landau (FPL) equation in the nonhomogeneous case is presented. The method couples, through a time-splitting algorithm, a finite-volume scheme for the transport with a fast spectral solver for the efficient solution of the collis