Numerical approximation of the Vlasov–Poisson–Fokker–Planck system in two dimensions

A numerical method is developed for approximating the solution to the Vlasov–Poisson–Fokker–Planck system in two spatial dimensions. The method generalizes the approximation for the system in one dimension given in [S. Wollman, E. Ozizmir, Numerical approximation of the Vlasov–Poisson–Fokker–Planck...

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Bibliographic Details
Published in:Journal of computational physics 2009-10, Vol.228 (18), p.6629-6669
Main Authors: Wollman, Stephen, Ozizmir, Ercument
Format: Article
Language:English
Subjects:
Collisional plasma
Computational techniques
Deterministic particle method
Exact sciences and technology
Mathematical methods in physics
Physics
Two-dimensional Vlasov–Poisson–Fokker–Planck system
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Summary:A numerical method is developed for approximating the solution to the Vlasov–Poisson–Fokker–Planck system in two spatial dimensions. The method generalizes the approximation for the system in one dimension given in [S. Wollman, E. Ozizmir, Numerical approximation of the Vlasov–Poisson–Fokker–Planck system in one dimension, J. Comput. Phys. 202 (2005) 602–644]. The numerical procedure is based on a change of variables that puts the convection–diffusion equation into a form so that finite difference methods for parabolic type partial differential equations can be applied. The computational cycle combines a type of deterministic particle method with a periodic interpolation of the solution along particle trajectories onto a fixed grid. computational work is done to demonstrate the accuracy and effectiveness of the approximation method. Parts of the numerical procedure are adapted to run on a parallel computer.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.05.027