Numerical approximation of the Vlasov-Poisson-Fokker-Planck system in two dimensions. (English) Zbl 1175.82060
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 and E. Ozizmir, J. Comput. Phys. 202, No. 2, 602–644 (2005; Zbl 1067.82057)]. 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.
MSC:
| 82D10 | Statistical mechanics of plasmas |
| 76M28 | Particle methods and lattice-gas methods |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
| 76R50 | Diffusion |
Keywords:
collisional plasma; two-dimensional Vlasov-Poisson-Fokker-Planck system; deterministic particle methodCitations:
Zbl 1067.82057References:
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