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

  • Authors:

  • Stephen Wollman;Ercument Ozizmir

  • Affiliations:

  • The College of Staten Island, CUNY, 2800 Victory Boulevard, Staten Island, NY 10314, USA;The College of Staten Island, CUNY, 2800 Victory Boulevard, Staten Island, NY 10314, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

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.