Particle simulation methods for the Landau-Fokker-Planck equation with uncertain data

Andrea Medaglia*, Lorenzo Pareschi, Mattia Zanella

*Corresponding author for this work

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The design of particle simulation methods for collisional plasma physics has always represented a challenge due to the unbounded total collisional cross section, which prevents a natural extension of the classical Direct Simulation Monte Carlo (DSMC) method devised for the Boltzmann equation. One way to overcome this problem is to consider the design of Monte Carlo algorithms that are robust in the so-called grazing collision limit. In the first part of this manuscript, we will focus on the construction of collision algorithms for the Landau-Fokker-Planck equation based on the grazing collision asymptotics and which avoids the use of iterative solvers. Subsequently, we discuss problems involving uncertainties and show how to develop a stochastic Galerkin projection of the particle dynamics which permits to recover spectral accuracy for smooth solutions in the random space. Several classical numerical tests are reported to validate the present approach.

Original languageEnglish
Article number112845
JournalJournal of Computational Physics
Early online date13 Feb 2024
Publication statusPublished - 15 Apr 2024


  • Landau-Fokker-Planck equation
  • Particle methods
  • Plasma physics
  • Stochastic Galerkin methods
  • Uncertainty quantification

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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