Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties

Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
13 Downloads (Pure)

Abstract

The study of uncertainty propagation is of fundamental importance in plasma physics simulations. To this end, in the present work we propose a novel stochastic Galerkin (sG) particle method for collisional kinetic models of plasmas under the effect of uncertainties. This class of methods is based on a generalized polynomial chaos (gPC) expansion of the particles' position and velocity. In details, we introduce a stochastic particle approximation for the Vlasov-Poisson system with a BGK term describing plasma collisions. A careful reformulation of such dynamics is needed to perform the sG projection and to obtain the corresponding system for the gPC coefficients. We show that the sG particle method preserves the main physical properties of the problem, such as conservations and positivity of the solution, while achieving spectral accuracy for smooth solutions in the random space. Furthermore, in the fluid limit the sG particle solver is designed to possess the asymptotic-preserving property necessary to obtain a sG particle scheme for the limiting Euler-Poisson system, thus avoiding the loss of hyperbolicity typical of conventional sG methods based on finite differences or finite volumes. We tested the schemes considering the classical Landau damping problem in the presence of both small and large initial uncertain perturbations, the two stream instability and the Sod shock tube problems under uncertainties. The results show that the proposed method is able to capture the correct behavior of the system in all test cases, even when the relaxation time scale is very small.

Original languageEnglish
Article number112011
JournalJournal of Computational Physics
Volume479
Early online date14 Feb 2023
DOIs
Publication statusPublished - 15 Apr 2023

Keywords

  • Asymptotic-preserving schemes
  • BGK model
  • Particle methods
  • Plasma physics
  • Stochastic Galerkin methods
  • Uncertainty quantification

ASJC Scopus subject areas

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

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