A particle method for the homogeneous Landau equation

Jose A. Carrillo, Jingwei Hu, Li Wang, Jeremy Wu

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We propose a novel deterministic particle method to numerically approximate the Landau equation for plasmas. Based on a new variational formulation in terms of gradient flows of the Landau equation, we regularize the collision operator to make sense of the particle solutions. These particle solutions solve a large coupled ODE system that retains all the important properties of the Landau operator, namely the conservation of mass, momentum and energy, and the decay of entropy. We illustrate our new method by showing its performance in several test cases including the physically relevant case of the Coulomb interaction. The comparison to the exact solution and the spectral method is strikingly good maintaining 2nd order accuracy. Moreover, an efficient implementation of the method via the treecode is explored. This gives a proof of concept for the practical use of our method when coupled with the classical PIC method for the Vlasov equation.

Original languageEnglish (US)
Article number100066
JournalJournal of Computational Physics: X
Volume7
DOIs
StatePublished - Jun 2020

Bibliographical note

Publisher Copyright:
© 2020 The Authors

Keywords

  • Deterministic particle methods
  • Gradient flows
  • Landau equation for plasmas
  • Treecode

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