Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

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Abstract

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov–Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as f=E[ρf]+g, where E is a local equilibrium distribution, depending on the macroscopic moments ρf=∫Refdv=〈ef〉R, where [Formula presented], and g, the microscopic distribution, is defined such that 〈eg〉R=0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for ρf and g. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the 〈eg〉R=0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. We present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for f.

Original languageEnglish
Article number111227
JournalJournal of Computational Physics
Volume462
DOIs
StatePublished - Aug 1 2022

Funding

This research has been supported by the DOE Office of Advanced Scientific Computing Research through the SciDAC Partnership Center for High-fidelity Boundary Plasma Simulation under contract DE-AC05-00OR22725 with Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC for the U.S. Department of Energy.

Keywords

  • Discontinuous Galerkin
  • Hyperbolic conservation laws
  • Implicit-explicit
  • Kinetic equation
  • Lenard–Bernstein
  • Vlasov–Poisson

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