A Conservative Scheme for Vlasov Poisson Landau modeling collisional plasmas

TL;DR

This paper introduces a deterministic, conservative numerical scheme for the Vlasov-Poisson-Landau system in collisional plasmas, combining time-splitting, spectral, and discontinuous Galerkin methods with parallel computing.

Contribution

A novel conservative solver that accurately couples Vlasov-Poisson and Landau equations using specialized conservation routines and hybrid parallelization.

Findings

Successfully models Landau damping phenomena.

Accurately captures two-stream instability dynamics.

Demonstrates efficiency of parallel implementation.

Abstract

We have developed a deterministic conservative solver for the inhomogeneous Fokker-Planck-Landau equation coupled with the Poisson equation, which is a {classical mean-field} primary model for collisional plasmas. Two subproblems, i.e. the Vlasov-Poisson problem and homogeneous Landau problem, are obtained through time-splitting methods, and treated separately by the Runge-Kutta Discontinuous Galerkin method and a conservative spectral method, respectively. To ensure conservation when projecting between the two different computing grids, a special conservation routine is designed to link the solutions of these two subproblems. This conservation routine accurately enforces conservation of moments in Fourier space. The entire numerical scheme is implemented with parallelization with hybrid MPI and OpenMP. Numerical experiments are provided to study linear and nonlinear Landau Damping problems and two-stream flow problem as well.