Quadrature-based moment methods for kinetic plasma simulations

Quadrature-based moment methods (QBMM) are applied to plasma physics problems represented by the Vlasov-Poisson system of equations. QBMM are a  computationally advantageous alternative to both direct and Lagrangian particle solvers, able to provide a noise-free solution to the Vlasov-Poisson system of equations and capture non-equilibrium velocity distribution functions (VDF) without excessive computational cost. To provide a closure of the moment equations, the VDF is assumed to be represented by the sum of weighted kernel functions that are placed at given velocity abscissas. The weights and abscissas on which the VDF depend are retrieved through a non-linear inversion procedure that relies on the transported moments. Two QBMM approaches, QMOM¹ (Dirac delta kernels) and EQMOM² (Gaussian kernels) are applied to canonical one-dimensional plasma physics problems. The results of QBMM compare favorably to that of a direct solver but at a lower computational cost. The proposed methods appear to be a promising alternative to existing solvers for multi-fluid kinetic plasma simulations.

1 R. Fox, J. Comp. Phys., 227, 12, 2008

2 C. Chalons et al., Mult. Mod. & Sim., 15, 4, 2017