Quadrature-based moment methods for kinetic plasma simulations

Abstract

Quadrature-based moment methods (QBMM) are applied to rarefied gas flow and plasma physics problems represented by the Boltzmann equation or the Vlasov-Poisson system of equations. QBMM are a computationally advantageous alternative to both direct Eulerian and Lagrangian particle solvers, able to provide a noise-free solution to the Boltzmann equation 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. Three QBMM approaches, QMOM (Dirac delta kernels), HyQMOM (hyperbolic QMOM), and EQMOM (Gaussian kernels), are applied to canonical one-dimensional rarefied gas flow and plasma physics problems. A new algorithm for EQMOM that is able to treat pathological VDFs and provide control over large abscissas for more than two nodes is developed. QMOM and EQMOM are suitable for problems where the flow does not have shock-like features (for QMOM) or a discontinuity in the VDF (for EQMOM) and where the VDF is far from non-equilibrium and features strong phase-mixing. HyQMOM is generally applicable to all test problems and yields good representations of both the moments and the VDF. HyQMOM also provides significant wall-time improvement (factor of 10–100) compared to other direct Eulerian solvers.