A Class of Quadrature-Based Moment-Closure Methods with Application to the Vlasov-Poisson-Fokker-Planck System in the High-Field Limit

TL;DR

This paper develops quadrature-based moment-closure methods with high-order DG schemes to efficiently approximate the Vlasov-Poisson-Fokker-Planck system in the high-field limit, demonstrating their asymptotic-preserving property.

Contribution

It introduces a high-order DG scheme for quadrature-based moment-closure models applied to the Vlasov-Poisson-Fokker-Planck system, showing their asymptotic-preserving behavior.

Findings

The scheme accurately captures high-field limit behavior.

Numerical results confirm asymptotic-preserving property.

The methods effectively reduce dimensionality of kinetic models.

Abstract

Quadrature-based moment-closure methods are a class of approximations that replace high-dimensional kinetic descriptions with lower-dimensional fluid models. In this work we investigate some of the properties of a sub-class of these methods based on bi-delta, bi-Gaussian, and bi-B-spline representations. We develop a high-order discontinuous Galerkin (DG) scheme to solve the resulting fluid systems. Finally, via this high-order DG scheme and Strang operator splitting to handle the collision term, we simulate the fluid-closure models in the context of the Vlasov-Poisson-Fokker-Planck system in the high-field limit. We demonstrate numerically that the proposed scheme is asymptotic-preserving in the high-field limit.