A class of quadrature-based moment-closure methods with application to the Vlasov–Poisson–Fokker–Planck system in the high-field limit

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-BB-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.