Charge-and-energy conserving moment-based accelerator for a multi-species Vlasov–Fokker–Planck–Ampère system, part I: Collisionless aspects

Abstract

In this study, we propose a charge, momentum, and energy conserving discretization for the 1D–1V Vlasov–Ampère system of equations on an Eulerian grid. The new conservative discretization is nonlinear in nature, but can be efficiently converged with a moment-based nonlinear accelerator algorithm. We demonstrate the conservation and convergence properties of the scheme with various numerical examples, including a multi-scale ion–acoustic shockwave problem.