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

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.