An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Amp\`ere system

TL;DR

This paper introduces a highly efficient, conservative, time-implicit solver for the fully kinetic 1D-2V Vlasov-Ampère system with adaptive velocity-space meshing, ensuring accuracy and conservation in complex plasma simulations.

Contribution

It presents a novel implicit Eulerian solver with adaptive velocity transformation and high-order/low-order acceleration for the Vlasov-Ampère system, improving efficiency and conservation.

Findings

Solver conserves mass, momentum, and energy.

Demonstrates accuracy on canonical plasma problems.

Achieves efficiency in multiscale ion-acoustic shock simulations.

Abstract

We consider the solution of the fully kinetic (including electrons) Vlasov-Amp\`ere system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.