A Vlasov Algorithm Derived from Phase Space Conservation

TL;DR

This paper introduces a novel Vlasov algorithm based on phase space conservation, utilizing particle-pushing methods and grid convolution to improve flexibility and accuracy in solving the Vlasov equation.

Contribution

It proposes a new approach that models the Vlasov equation as a conservative flow on phase space, differing from traditional PDE grid methods.

Findings

Demonstrates numerical examples validating the algorithm

Shows flexibility in grid definitions independent of phase space flow

Comments on the algorithm's properties and potential advantages

Abstract

Existing approaches to solving the Vlasov equation treat the system as a partial differential equation on a phase space grid, and track in either an Eulerian, Lagrangian, or semi-Lagrangian picture. We present an alternative approach, which treats the Vlasov equation as a conservative flow on phase space, and derives its equations of motion using particle-pushing algorithms akin to particle-in-cell methods. Deposition to the grid is determined from the convolution of local basis functions. This approach has the benefit of allowing flexible definitions in the grid, which are decoupled from how the phase space flow evolves. We present numerical examples and comment on the various properties of the algorithm.