A Forward semi-Lagrangian Method for the Numerical Solution of the Vlasov Equation

TL;DR

This paper introduces a forward semi-Lagrangian numerical method for solving the nonlinear Vlasov equation, enabling explicit high-order time schemes and improving computational efficiency in plasma simulations.

Contribution

A novel forward semi-Lagrangian approach based on explicit characteristic integration for the Vlasov equation, simplifying high-order scheme development.

Findings

Enables explicit high-order time integration schemes.

Improves computational efficiency for plasma simulations.

Facilitates development of advanced numerical methods.

Abstract

This work deals with the numerical solution of the Vlasov equation. This equation gives a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation for the computation of the self-consistent electric field. The coupled model is non linear. A new semi-Lagrangian method, based on forward integration of the characteristics, is developed. The distribution function is updated on an eulerian grid, and the pseudo-particles located on the mesh's nodes follow the characteristics of the equation forward for one time step, and are deposited on the 16 nearest nodes. This is an explicit way of solving the Vlasov equation on a grid of the phase space, which makes it easier to develop high order time schemes than the backward method.