A forward semi-Lagrangian method for the numerical solution of the Vlasov equation

Nicolas Crouseilles; Thomas Respaud; Eric Sonnendrücker

doi:10.1016/j.cpc.2009.04.024

A forward semi-Lagrangian method for the numerical solution of the Vlasov equation

Nicolas Crouseilles, Thomas Respaud, Eric Sonnendrücker

INRIA Institut National de Recherche en Informatique et en Automatique

Research output: Contribution to journal › Article › peer-review

94 Scopus citations

Abstract

This work deals with the numerical solution of the Vlasov equation, which provides a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation. A new forward semi-Lagrangian method is developed. The distribution function is updated on a Eulerian grid, and the pseudo-particles located on the mesh 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.

Original language	English
Pages (from-to)	1730-1745
Number of pages	16
Journal	Computer Physics Communications
Volume	180
Issue number	10
DOIs	https://doi.org/10.1016/j.cpc.2009.04.024
State	Published - Oct 2009
Externally published	Yes

Keywords

Eulerian solvers for Vlasov
Plasma simulation
Runge-Kutta
Semi-Lagrangian method

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10.1016/j.cpc.2009.04.024

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abstract = "This work deals with the numerical solution of the Vlasov equation, which provides a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation. A new forward semi-Lagrangian method is developed. The distribution function is updated on a Eulerian grid, and the pseudo-particles located on the mesh 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.",

keywords = "Eulerian solvers for Vlasov, Plasma simulation, Runge-Kutta, Semi-Lagrangian method",

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AU - Respaud, Thomas

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N2 - This work deals with the numerical solution of the Vlasov equation, which provides a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation. A new forward semi-Lagrangian method is developed. The distribution function is updated on a Eulerian grid, and the pseudo-particles located on the mesh 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.

AB - This work deals with the numerical solution of the Vlasov equation, which provides a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation. A new forward semi-Lagrangian method is developed. The distribution function is updated on a Eulerian grid, and the pseudo-particles located on the mesh 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.

KW - Eulerian solvers for Vlasov

KW - Plasma simulation

KW - Runge-Kutta

KW - Semi-Lagrangian method

UR - https://www.scopus.com/pages/publications/69349090877

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SP - 1730

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JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 10

ER -

A forward semi-Lagrangian method for the numerical solution of the Vlasov equation

Abstract

Keywords

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