Open Access

A conservative and non-oscillatory scheme for Vlasov code simulations

Earth, Planets and Space200860:BF03352826

DOI: 10.1186/BF03352826

Received: 25 September 2007

Accepted: 9 April 2008

Published: 4 August 2008

Abstract

A new numerical positive interpolation technique for conservation laws and its application to Vlasov code simulations are presented. In recent Vlasov simulation codes, the Vlasov equation is solved based on the numerical interpolation method because of its simplicity of algorithm and its ease of programming. However, a large number of grid points are needed in both configuration and velocity spaces to suppress numerical diffusion. In this paper we propose a new high-order interpolation scheme for Vlasov simulations. The current scheme is non-oscillatory and conservative and is well-designed for Vlasov simulations. This is compared with the latest interpolation schemes by performing one-dimensional electrostatic Vlasov simulations.

Key words

Vlasov equation hyperbolic equation numerical interpolation conservation laws