Earth Planets Space, Vol. 60 (No. 7), pp. 773-779, 2008
Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8601, Japan
(Received September 25, 2007; Revised February 28, 2008; Accepted April 9, 2008; Online published August 4, 2008)
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.