Abstract
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.
Highlights
Kinetic simulations are essential approaches to the study of nonlinear microscopic processes in space plasmas
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
An advantage of Vlasov codes is that thermal fluctuations, which are strongly enhanced in particle-in-cell simulations, can be suppressed
Summary
Kinetic simulations are essential approaches to the study of nonlinear microscopic processes in space plasmas. A limitation on the number of particles gives rise to numerical thermal fluctuations Another approach is Vlasov simulation, which follows the spatial and temporal development of distribution functions in the position-velocity phase space. Umeda et al (2006) compared recent interpolation schemes for long-time and nonlinear kinetic processes in space plasmas They concluded that non-oscillatory, shapepreserving, conservative, positivity-preserving, low numerical diffusion, and computer-memory saving are necessary properties of interpolation schemes for Vlasov simulations. The numerical flux is given as ν fi+1 It is well-known that a high-order scheme is oscillatory and generates new extrema, i.e., local maximum or minimum (Godunov, 1959). The present scheme is a modified version of the PFC scheme
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