A mass conservative scheme for solving the Vlasov–Poisson equation using characteristic curve

摘要

In this paper, we introduce a mass conservative scheme for solving the Vlasov–Poisson equation. This scheme is based on an Eulerian approach and is constructed using an interpolation scheme with limiters. In order to preserve the mass, the difference in the values for numerical flux functions on each cell is used; for this, the flux functions are constructed by preserving both the solution along a characteristics and the mass in each cell. We mainly investigate the conservation of L1 and L2 norms of the distribution function, total energy, entropy, and minimum value. In addition, we show that this scheme is bounded on the total variation. To demonstrate the efficiency of the proposed scheme, this scheme is compared with the flux balance scheme, Positive and Flux Conservative scheme, Umeda’s scheme, and fifth order WENO reconstruction finite volume scheme.