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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:324

Article

Yi, Dokkyun¹  Bu, Sunyoung² 

[1] Daegu Univ, Div Creat Integrated Gen Studies, Kyungsangbukdo 712714, South Korea

[2] Hongik Univ, Dept Liberal Arts, Sejong 30016, South Korea

关键词: Conservative scheme;    Vlasov equation;    Landau damping;   

DOI  :  10.1016/j.cam.2017.04.019

来源: Elsevier

【 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 L-1 and L-2 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. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free