A conservative semi-Lagrangian HWENO method for the Vlasov equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:323

Article

Cai, Xiaofeng¹  Qiu, Jianxian^1,2  Qiu, Jing-Mei³ 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[2] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Fujian, Peoples R China

[3] Univ Houston, Dept Math, Houston, TX 77204 USA

关键词: Mass conservative;    Semi-Lagrangian scheme;    HWENO reconstruction;    Vlasov-Poisson system;    Landau damping;    Two-stream instability;   

DOI  :  10.1016/j.jcp.2016.07.021

来源: Elsevier

【 摘 要 】

In this paper, we propose a high order conservative semi-Lagrangian (SL) finite difference Hermite weighted essentially non-oscillatory (HWENO) method for the Vlasov equation based on dimensional splitting. HWENO was first proposed for solving nonlinear hyperbolic problems by evolving both function values and its first derivative values (Qiu and Shu (2004)[23]). The major advantage of HWENO, compared with the original WENO, lies in its compactness in reconstruction stencils. There are several new ingredients in this paper. Firstly we propose a mass-conservative SL HWENO scheme for a 1-D equation by working with a flux-difference form, following the work of Qiu and Christlieb (2010)[25]. Secondly, we propose a proper splitting for equations of partial derivatives in HWENO framework to ensure local mass conservation. The proposed fifth order SL HWENO scheme with dimensional splitting has been tested to work well in capturing filamentation structures without oscillations when the time step size is within the Eulerian CFL constraint. However, when the time stepping size becomes larger, numerical oscillations are observed for the 'mass conservative' dimensional splitting HWENO scheme, as there are extra source terms in equations of partial derivatives. In this case, we introduce WENO limiters to control oscillations. Classical numerical examples on linear passive transport problems, as well as the nonlinear Vlasov-Poisson system, have been tested to demonstrate the performance of the proposed scheme. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free