中国物理B ›› 2018, Vol. 27 ›› Issue (2): 20202-020202.doi: 10.1088/1674-1056/27/2/020202

• GENERAL • 上一篇    下一篇

A local energy-preserving scheme for Zakharov system

Qi Hong(洪旗), Jia-ling Wang(汪佳玲), Yu-Shun Wang(王雨顺)   

  1. 1. Graduate School of China Academy of Engineering Physics, Beijing 100088, China;
    2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;
    3. Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
  • 收稿日期:2017-08-11 修回日期:2017-10-16 出版日期:2018-02-05 发布日期:2018-02-05
  • 通讯作者: Jia-ling Wang E-mail:wjl19900724@126.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11771213) and the Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology (Grant No. 2243141701090).

A local energy-preserving scheme for Zakharov system

Qi Hong(洪旗)1, Jia-ling Wang(汪佳玲)2, Yu-Shun Wang(王雨顺)3   

  1. 1. Graduate School of China Academy of Engineering Physics, Beijing 100088, China;
    2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;
    3. Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
  • Received:2017-08-11 Revised:2017-10-16 Online:2018-02-05 Published:2018-02-05
  • Contact: Jia-ling Wang E-mail:wjl19900724@126.com
  • About author:02.60.Cb; 02.70.Bf; 02.60.Lj
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11771213) and the Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology (Grant No. 2243141701090).

摘要: In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local time-space region which is independent of the boundary condition and more essential than the global energy conservation law. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose a local energy-preserving (LEP) scheme for the system. The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region. With homogeneous Dirchlet boundary conditions, the proposed LEP scheme also possesses the discrete global mass and energy conservation laws. The theoretical properties are verified by numerical results.

关键词: Zakharov system, local energy-preserving scheme, global mass and energy conservation laws

Abstract: In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local time-space region which is independent of the boundary condition and more essential than the global energy conservation law. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose a local energy-preserving (LEP) scheme for the system. The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region. With homogeneous Dirchlet boundary conditions, the proposed LEP scheme also possesses the discrete global mass and energy conservation laws. The theoretical properties are verified by numerical results.

Key words: Zakharov system, local energy-preserving scheme, global mass and energy conservation laws

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
02.70.Bf (Finite-difference methods) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)