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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (3): 319-330.doi: 10.3969/j.issn.1005-3085.2016.03.010

• • 上一篇    

Navier-Stokes方程自由面数值模拟

黄玉萍,   罗志强   

  1. 昆明理工大学理学院，昆明 650500
  • 收稿日期:2015-03-13 接受日期:2015-11-10 出版日期:2016-06-15 发布日期:2016-08-15
  • 通讯作者: 罗志强 E-mail: zql1009@126.com
  • 基金资助:
    国家自然科学基金 (11561037)；云南省教委研究基金 (2015z035).

Numerical Simulation of Free Surface for Navier-Stokes Equations

HUANG Yu-ping,   LUO Zhi-qiang   

  1. School of Science, Kunming University of Science and Technology, Kunming 650500
  • Received:2015-03-13 Accepted:2015-11-10 Online:2016-06-15 Published:2016-08-15
  • Contact: Z. Luo. E-mail address: zql1009@126.com
  • Supported by:
    The National Natural Science Foundation of China (11561037); the Research Foundation of Educational Commission of Yunnan Province of China (2015z035).

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摘要： 本文建立了不可压缩Navier-Stokes方程的Crank-Nicolson有限差分方法，数值模拟二维水槽的自由面波高．数值模拟研究了在不同的激励加速度和雷诺数下自由面波高，目前的数值方法很好地吻合了之前出版的结果．数值解结果表明自由面波高随时间在逐步地衰减，拍的周期数随雷诺数的增加也在减少．最后，自由面的波高随雷诺数的减少自由面的波高保持一个相对的稳定的波高．

关键词: Navier-Stokes方程, 有限差分方法, Reynolds数, 耗散现象

Abstract:

A Crank-Nicolson finite difference method for incompressible Navier-Stokes equations is developed and is applied to find the numerical solution of wave elevation on the free surface in a two dimensional tank. The numerical simulation of wave elevation on the free surface is studied with different excited accelerations and Reynolds number. From the benchmarks, the proposed finite difference method agrees well with the previous published works. As shown in the numerical results, we draw a conclusion that the wave elevations decay gradually with time. The number of the beating periods diminish gradually when the Reynolds number decreases. Finally, we find that the wave elevations on the free surface keep a related stable height, when the Reynolds number decreases.

Key words: Navier-Stokes equations, finite difference method, Reynolds number, dissipative phenomenon

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