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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (11): 1475-1488.doi: https://doi.org/10.1007/s10483-011-1516-6

• Articles • 上一篇    下一篇

Sloshing simulation of standing wave with time-independent finite difference method for Euler equations

罗志强1 陈志敏2   

  1. 1. Department of System Science and Applied Mathematics, School of Science, Kunming University of Science and Technology, Kunming 650083, P. R. China;
    2. School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK
  • 收稿日期:2010-12-20 修回日期:2011-09-07 出版日期:2011-11-03 发布日期:2011-11-03

Sloshing simulation of standing wave with time-independent finite difference method for Euler equations

LUO Zhi-Qiang1, CHEN Zhi-Min2   

  1. 1. Department of System Science and Applied Mathematics, School of Science, Kunming University of Science and Technology, Kunming 650083, P. R. China;
    2. School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK
  • Received:2010-12-20 Revised:2011-09-07 Online:2011-11-03 Published:2011-11-03

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588

被引次数

7

摘要： The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional (2D) tank are studied. The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid. A time-independent finite difference method, which is developed by Bangfuh Chen, is used to solve the Euler equations for incompressible and inviscid fluids. The numerical results agree well with the analytic solutions and previously published results. The sloshing profiles of surge and heave motion with initial standing waves are presented. The results show very clear nonlinear and beating phenomena.

Abstract: The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional (2D) tank are studied. The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid. A time-independent finite difference method, which is developed by Bangfuh Chen, is used to solve the Euler equations for incompressible and inviscid fluids. The numerical results agree well with the analytic solutions and previously published results. The sloshing profiles of surge and heave motion with initial standing waves are presented. The results show very clear nonlinear and beating phenomena.

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