HAN Hong-yang, LUO Zhi-qiang. Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2016, 37(9): 953-968. doi: 10.21656/1000-0887.370118
Citation: HAN Hong-yang, LUO Zhi-qiang. Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2016, 37(9): 953-968. doi: 10.21656/1000-0887.370118

Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations

doi: 10.21656/1000-0887.370118
Funds:  The National Natural Science Foundation of China(11561037)
  • Received Date: 2016-04-14
  • Rev Recd Date: 2016-07-16
  • Publish Date: 2016-09-15
  • A predictor-corrector finite difference method based on the linearized Navier-Stokes equations was developed to numerically simulate the single- and double-vortex motions in 2D rectangular water tanks. Numerical results obtained with the present method were compared with the linearized analytical solution and previously published numerical results, and the agreements were pretty good. It is found that the free surface wave oscillates with a decaying amplitude in the case of viscous fluid, and as the Reynolds number increases, the free surface wave elevation decays more slowly. Under the short-period pitching excitation, a clear single vortex cycle occurs at different Reynolds numbers. However, the single vortex will change to double ones in the case of a long-period pitching excitation, only when the Reynolds number is small to some extent.
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  • [1]
    Abramson H N.The Dynamic Behavior of Liquids in Moving Containers [M]. Washington D C: National Aeronautics and Space Administration, 1966.
    Ibrahim R A.Liquid Sloshing Dynamics, Theory and Applications [M]. Cambridge University Press, 2005.
    Faltinsen O M, Timokha A N.Sloshing [M]. Cambridge University Press, 2009.
    XIN Zhou-ping, Yanagisawa T. Zero-viscosity limit of the linearized Navier-Stokes equations for a compressible viscous fluid in the half-plane[J].Communications on Puer and Applied Mathematics,1999,52(4): 479-541.
    Harlow F H, Welch J E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface[J].Physics of Fluids,1965,8(12): 2182-2189.
    Oden J T. Finite-element analogue of Navier-Stokes equations[J].Journal of the Engineering Mechanics Division,1970,96(4): 529-534.
    Sames P C, Marcouly D, Schellin T E. Sloshing in rectangular and cylindrical tanks[J].Journal of Ship Research,2002,46(3): 186-200.
    YUE Bao-zeng, LIU Yan-zhu. ALE finite element method for free surface Navier-Stokes flow using fractional step methods[J].Journal of Hydrodynamics,2003,18(4): 463-469.
    YANG Wei, LIU Shu-hong, LIN Hong. Viscous liquid sloshing damping in cylindrical container using a volume of fluid method[J].Science in China Series E: Technological Sciences,2009,52(6): 1484-1492.
    Lee H C. Weighted least-squares finite element methods for the linearized Navier-Stokes equations[J].International Journal of Computer Mathematics,2014,91(9): 1964-1985.
    CHEN Bang-fuh, Nokes R. Time-independent finite difference analysis of fully non-linear and viscous fluid sloshing in a rectangular tank[J].Journal of Computational Physics,2005,209(1): 47-81.
    CHEN Bang-fuh, WU Chih-hua. Effects of excitation angle and coupled heave-surge-sway motion on fluid sloshing in a three-dimensional tank[J].Journal of Marine Science and Technology,2011,16(1): 22-50.
    WU Chih-hua, CHEN Bang-fuh. Transient response of sloshing fluid in a three dimensional tank[J].Journal of Marine Science and Technology,2012,20(1): 26-37.
    WU Chih-hua, Faltinsen O M, CHEN Bang-fuh. Dynamics of vortex evolution in a 2D baffled tank[J].Computers and Mathematics With Applications,2016,71(1): 1-28.
    罗纪生, 周恒. 湍流边界层底层相干结构的一个理论模型[J]. 应用数学和力学, 1993,14(11): 939-947.(LUO Ji-sheng, ZHOU Heng. A theoretical model of the coherent structure in the wall region of a turbulent boundary layer[J].Applied Mathematics and Mechanics,1993,14(11): 939-947.(in Chinese))
    滕斌, 赵明, 何广华. 三维势流场的比例边界有限元求解方法[J]. 计算力学学报, 2006,23(3): 301-306.(TENG Bin, ZHAO Ming, HE Guang-hua. Computation of potential flow around three-dimensional obstacles by a scaled boundary finite-element method[J].Chinese Journal of Computational Mechanics,2006,23(3): 301-306.(in Chinese))
    菅永军, 鄂学全, 柏威. 参数激励圆柱形容器中的非线性Faraday波[J]. 应用数学和力学,2003,24(10): 1057-1068.(JIAN Yong-jun, E Xue-quan, BAI Wei. Nonlinear Faraday waves in a parametrcally excited circular cylindrical container[J].Applied Mathematics and Mechanics,2003,24(10): 1057-1068.(in Chinese))
    何银年. Navier-Stokes方程的有限元边界元耦合方法[J]. 计算物理, 2002,19(3): 217-220.(HE Yin-nian. The coupling method of FE and BE for the Navier-Stokes equation[J].Chinese Journal of Computational Physics,2002,19(3): 217-220.(in Chinese))
    LI Xin-liang, FU De-xun, MA Yan-wen, XIAN Liang. Direct numerical simulation of compressible turbulent flows[J].Acta Mechanica Sinica,2010,26(6): 795-806.
    陈豫眉, 谢小平. 非定常线性化Navier-Stokes方程的非协调流线扩散有限元法分析[J]. 应用数学和力学, 2010,31(7): 822-834.(CHEN Yu-mei, XIE Xiao-ping. Streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations[J].Applied Mathematics and Mechanics,2010,31(7): 822-834.(in Chinese))
    LUO Zhi-qiang, CHEN Zhi-min. Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations[J].Applied Mathematics and Mechanics(English Edition),2013,34(8): 931-944.
    罗志强, 陈志敏. 基于σ坐标变换下的Navier-Stokes方程数值模拟[J]. 南开大学学报(自然科学版), 2012,45(2): 55-61.(LUO Zhi-qing, CHEN Zhi-min. Numerical simulation of incompressible Navier-Stokes equations with σ coordinate transformations[J].Acta Scientiarum Naturalium Universitatis Nankaiensis,2012,45(2): 55-61.(in Chinese))
    WU Guo-xiong, Taylor R E, Greaves D M. The effect of viscosity on the transient free-surface waves in a two-dimensional tank[J].Journal of Engineering Mathematics,2001,40(1): 77-90.
    Mei C C.The Applied Dynamics of Ocean Surface Waves[M]//Liu L F, ed.Advanced Series on Ocean Engineering.Vol1. World Scientific Publishing Co Pte Ltd, 1989.
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