H.Saghi, M.J.Ketabdari, S.Booshi. Generation of Linear and Nonlinear Waves in a Numerical Wave Tank Using CT-VOF Method[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1102-1114. doi: 10.3879/j.issn.1000-0887.2012.09.007
Citation: H.Saghi, M.J.Ketabdari, S.Booshi. Generation of Linear and Nonlinear Waves in a Numerical Wave Tank Using CT-VOF Method[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1102-1114. doi: 10.3879/j.issn.1000-0887.2012.09.007

Generation of Linear and Nonlinear Waves in a Numerical Wave Tank Using CT-VOF Method

doi: 10.3879/j.issn.1000-0887.2012.09.007
  • Received Date: 2011-06-06
  • Rev Recd Date: 2011-12-28
  • Publish Date: 2012-09-15
  • A two-dimensional numerical model was developed for wave simulation and propagation in a wave flume. The fluid flow was assumed to be viscous and incompressible and NavierStokes and continuity equations were used as governing equations. Standard k-ε model was used to model turbulent flow. The Navier-Stokes equations were discretized using staggered grids finite difference method and solved by SMAC method. Waves were generated and propagated using a piston type wave maker. An open boundary condition was used at the end of numerical flume. Some standard tests such as lid-driven cavity, constant unidirectional velocity field, shearing flow and dambreak on dry bed were performed to validate the model. To demonstrate the capability and accuracy of the present method, the results of generated waves were compared with available wave theories. Finally, clustering technique (CT) was used for mesh generation and the best condition was suggested.
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  • [1]
    Contento G. Numerical wave tank computations of nonlinear motions of two-dimensional arbitrarily shaped free floating bodies[J]. Ocean Engineering, 2000, 27(5): 531-556.
    [2]
    Grilli S T, Vogelmenn S, Watts P. Development of a 3D numerical wave tank for modeling tsunami generation by underwater landslides[J]. Engineering Analysis With Boundary Elements, 2002, 26(4): 301-313.
    [3]
    Fochesato C, Grilli S, Dias F. Numerical modeling of extreme rogue waves generated by directional energy focusing[J]. Wave Motion, 2007, 44(5): 395-416.
    [4]
    Ducrozet G, Bonnefoy F, Le Touzé D, Ferrant P. A modified high-order spectral method for wavemaker modeling in a numerical wave tank[J]. European Journal of Mechanics B/Fluids, 2012, 34:19-34.
    [5]
    Park J C, Kim M H, Miyata H, Chun H H. Fully nonlinear numerical wave tank (NWT) simulations and wave run-up prediction around 3-D structures[J]. Ocean Engineering, 2003, 30(15): 1969-1996.
    [6]
    Li Y, Lin M. Regular and irregular wave impacts on floating body[J]. Ocean Engineering, 2012, 42: 93-101.
    [7]
    Rudman M. Volume-tracking methods for interfacial flow calculations[J]. International Journal for Numerical Methods in Fluids, 1997, 24: 671-691.
    [8]
    Troch P, De Rouck J. An active wave generating-absorbing boundary condition for VOF type numerical model[J]. Coastal Engineering, 1999, 38(4): 223-247.
    [9]
    Choi J W, Yoon S B. Numerical simulation using momentum source wave-maker applied RANSE equation model[J]. Coastal Engineering, 2009, 56(10): 1043-1060.
    [10]
    Zhao X Z, Hu C H, Sun Z C. Numerical simulation of extreme wave generation using VOF method[J]. Journal of Hydrodynamics, 2010, 22(4): 466-477.
    [11]
    Schffer H A, Steenberg C M. Second-order wavemaker theory for multidirectional waves[J]. Ocean Engineering, 2003, 30(10): 1203-1231.
    [12]
    TENG Bin, NING De-zhi. A simplified model for extreme-wave kinematics in deep sea[J]. J Marine Sci Appl, 2009, 8(1): 27-32.
    [13]
    魏岗, 乐嘉春, 戴世强. 有限深度两层流体系统中运动点源生成的内波及其与自由面的相互作用[J]. 应用数学和力学,2003, 24(9): 906-918.(WEI Gang, LE Jia-chun, DAI Shi-qiang. Surface effects on internal wave generated by a moving source in a two-layer fluid of finite depth[J]. Applied Mathematics and Mechanics(English Edition), 2003, 24(9): 1025-1040.)
    [14]
    Lara J L, Garcia N, Losada I J. RANS modelling applied to random wave interaction with submerged permeable structure[J]. Coastal Engineering, 2006, 113(3): 396-417.
    [15]
    Lin P, Karunarathna S A S. Numerical study of solitary wave interaction with porous breakwaters[J]. Journal of Waterway, Port, Coastal and Ocean Engineering, 2007, 133(5): 352-363.
    [16]
    Shin S, Bae S Y, Kim I C, Kim Y J, Yoo H K. Simulation of free surface flows using the flux-difference splitting scheme on the hybrid Cartesian/immersed boundary method[J]. International Journal for Numerical Methods in Fluids, 2012, 68(3): 360-376.
    [17]
    Rafei R. Numerical solution of incompressible 3D turbulent flow in a spiral channel[D]. M Sc Thesis. Tehran, Iran: Amirkabir University of Technology, 2004.
    [18]
    Li C W, Zang Y F. Simulation of free surface recirculating flows in semi-enclosed water bodies by a k-w model[J]. Applied Mathematical Modeling, 1998, 22(3): 153-164.
    [19]
    Gao H, Gu H Y, Guo L J. Numerical study of stratified oil-water two-phase turbulent flow in a horizontal tube[J]. Int J Heat Mass Transfer, 2003, 46(4): 749-754.
    [20]
    Ren B, Wang Y. Numerical simulation of random wave slamming on structures in the splash zone[J]. Ocean Engineering, 2004, 31(5/6): 547-560.
    [21]
    Shen Y M, Ng C O, Zheng Y H. Simulation of wave propagation over a submerged bar using the VOF method with a two-equation k-ε turbulence modeling[J]. Ocean Engineering, 2004, 31(1): 87-95.
    [22]
    Mirbagheri S M H, Dadashzadeh M, Serajzadeh S, Taheri A K, Davami P. Modeling the effect of mould wall roughness on the melt flow simulation in casting process[J]. Applied Mathematical Modeling, 2004, 28(11): 933-956.
    [23]
    Geuyffier D, Li J, Nadim A, Scardovelli R, Zaleski S. Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows[J]. Journal of Computational Physics, 1999, 152(2): 423-456.
    [24]
    Harvie D J E, Fletcher D F. A new volume of fluid advection algorithm: the defined donating region scheme[J]. International Journal for Numerical Methods in Fluids, 2001, 35(2): 151-172.
    [25]
    Ketabdari M J, Nobari M R H, Larmaei M M. Simulation of waves group propagation and breaking in coastal zone using a Navier-Stokes solver with an improved VOF free surface treatment[J]. Applied Ocean Research, 2008, 30(2): 130-143.
    [26]
    Hur D S, Mizutani M. Numerical estimation of the wave forces acting on a three-dimensional body on submerged breakwater[J]. Coast Eng, 2003, 47(3): 329-345.
    [27]
    Duff E S. Fluid flow aspects of solidification modeling, simulation of low pressure Die casting[D]. PhD Thesis. Brisbane: University of Queenland, 1999.
    [28]
    Ghia U, Ghia K N, Shin C T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method[J]. Journal of Computational Physics, 1982, 48(3): 387-411.
    [29]
    Scardovelli R, Zaleski S. Interface reconstruction with least-square fit and split Eulerian-Lagrangian advection[J]. International Journal of Numerical Methods in Fluids, 2003, 41(3): 251-274.
    [30]
    Martin J C, Moyce W J. An experimental study of the collapse of liquid columns on a rigid horizontal plane[J]. Philosophical Transaction of the Royal Society of London, 1952, 244(882): 312-324.
    [31]
    Shen Y M, Ng C O, Zheng Y H. Simulation of wave propagation over a submerged bar using the VOF method with a two-equation k-ε turbulence modeling[J]. Ocean Eng, 2004, 31(1): 87-95.
    [32]
    Boussinesq M J. Théorie de l’intumescence liquide, appelée onde solitaire ou de translation se propageant dans un canal rectangulaire[J]. C R Acad Sci(Paris), 1871, 72: 755-759.
    [33]
    Rayleigh L. On waves[J]. Phil Mag, 1876, 1: 257-279.
    [34]
    Clamond D, Germain J P. Interaction between a Stokes wave packet and a solitary wave[J]. Eur J Mech B/Fluids, 1999, 18(1): 67-91.
    [35]
    Temperville A. Contribution  l’étude des ondes de gravité en eau peu profonde[D]. Thèse d’Etat. Université Joseph Fourier-Grenoble I, 1985.
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