Numerical simulation of wave transformation and runup incorporating porous media wave absorber and turbulence models

Abstract A numerical wave tank is first established using the Navier–Stokes equations and the VOF method assuming laminar flow. The standard k–e, realizable k–e and RNG k–e turbulent models are then incorporated to the numerical tank. An effective numerical method for wave absorption utilizing the energy-dissipating property of porous media is also included. To validate the accuracy of the proposed models, the propagation of a solitary wave, where analytical solution is available for comparison, is first simulated. This is followed by the simulation of irregular wave runup on a composite seawall, wave propagation over submerged bars and wave refraction and diffraction over an elliptic shoal, where experimental data are available for comparison. All computed results agree well with either the analytical solution or the experimental data.

[1]  D. A. Barry,et al.  Numerical simulation of surf-swash zone motions and turbulent flow , 2009 .

[2]  Pengzhi Lin,et al.  A numerical study of breaking waves in the surf zone , 1998, Journal of Fluid Mechanics.

[3]  I. A. Svendsen,et al.  BREAKING CRITERION AND CHARACTERISTICS FOR SOLITARY WAVES ON SLOPES , 1997 .

[4]  S. Shao,et al.  Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling , 2006 .

[5]  Pierre Lubin,et al.  Three-dimensional Large Eddy Simulation of air entrainment under plunging breaking waves , 2006 .

[6]  C. Vincent,et al.  REFRACTION-DIFFRACTION OF IRREGULAR WAVES OVER A MOUND , 1989 .

[7]  Emilio F. Campana,et al.  A level set technique applied to unsteady free surface flows , 2001 .

[8]  Hitoshi Gotoh,et al.  SPH-LES Model for Numerical Investigation of Wave Interaction with Partially Immersed Breakwater , 2004 .

[9]  Akihide Tada,et al.  Applicability of numerical models to nonlinear dispersive waves , 1995 .

[10]  Scott F. Bradford.  Numerical Simulation of Surf Zone Dynamics , 2000 .

[11]  Stéphane Zaleski,et al.  TWO-DIMENSIONAL NAVIER-STOKES SIMULATION OF BREAKING WAVES , 1996, comp-gas/9605002.

[12]  Philippe Fraunié,et al.  Solitary wave breaking on sloping beaches: 2-D two phase flow numerical simulation by SL-VOF method , 2001 .

[13]  Chebyshev Finite-Spectral Method for 1D Boussinesq-Type Equations , 2006 .

[14]  Michael Selwyn Longuet-Higgins,et al.  The deformation of steep surface waves on water - I. A numerical method of computation , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[15]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986 .

[16]  Y. Li,et al.  Numerical modelling of multi-directional irregular waves through breakwaters , 2000 .

[17]  V. C. Patel,et al.  Numerical simulation of unsteady multidimensional free surface motions by level set method , 2003 .

[18]  Jurjen A. Battjes,et al.  Numerical simulation of nonlinear wave propagation over a bar , 1994 .

[19]  Franklin Liu,et al.  Modeling wave runup with depth-integrated equations , 2002 .

[20]  T. Shih,et al.  A new k-ϵ eddy viscosity model for high reynolds number turbulent flows , 1995 .

[21]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986, Physical review letters.

[22]  Qun Zhao,et al.  Numerical simulation of breaking waves by a multi-scale turbulence model , 2004 .

[23]  C. M. Lemos.  A simple numerical technique for turbulent flows with free surfaces , 1992 .

[24]  Kuang-An Chang,et al.  Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part II: Cnoidal waves , 2001 .

[25]  Phung Dang Hieu,et al.  Numerical simulation of breaking waves using a two-phase flow model , 2004 .

[26]  Jurjen A. Battjes,et al.  Experimental investigation of wave propagation over a bar , 1993 .

[27]  Ching Jer Huang,et al.  Numerical Simulation of Nonlinear Viscous Wavefields Generated by Piston-Type Wavemaker , 1998 .

[28]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[29]  Chiu-On Ng,et al.  Simulation of wave propagation over a submerged bar using the VOF method with a two-equation k-e turbulence modeling , 2004 .

[30]  B. Launder,et al.  Lectures in mathematical models of turbulence , 1972 .

[31]  Ira Didenkulova,et al.  Two- and three-dimensional computation of solitary wave runup on non-plane beach , 2008 .

[32]  Ying Li,et al.  Solitary Wave Runup on Plane Slopes , 2001 .

[33]  Erik Damgaard Christensen,et al.  Large eddy simulation of breaking waves , 2001 .