A new fully non‐hydrostatic 3D free surface flow model for water wave motions

A new fully non-hydrostatic model is presented by simulating three-dimensional free surface flow on a vertical boundary-fitted coordinate system. A projection method, known as pressure correction technique, is employed to solve the incompressible Euler equations. A new grid arrangement is proposed under a horizontal Cartesian grid framework and vertical boundary-fitted coordinate system. The resulting model is relatively simple. Moreover, the discretized Poisson equation for pressure correction is symmetric and positive definite, and thus it can be solved effectively by the preconditioned conjugate gradient method. Several test cases of surface wave motion are used to demonstrate the capabilities and numerical stability of the model. Comparisons between numerical results and analytical or experimental data are presented. It is shown that the proposed model could accurately and effectively resolve the motion of short waves with only two layers, where wave shoaling, nonlinearity, dispersion, refraction, and diffraction phenomena occur. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[2]  R. T. Cheng,et al.  SEMI-IMPLICIT FINITE DIFFERENCE METHODS FOR THREE-DIMENSIONAL SHALLOW WATER FLOW , 1992 .

[3]  Jeffrey W. Gartner,et al.  Tidal, Residual, Intertidal Mudflat (TRIM) Model and its Applications to San Francisco Bay, California , 1993 .

[4]  Harry B. Bingham,et al.  On the accuracy of finite-difference solutions for nonlinear water waves , 2007 .

[5]  Harry B. Bingham,et al.  Numerical solutions of fully non‐linear and highly dispersive Boussinesq equations in two horizontal dimensions , 2004 .

[6]  Roger Alexander Falconer,et al.  An implicit numerical algorithm for solving non-hydrostatic free-surface flow problems , 2001 .

[7]  Marcel Zijlema,et al.  Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure , 2008 .

[8]  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 .

[9]  Marcel Zijlema,et al.  Further experiences with computing non‐hydrostatic free‐surface flows involving water waves , 2005 .

[10]  Vincenzo Casulli,et al.  A SEMI-IMPLICIT FINITE DIFFERENCE METHOD FOR NON-HYDROSTATIC, FREE-SURFACE FLOWS , 1999 .

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

[12]  A three‐dimensional non‐hydrostatic vertical boundary fitted model for free‐surface flows , 2008 .

[13]  Per A. Madsen,et al.  A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry , 2006 .

[14]  A 3‐D non‐hydrostatic pressure model for small amplitude free surface flows , 2006 .

[15]  Chin H. Wu,et al.  A new efficient 3D non-hydrostatic free-surface flow model for simulating water wave motions , 2006 .

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

[17]  Hengliang Yuan,et al.  An implicit three‐dimensional fully non‐hydrostatic model for free‐surface flows , 2004 .

[18]  Pengzhi Lin,et al.  A σ‐coordinate three‐dimensional numerical model for surface wave propagation , 2002 .

[19]  Marcel Zijlema,et al.  An accurate and efficient finite‐difference algorithm for non‐hydrostatic free‐surface flow with application to wave propagation , 2003 .

[20]  Chin H. Wu,et al.  An efficient and accurate non‐hydrostatic model with embedded Boussinesq‐type like equations for surface wave modeling , 2009 .

[21]  A. C. Radder,et al.  Verification of numerical wave propagation models for simple harmonic linear water waves , 1982 .

[22]  J. Berkhoff,et al.  Mathematical models for simple harmonic linear water waves: Wave diffraction and refraction , 1976 .

[23]  Xinjian Chen.  A fully hydrodynamic model for three‐dimensional, free‐surface flows , 2003 .

[24]  Hamn-Ching Chen,et al.  CFD simulations of wave–current-body interactions including greenwater and wet deck slamming , 2009 .

[25]  Harry B. Bingham,et al.  An efficient flexible-order model for 3D nonlinear water waves , 2009, J. Comput. Phys..

[26]  Serdar Beji,et al.  A FULLY-DISPERSIVE NONLINEAR WAVE MODEL AND ITS NUMERICAL SOLUTIONS , 1995 .

[27]  Hengliang Yuan,et al.  Fully Nonhydrostatic Modeling of Surface Waves , 2006 .

[28]  Robert L. Street,et al.  On Simulation of Turbulent Nonlinear Free-Surface Flows , 1999 .

[29]  Dong-Soo Hur,et al.  Numerical estimation of the wave forces acting on a three-dimensional body on submerged breakwater , 2003 .