A meshless numerical wave tank for simulation of nonlinear irregular waves in shallow water

Time domain simulation of the interaction between offshore structures and irregular waves in shallow water becomes a focus due to significant increase of liquefied natural gas (LNG) terminals. To obtain the time series of irregular waves in shallow water, a numerical wave tank is developed by using the meshless method for simulation of 2D nonlinear irregular waves propagating from deep water to shallow water. Using the fundamental solution of Laplace equation as the radial basis function (RBF) and locating the source points outside the computational domain, the problem of water wave propagation is solved by collocation of boundary points. In order to improve the computation stability, both the incident wave elevation and velocity potential are applied to the wave generation. A sponge damping layer combined with the Sommerfeld radiation condition is used on the radiation boundary. The present model is applied to simulate the propagation of regular and irregular waves. The numerical results are validated by analytical solutions and experimental data and good agreements are observed.

[1]  Xiong Zhang,et al.  Meshless methods based on collocation with radial basis functions , 2000 .

[2]  Nan-Jing Wu,et al.  Meshless numerical simulation for fully nonlinear water waves , 2006 .

[3]  Xiaoming Wang,et al.  Subelement Division Scheme in a Numerical Wave Tank that Uses Higher-Order Boundary Element Method , 2007 .

[4]  R. Coifman,et al.  Fast wavelet transforms and numerical algorithms I , 1991 .

[5]  Pei Wang,et al.  An efficient numerical tank for non-linear water waves, based on the multi-subdomain approach with BEM , 1995 .

[6]  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.

[7]  Dezhi Ning,et al.  Numerical simulation of fully nonlinear irregular wave tank in three dimension , 2007 .

[8]  W. Hackbusch,et al.  On the fast matrix multiplication in the boundary element method by panel clustering , 1989 .

[9]  Guirong Liu,et al.  A point interpolation meshless method based on radial basis functions , 2002 .

[10]  G. Wu,et al.  Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 1: methodology and numerical procedure , 2001 .

[11]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[12]  Riccardo Codiglia,et al.  Nonlinear effects in 2D transient nonbreaking waves in a closed flume , 2001 .

[13]  Hideaki Miyata,et al.  Fully non‐linear free‐surface simulations by a 3D viscous numerical wave tank , 1999 .

[14]  Stephan T. Grilli,et al.  Numerical study of three-dimensional overturning waves in shallow water , 2006, Journal of Fluid Mechanics.

[15]  Alain H. Clément,et al.  Recent Research And Development of Numerical Wave Tank - A Review , 1999 .

[16]  J. H. Kyoung,et al.  Numerical Computations for a Nonlinear Free Surface Problem in Shallow Water , 2003 .

[17]  Per A. Madsen,et al.  A REVIEW OF BOUSSINESQ-TYPE EQUATIONS FOR SURFACE GRAVITY WAVES , 1999 .

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

[19]  Philippe Fraunié,et al.  Numerical Analysis of the Internal Kinematics And Dynamics of 3-D Breaking Waves On Slopes , 2004 .

[20]  Boo Cheong Khoo,et al.  Wave propagation in a fully nonlinear numerical wave tank: A desingularized method , 2006 .

[21]  V. Rokhlin.  Rapid solution of integral equations of classical potential theory , 1985 .

[22]  Hyun Gyu Kim,et al.  A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods , 1999 .

[23]  J. Larsen,et al.  Open boundaries in short wave simulations — A new approach , 1983 .

[24]  Hai-Xiang Lin,et al.  Structured parallelisation of the flow simulation package TRIWAQ , 1995, HPCN Europe.

[25]  YuanTong Gu,et al.  Meshless methods coupled with other numerical methods , 2005 .