QALE‐FEM for numerical modelling of non‐linear interaction between 3D moored floating bodies and steep waves

This paper presents further development of the QALE-FEM (Quasi Arbitrary Lagrangian-Eulerian Finite Element Method) based on a fully nonlinear potential theory to numerically simulate nonlinear responses of 3D moored floating bodies to steep waves. In the QALE-FEM (recently developed by the authors and applied to 2D floating bodies), the complex unstructured mesh is generated only once at the beginning of calculation and is moved to conform to the motion of boundaries at other time steps by using a robust spring analogy method specially suggested for this kind of problems, avoiding the necessity of high cost remeshing. In order to tackle challenges associated with 3D floating bodies, several new numerical techniques are developed in this paper. These include the technique for moving the mesh near body surfaces, the scheme for calculating velocity on 3D body surfaces and the ISITIMFB-M (Iterative Semi-Implicit Time Integration Method for Floating Bodies - Modified) procedure that is more efficient for dealing with the full coupling between waves and bodies. Using the newly developed techniques and methods, various cases for 3D floating bodies with motions of up to 6 degrees of freedom (DoFs) are simulated. These include a SPAR platform, a barge-type floating body and one or two Wigley Hulls in head seas or in oblique waves. For some selected cases, the numerical results are compared with experimental data available in the public domain and satisfactory agreements are achieved. Many results presented in this paper have not been found elsewhere to the best knowledge of the authors.

[2]  Alistair G.L. Borthwick,et al.  Wave–structure interaction using coupled structured–unstructured finite element meshes , 2003 .

[3]  Qingwei Ma,et al.  Finite element simulations of fully non-linear interaction between vertical cylinders and steep waves. Part 2: Numerical results and validation , 2001 .

[4]  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 .

[5]  Frédéric Dias,et al.  A fast method for nonlinear three-dimensional free-surface waves , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  A. P. Shashikala,et al.  Dynamics of a moored barge under regular and random waves , 1997 .

[7]  Oliver A. Shergold,et al.  Mechanisms of deep penetration of soft solids, with application to the injection and wounding of skin , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[8]  A. Andonowati,et al.  Applying the finite element method in numerically solving the two dimensional free-surface water wave equations , 1998 .

[9]  Eugenio Oñate,et al.  Fluid-structure interaction using the particle finite element method , 2006 .

[10]  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.

[11]  K. R. Drake,et al.  Interactions between nonlinear water waves and non-wall-sided 3D structures , 2007 .

[12]  Stephan T. Grilli,et al.  A fully non‐linear model for three‐dimensional overturning waves over an arbitrary bottom , 2001 .

[13]  A Nonlinear Simulation Method of 3-D Body Motions in Waves (1st Report) : Formulation of the Method with Acceleration Potential , 1995 .

[14]  R. Eatock Taylor,et al.  The coupled finite element and boundary element analysis of nonlinear interactions between waves and bodies , 2003 .

[15]  Wei Bai,et al.  Higher-order boundary element simulation of fully nonlinear wave radiation by oscillating vertical cylinders , 2006 .

[16]  Katsuji Tanizawa,et al.  Development of a 3D-NWT for simulation of running ship motions in waves , 2001 .

[17]  Qingwei Ma,et al.  Effects of an Arbitrary Sea Bed On Responses of Moored Floating Structures to Steep Waves , 2007 .

[18]  M. S. Celebi,et al.  Nonlinear transient wave–body interactions in steady uniform currents , 2001 .

[19]  Stephan T. Grilli,et al.  Modeling of Breaking and Post-breaking Waves on Slopes by Coupling of BEM and VOF Methods , 2003 .

[20]  Qingwei Ma,et al.  Meshless local Petrov-Galerkin method for two-dimensional nonlinear water wave problems , 2005 .

[21]  Giorgio Contento,et al.  Numerical wave tank computations of nonlinear motions of two-dimensional arbitrarily shaped free floating bodies , 2000 .

[22]  R. L. Davies,et al.  Neptune Project: Spar History and Design Considerations , 1997 .

[23]  G. X. Wu,et al.  Simulation of nonlinear interactions between waves and floating bodies through a finite-element-based numerical tank , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[24]  Weoncheol Koo,et al.  Freely floating-body simulation by a 2D fully nonlinear numerical wave tank , 2004 .

[25]  R. Eatock Taylor,et al.  Finite element analysis of two-dimensional non-linear transient water waves , 1994 .

[26]  Shiqiang Yan.  Numerical simulation of nonlinear response of moored floating structures to steep waves , 2006 .

[27]  Pierre Ferrant,et al.  Run-up on a body in waves and current. Fully nonlinear and finite-order calculations , 2000 .

[28]  Roland W. Lewis,et al.  Three-dimensional unstructured mesh generation: Part 2. Surface meshes , 1996 .

[29]  Charbel Farhat,et al.  A three-dimensional torsional spring analogy method for unstructured dynamic meshes , 2002 .

[30]  T Vinje,et al.  NONLINEAR SHIP MOTIONS , 1981 .

[31]  P. George,et al.  3D Delaunay mesh generation coupled with an advancing-front approach , 1998 .

[32]  R. Lewis,et al.  Three-dimensional unstructured mesh generation: Part 3. Volume meshes , 1996 .

[33]  Günther Clauss,et al.  Numerical simulation of nonlinear transient waves and its validation by laboratory data , 1999 .

[34]  Katsuji Tanizawa,et al.  Estimation of Wave Drift Force By Numerical Wave Tank , 1999 .

[35]  C. Z. Wang,et al.  An unstructured-mesh-based finite element simulation of wave interactions with non-wall-sided bodies , 2006 .

[36]  J. M. Watt.  Numerical Initial Value Problems in Ordinary Differential Equations , 1972 .

[37]  M Kashiwagi.  Non-linear simulations of wave-induced motions of a floating body by means of the mixed Eulerian-Lagrangian method , 2000 .

[38]  Rodney Eatock Taylor.  On Modelling the Diffraction of Water Waves , 2007 .

[39]  Dick K. P. Yue,et al.  Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 2. Nonlinear waves and forces on a body , 2001, Journal of Fluid Mechanics.

[40]  Arthur M. Reed,et al.  Modern Seakeeping Computations for Ships , 2001 .

[41]  Q. W. Ma,et al.  Numerical simulation of fully nonlinear interaction between steep waves and 2D floating bodies using the QALE-FEM method , 2007, J. Comput. Phys..

[42]  K. Tanizawa.  A Nonlinear Simulation Method of 3-D Body Motions in Waves (1st Report) , 1995 .

[43]  Stephan T. Grilli,et al.  Shoaling of Periodic Waves Over Barred-Beaches In a Fully Nonlinear Numerical Wave Tank , 1999 .

[44]  Philippe Guyenne,et al.  A Fully Nonlinear Model for Three-dimensional Overturning Waves over Arbitrary Bottom 1 , 1997 .

[45]  S. Yan,et al.  Quasi ALE finite element method for nonlinear water waves , .

[46]  Stephan T. Grilli,et al.  Numerical Modeling of Extreme Wave Slamming on Cylindrical Offshore Support Structures , 2006 .

[47]  Yusong Cao,et al.  Three‐dimensional desingularized boundary integral methods for potential problems , 1991 .

[48]  G. X. Wu,et al.  Time stepping solutions of the two-dimensional nonlinear wave radiation problem , 1995 .

[49]  Minoo H. Patel,et al.  On the non-linear forces acting on a floating spar platform in ocean waves , 2001 .

[50]  Qingwei Ma,et al.  QALE‐FEM for modelling 3D overturning waves , 2009 .

[51]  J. Batina.  Unsteady Euler airfoil solutions using unstructured dynamic meshes , 1989 .

[52]  Wei Bai,et al.  Numerical simulation of fully nonlinear regular and focused wave diffraction around a vertical cylinder using domain decomposition , 2007 .

[53]  Masashi Kashiwagi.  Full-Nonlinear Simulations of Hydrodynamic Forces on a Heaving Two-Dimensional Body , 1996 .

[54]  Qingwei Ma,et al.  Numerical simulation of nonlinear interaction between structures and steep waves , 1998 .

[55]  M. S. Celebi,et al.  Fully Nonlinear 3-D Numerical Wave Tank Simulation , 1998 .

[56]  Carlo L. Bottasso,et al.  The ball-vertex method: a new simple spring analogy method for unstructured dynamic meshes , 2005 .

[57]  Rainald Löhner,et al.  An unstructured-grid based volume-of-fluid method for extreme wave and freely-floating structure interactions , 2006 .

[58]  Moo-Hyun Kim,et al.  Fully nonlinear interactions of waves with a three-dimensional body in uniform currents , 1998 .

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