Applicability of the method of fundamental solutions to interaction of fully nonlinear water waves with a semi-infinite floating ice plate

Abstract In this research effort, a meshless numerical model was developed to study the hydroelastic interaction of an incident wave with a semi-infinite horizontal floating plate. It is assumed that the fluid is homogenous, inviscid and incompressible. Fundamental solution of the governing Laplace equation is considered to be radial basis functions. In this method, only a few boundary points are located on the boundary. Moreover, there are a few source points that are located outside the computational domain. Two additional source points are introduced to deal with the plate's edge conditions. The problem is solved using collocations at only a few boundary points. When density and thickness of the plate are reduced to zero, good agreements with other numerical works are observed.

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

[2]  Feng Xu,et al.  An Optimization of Eigenfunction Expansion Method for the Interaction of Water Waves with an Elastic Plate , 2009 .

[3]  Ching-Jer Huang,et al.  Generation and propagation of water waves in a two-dimensional numerical viscous wave flume , 2004 .

[4]  E. Kansa.  MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[5]  T. Yip,et al.  Scattering of surface waves by a semi-infinite floating elastic plate , 2001 .

[6]  D. L. Young,et al.  Computation of Nonlinear Free-Surface Flows by a Meshless Numerical Method , 2008 .

[7]  Feng Xu,et al.  Wave scattering by a thin elastic plate floating on a two-layer fluid , 2010 .

[8]  A. G. Greenhill.  Wave Motion in Hydrodynamics , 1886 .

[9]  V. Squire.  Synergies Between VLFS Hydroelasticity And Sea-Ice Research , 2008 .

[10]  Yusong Cao,et al.  NUMERICAL COMPUTATIONS OF TWO-DIMENSIONAL SOLITARY WAVES GENERATED BY MOVING DISTURBANCES , 1993 .

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

[12]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[13]  Masashi Kashiwagi.  Research on hydroelastic responses of VLFS : Recent progress and future work , 1999 .

[14]  Kazuo Nadaoka,et al.  Development of a numerical wave tank for analysis of nonlinear and irregular wave field , 1991 .

[16]  Ole Secher Madsen,et al.  On the generation of long waves , 1971 .

[17]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[18]  Qian Wang,et al.  Unstructured MEL modelling of nonlinear unsteady ship waves , 2005 .

[19]  V. Squire.  Of ocean waves and sea-ice revisited , 2007 .

[20]  Michael Isaacson.  Nonlinear-wave effects on fixed and floating bodies , 1982 .

[21]  M. Meylan,et al.  Wave scattering by an ice floe of variable thickness , 2011 .

[22]  Colin Fox,et al.  On the oblique reflexion and transmission of ocean waves at shore fast sea ice , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

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

[24]  E. Kansa.  Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[25]  Dick K. P. Yue,et al.  Numerical simulations of nonlinear axisymmetric flows with a free surface , 1987, Journal of Fluid Mechanics.

[26]  Eiichi Watanabe,et al.  Hydroelastic analysis of pontoon-type VLFS: a literature survey , 2004 .

[27]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[28]  Liang Cheng,et al.  Modified eigenfunction expansion methods for interaction of water waves with a semi-infinite elastic plate , 2001 .

[29]  J. Reddy.  An introduction to the finite element method , 1989 .