Scaled boundary FEM solution of short-crested wave diffraction by a vertical cylinder

Abstract The scaled boundary finite-element method (SBFEM) is a novel semi-analytical method developed in the elasto-statics and elasto-dynamics areas that has the advantages of combining the finite-element method with the boundary-element method. The SBFEM method weakens the governing differential equation in the circumferential direction and solves the weakened equation analytically in the radial direction. It has the inherent advantage of solving the unbounded fluid dynamic problem. In this paper, the boundary-value problem composed of short-crested waves diffracted by a vertical circular cylinder is solved by SBFEM. Only the cylinder boundary is discretized with curved surface finite-elements on the circumference of the cylinder, while the radial differential equation is solved completely analytically. The computation of the diffraction force based on the present SBFEM solution demonstrates a high accuracy achieved with a small number of surface finite elements. The method can be extended to solve more complex wave–structure interaction problems resulting in direct engineering applications.

[1]  Song-Ping Zhu,et al.  Second-order wave diffraction forces on a vertical circular cylinder due to short-crested waves , 1995 .

[2]  Vallam Sundar,et al.  DIFFRACTED WAVE FIELD AND DYNAMIC PRESSURES AROUND A VERTICAL CYLINDER , 1990 .

[3]  C. Vendhan,et al.  Dynamic pressure distribution on a cylinder due to wave diffraction , 1989 .

[4]  Per A. Madsen,et al.  Short-crested waves in deep water: a numerical investigation of recent laboratory experiments , 2006, Journal of Fluid Mechanics.

[5]  Song-Ping Zhu,et al.  Diffraction of short-crested waves around a circular cylinder , 1993 .

[6]  Carlos Alberto Brebbia,et al.  Diffraction of water waves for vertical cylinders using boundary elements , 1983 .

[7]  Dong-Sheng Jeng,et al.  COMPUTATIONS OF THE ALMOST HIGHEST SHORT-CRESTED WAVES IN DEEP WATER , 1994 .

[8]  Subrata K. Chakrabarti,et al.  Interaction of Waves with Large Vertical Cylinder , 1975 .

[9]  Subrata K. Chakrabarti.  Steady drift force on vertical cylinder - viscous vs. potential , 1984 .

[10]  R. C. McCAMY.  Wave forces on piles: A diffraction theory, Tech. Memo. , 1954 .

[11]  N. Jothi Shankar,et al.  Wave loads on large vertical cylinders: A design method , 1984 .

[12]  R. A. Fuchs,et al.  On the theory of short-crested oscillatory waves , 1952 .

[13]  Derek B. Ingham,et al.  Boundary element methods for determining the fluid velocity in potential flow , 1993 .

[14]  R C MacCamy,et al.  Wave forces on piles: a diffraction theory , 1954 .

[15]  Andrew Deeks,et al.  Potential flow around obstacles using the scaled boundary finite‐element method , 2003 .

[16]  C. Mei.  The applied dynamics of ocean surface waves , 1983 .

[17]  Song-Ping Zhu,et al.  Numerical calculation of forces induced by short-crested waves on a vertical cylinder of arbitrary cross-section , 1994 .

[18]  Paul A. Martin,et al.  The scattering of regular surface waves by a fixed, half-immersed, circular cylinder , 1983 .