A Hybrid Integral Equation Method for Wave Forces on Three-Dimensional Offshore Structures

1987 ◽  
Vol 109 (3) ◽  
pp. 229-236 ◽  
Author(s):  
M. M. F. Yuen ◽  
F. P. Chau
Keyword(s):  
Integral Equation ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Offshore Structures ◽  
Equation Method ◽  
Wave Forces ◽  
Test Cases ◽  
Outer Domain ◽  
Hybrid Integral

Wave forces on arbitrary-shaped three-dimensional offshore structures are analyzed by the proposed hybrid integral equation method. Eigenfunction expansion is used to represent velocity potential in the outer domain, while a set of integral equations is developed for the inner domain encompassing the structure. A floating dock and a step cylinder are used as test cases showing the validity of the method.

Steep Wave Forces on Large Offshore Structures

1983 ◽  
Vol 23 (01) ◽  
pp. 184-190
Author(s):  
Michael de St. Q. Isaacson
Keyword(s):  
Integral Equation ◽  
Shallow Water ◽  
Integral Equation Method ◽  
Offshore Structures ◽  
Second Order ◽  
Equation Method ◽  
Wave Forces ◽  
Time Stepping ◽  
Green’S Theorem ◽  
Typical Design

Abstract A new numerical method for calculating the interaction of steep (nonlinear)ocean waves with large coastal or offshore structures of arbitrary shape is described. The evolution of the flow, and in particular the loads on the structure and the runup around it, are obtained by a time-stepping procedure in which the flow at each time step is calculated by an integral equation method based on Green's theorem. A few comparisons are made with available solutions and results are presented for a typical design wave in shallow water. The method is capable of predicting forces caused by steep waves accurately and without prohibitive computer effort. Introduction The prediction of wave forces on large offshore structures on the basis of linear diffraction theory, which is formally valid for small-amplitude sinusoidal waves, is now an established part of offshore design procedure. Reviews of the approaches generally used have been given by Hogben etal.,1 Isaacson,2 and Sarpkaya and Isaacson.3 To account more realistically for the effect of large wave heights, research recently has been directed primarily toward developing a second approximation based on the Stokes expansion procedure. However, such an approach is of practical value only under restricted conditions, as in the case of anundisturbed wave train described by Stokes second-order theory. In particular, nonlinear wave effects are expected to be of greatest importance for steep shallower waves, and these are precisely the conditions in which a Stokes second-order solution becomes invalid. A numerical solution to the complete boundary value problem without any wave height perturbation procedure is clearly desirable. The approach outlined here is described in detail by Isaacson.4 In this method, the wave diffraction is treated as a transient problem with known initial conditions corresponding to still water in the vicinity of the structure and a prescribed incident wave form approaching the structure. The development of the flow then can be obtained by a time-stepping procedure, in which the velocity potential of the flow at any one instant is obtained by an integral equation method basedon Green's theorem. Comparison with known diffraction solutions can be made only for relatively restricted situations. A few such comparisons have been carried out and arequite favorable. Results also are presented for a typical design wave in shallow water, and these are found to differ significantly from linear theory predictions.

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