AN EXTENDED BOUNDARY INTEGRAL-EQUATION METHOD FOR THE REMOVAL OF IRREGULAR FREQUENCY-EFFECTS

Numerical techniques for the analysis of wave-body interactions are de veloped by the combined use of two boundary integral equation formulat ions. The velocity potential, which is expressed in a perturbation exp ansion, is obtained directly from the application of Green's theorem ( the potential formulation), while the fluid velocity is obtained from the gradient of the alternative form where the potential is represente d by a source distribution (the source formulation). In both formulati ons, the integral equations are modified to remove the effect of the i rregular frequencies. It is well known from earlier works that if the normal velocity is prescribed on the interior free surface, inside the body, an extended boundary integral equation can be derived which is free of the irregular frequency effects. It is shown here that the val ue of the normal velocity on the interior free surface must be continu ous with that outside the body, to avoid a logarithmic singularity in the source strength at the waterline. Thus the analysis must be carrie d out sequentially in order to evaluate the fluid velocity correctly: first for the velocity potential and then for the source strength. Com putations are made to demonstrate the effectiveness of the extended bo undary integral euations in the potential and source formulations. Res ults are shown which include the added-mass and damping coefficients a nd the first-order wave-exciting forces for simple three-dimensional b odies and the second-order forces on a tension-leg-platform The latter example illustrates the importance of removing irregular frequency ef fects in the context of second-order wave loads.