A Higher-Order Panel Method for Third-Harmonic Diffraction Problems

Ringing, the high-frequency response of a structure to relatively low-frequency waves, has been a great concern in offshore engineering. To investigate this phenomenon, we solve the third-harmonic diffraction problem using a three-dimensional higher-order panel method in the low-frequency range. In this thesis, the boundary integral equations are derived from two different theories , based on complementary assumptions. For the long-wave approximation theory, the free surface condition is an inhomogeneous Neumann condition, satisfied on the moving first-order wave elevation. For the conventional perturbation theory, the free surface condition is satisfied on the mean free surface. Based on the long-wave assumption in both theories, the forcing function is assumed to be a localized function, and the contribution from the second-harmonic potential to the third-harmonic forcing function is neglected. In the first theory, the second-and third-harmonic potentials are of the same order. The Green function 1/r + 1/r' is used. The integral equations have different forms for a body with a single column or multiple columns due to different first-order wave elevation. In the second theory, the second-and third-harmonic potentials are of different orders. The free surface Green function is used. Due to the numerical limitations and the computational effort required in the low-order panel method, a higher-order panel method using B-splines is applied to the nonlinear problems. The geometry and the potential are represented by B-splines. A least-square procedure is used to evaluate the potential on the free surface and the forcing function in B-spline forms. This thesis includes the numerical results of the second-and third-harmonic potentials and wave loads using the two theories. The results are obtained for a truncated cylinder and an array of four cylinders. The third-harmonic effects are significant in the numerical solutions. Acknowledgments I would like to express my greatest gratitude to my advisor, Professor Newman. His guidance and encouragement have motivated me in every way. His unparalleled experience and patience have taught me a great deal about hydrodynamics over the past five years. and Professor Ogilvie, for giving me invaluable advice and suggestions. Working in CHF group has been a pleasant experience, and I really enjoy the friendship from this group. Special thanks to Dr. Lee, who helped me understand WAMIT, to Dr. Maniar, who answered my numerous questions about B-splines, and to Prof. Nielsen, who was on my thesis committee while on sabbatical leave at MIT, and whose constructive comments were very appreciated.try Project "Water …