Modeling of 2-D nonlinear surface waves interacting with submerged bodies

Abstract

High-order spectral method, based on an asymptotic expansion and a pseudo-spectral method, has been adopted for last three decades with the aim of finding computationally less expensive, but robust numerical solutions for nonlinear surface wave problem in ideal fluid. Although there have been attempts to solve wave-body interaction problems using this method, the method has not yet been generalized fully to include the effects of finite water depth, floating body, etc. In this study, following the previous work done by Kent and Choi (2007), the non-linear wave-body interaction problem is decomposed into wave and body problems, but the formulation and numerical methods have been modified to find more simple and accurate numerical method. In particular, we modify the non-linear evolution equations regarding the free surface elevation and the free surface velocity potential in water of finite depth, and develop a numerical scheme to find the body velocity potential more accurately, when the body is in large amplitude motion, using a linear panel method. To determine the effectiveness and accuracy, we first apply this modified method to the infinite water depth case, and compare our results with other numerical results from previous studies. Then, we generalize this method to the finite water depth case, and vertical boundary case.