Nonlinear wave forces on a stationary vertical cylinder by HOBEM-NWT

Abstract

A Numerical Wave Tank (NWT) is developed using a higher-order boundary element method (HOBEM). Nine-node bi-quadratic elements are used to describe boundary surfaces and flow variables, and a double-node technique is used for the treatment of intersections. The Mixed Eulerian-Lagrangian (MEL) approach is applied to solve the initial/boundary-value problem and only the vertical movement of free surface is allowed for convenience especially at the waterline of a body. The fully nonlinear free surface condition is integrated in the time domain by Runge-Kutta fourth-order scheme (RK4). An artificial damping scheme is implemented along the free surface of a damping zone to prevent wave reflection at the end of the tank. Incident waves are generated by using either piston wave maker or feeding proper wave profile at the upstream boundary. Nonlinear wave forces are then obtained by integrating nonlinear pressure over the instantaneous wetted surface. An efficient and accurate method for obtaining the time derivative of velocity potential is devised using the property of RK4 scheme. Numerical test results for a bottom-mounted vertical cylinder (radius=depth) show reasonable agreement with Isaacson and Cheung's second-order diffraction computation. Various aspects of possible numerical instabilities, which are frequently encountered in nonlinear wave simulations, are also discussed.