Computation of transient fully nonlinear free surface waves and wave-body interactions

Transient and steady-state nonlinear free surface waves and wave-body interactions are investigated in a three-dimensional Numerical Wave Tank (NWT) using an indirect Desingularized Boundary Integral Equation Method (DBIEM) and a Mixed Eulerian-Lagrangian (MEL) time marching scheme. The Laplace equation is solved at each time step by using Rankine sources distributed outside the solution domain and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A regriding algorithm is devised to eliminate the possible instabilities without using artificial smoothing in the region of high gradients on the free surface. The incident waves are generated either by a piston type wavemaker or by feeding analytic forms on the input boundary. The outgoing waves are sufficiently dissipated by using spatially varying artificial damping on the free surface of the damping zone before they reach the downstream wall boundary. In some cases, side beaches are also implemented to minimize the side-wall reflection. Current-wave and current-wave-body interactions are also investigated in the same NWT for relatively low Froude numbers. Computations are performed by using a material node approach and constant current velocity. Effects of current speed and water depth on waves and wave-body interactions are studied in a NWT. Using Prandtl's acceleration potential concept, the NWT is further extended to be able to solve the fully-nonlinear interaction of waves with floating bodies. To assess the validity of numerical model we used, a series of numerical tests including numerical error, convergence, stability, wave reflection, mass/volume, and energy conservation tests were performed. To demonstrate the usefulness and accuracy of our numerical wave tank and computational techniques, we performed six different numerical applications of interest. First, free nonlinear propagation of large waves generated by either a piston type wave maker or an open boundary are studied in a three-dimensional NWT without a body. Subsequently, the nonlinear diffractions by a bottom-mounted and truncated vertical cylinders, for which experimental results and both linear (WAMIT) and second-order diffraction theory results are available, were investigated. Results showed that the agreement between present method and experiment was better correlated compared to perturbation-based methods. The free nonlinear propagation of waves with steady current (up to max., Fn = 0.1) and the nonlinear diffraction of a vertical cylinder for various wave and current conditions (up to max., Fn = 0.05) were studied in a NWT. The results showed that the material node approach in conjunction with the MEL method had limitation in case of relatively high current parameter. Finally, computations were performed for the fully nonlinear wave interactions with a freely-floating vertical cylinder. Body motions, forces and moment were obtained for two different incoming wave steepness. Then, added mass and damping coefficients were compared with the perturbation-based computation results.