BEM Computations of 3-D Fully Nonlinear Free-Surface Flows Caused by Advancing Surface Disturbances

Abstract

We report on recent developments and validations of a numerical model for free-surface waves generated by an advancing surface disturbance. The model is based on potential How theory with fully nonlinear free-surface boundary conditions. Equations are solved numerically in the time domain, using a 3-dimensional higher-order Boundary Element Method (HOBEM) combined with a 2nd-order explicit time updating. The generic model, developed in earlier work by Grilli et al. (2000, 2001), is extended in the paper to apply to the present forward-moving disturbance problem. We first assess both the accuracy, and convergence rate of the HOBEM for a typical mixed Dirichlet-Neumann problem corresponding to the boundary value problem, which is solved at every time step in the computations. As expected, the convergence rate is found to be 3rd order, and mass and energy are conserved within less than 1% for highly nonlinear waves when A least 8 third-order boundary elements are used per wavelength. To achieve sufficient numerical efficiency for large and finely discretized problems, we use the Fast Multipole Algorithm (N log N method) recently tested in the model by Fochesato and Dias (2006). As a validation application, we compute 3-D nonlinear free-surface waves caused by a moving pressure patch, such as created fly a Surface Effect Ship. Results show that the present methodology works quite well for numerical examples and gives reasonable wave resistance as compared with theory, and other computational results.