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

We report on our recent development and validation of a new numerical model for fully nonlinear free surface waves generated by an advancing free surface disturbance. This model is based on potential flow theory with fully nonlinear free surface boundary conditions, which we solve in the time domain using a three-dimensional (3D) higher-order Boundary Element Method (HOBEM) combined with a second-order explicit time updating, developed in earlier work (Grilli et al., 2000, 2001). The model is extended in the paper to apply to the forward speed problem. As a first step, the accuracy and rate of convergence of the HOBEM are assessed for a mixed Dirichlet-Neumann problem, which corresponds to the boundary value problem that is solved at every time step in time-domain computations. As expected, the convergence rate is found to be third-order and mass and energy are conserved within less than 1% for highly nonlinear waves, when using 8 third-order boundary elements per wavelength. To achieve sufficient numerical efficiency for large and finely discretized problems, we use the Fast Multipole Algorithm recently implemented in the model by Fochesato and Dias (2006). As a validation application, we compute 3D nonlinear free surface waves caused by a moving pressure patch such caused by Surface Effect Ships. Numerical results show that the present methodology works quite well and gives reasonable wave resistance for numerical examples, as compared with theory, and other computations.