Computation of Nonlinear Free-Surface Flows Using the Method of Fundamental Solutions

A meshless numerical model for nonlinear free surface water waves is presented in this paper, to demonstrate that the localized method of fundamental solutions (MFS) is a stable, accurate tool for simulating and modeling the nonlinear propagation of gravity waves in the approximation of irrotational, incompressible and the fluid is assumed to be inviscid. Using the fundamental solution of the Laplace equation as the radial basis function, the problem is solved by collocation of boundary points. The present model is a first applied to simulate the generation of monochromatic periodic gravity waves by applying a semi-analytical or semi-numerical method to resolve the nonlinear gravity waves propagation, have verified by different orders of linear problems. As an application we are interested in the mechanisms of the interaction of a rectangular obstacle fixed on the bottom of the numerical wave tank (NWT) in the presence of the waves in order to provide information on attenuation process, and validate the numerical tool that we have developed for the treatment of this problem.