Virtual source method simulation of progressive water waves

The virtual source method (VSM) has been developed to simulate water waves based upon the solution of Laplace’s equation for the velocity potential integral equations with full nonlinear surface conditions. The basis of the method is the use of specific Green’s functions for a rectangular ‘virtual domain’ which is an extension of the physical domain. The solution variables are frequency components of the velocity potential at the upper virtual boundary and these are found by specifying appropriate conditions on the physical boundaries (i.e. wavemaker, walls and wave surfaces). The authors have shown that the model successfully simulates both linear and nonlinear standing waves and simple sloshing problems and is more effective and efficient than simple boundary element methods for these problems. In this paper, we develop the VSM to generate nonlinear progressive waves in a numerical wave tank. In order to remove the transmitted energy of the waves and so reduce the reflection from the right wall of the tank, an artificial damping term is added to the free surface boundary condition. The VSM results are compared with those from both second order Stokes theory and from a boundary element method (BEM).