The virtual source approach to non-linear potential flow simulations

In this paper, we develop the Virtual Source Method for simulation of incompressible and irrotational fluid flows. The method is based upon the integral equations derived by using Green's identity with Laplace's equation for the velocity potential. The velocity potential within the fluid domain is completely determined by the potential on a virtual boundary located above the fluid. This avoids the need to evaluate singular integrals. Furthermore, the solution method developed here is meshless in space in that discretisation is in terms of the spectral components of the solution along this virtual boundary. These are determined by specifying non-linear boundary conditions on the velocity potential on the air/water surface using Bernoulli's equation. A fourth-order Runge-Kutta procedure is used to update the spectral components in time. The method is used to model high-amplitude standing waves and sloshing. Results are compared with theory where applicable and some interesting physical phenomena are identified.