Accuracy and Stability of Virtual Source Method for Numerical Simulations of Nonlinear Water Waves

Abstract

The virtual source method (VSM) developed by Langfeld et al., (2016) is based upon the integral equations derived by using Green’s identity with Laplace’s equation for the velocity potential. These authors presented preliminary results using the method to simulate standing waves. In this paper, we numerically model a non-linear standing wave by using the VSM to illustrate the energy and volume conservation. Analytical formulas are derived to compute the volume and potential energy while the kinetic energy is computed by numerical integration. Results are compared with both theory and boundary element method (BEM).