VIRTUAL SOURCE METHOD FOR MODELLING FULLY NONLINEAR PROGRESSIVE WATER WAVES

Abstract

This thesis describes the development of the Virtual source method (VSM) to generate linear and nonlinear water waves in a numerical wave tank (NWT) as well as the investigation of its global accuracy. The method is based upon the integral equations derived by using Green’s identity with Laplace’s equation for the velocity potential. BEM and VSM schemes are tested against a number of benchmark scenarios. The first test is the standing wave in a rectangular numerical wave tank. The BEM has shown to be up to 1st order accurate in time while VSM is up to 4th-order. Nonlinear effect beyond the second order are identified in the free surface due to Airy modes mixing in the VSM simulations. The VSM has been found to have excellent conservation of volume as the error is close to zero even for high amplitudes. The model has been developed to generate linear and nonlinear progressive waves by adding an inlet boundary condition at the left hand side of the tank. An artificial damping zone term are added in order to remove the transmitted energy of the waves and so reduce the reflection from the right wall of the tank. The effects of many parameters has been illustrated and very good agreement for both BEM and VSM schemes has been achieved when compared with theoretical solution. The VSMshows excellent agreement with with the experimental results in comparison with the solutions obtained by the other numerical schemes. Finally, the VSM is developed to generate tsunami by applying a body force into the fluid through the dynamic boundary condition at the free surface. The results of VSM model show a reasonable good agreement in terms of travelling speed and wave amplitude with other numerical models.