Numerical Simulation of Nonlinear Water Wave Problems

The main purpose of present paper aims at the establishment of a numerical model for solving the nonlinear water wave problems. The model is based on the Navier-Stokes equations with the consideration of a free-surface through the streamfunction-vorticity formulation. The main advantage of the streamfunction-vorticity formulation is that pressure field can be eliminated from the Navier-Stokes equations. To demonstrate the model feasibility, the present studies are first concentrated on problems including the collision of two solitary waves with different amplitudes, and the overtaking collision of two solitary waves. Then, the model is also applied to a solitary wave passes over the submerged obstacle in a viscous fluid. Finally, the application of present study is also to simulate the generation of solitary waves by underwater moving object. All examples give very promising results, those applications reveal that present formulation is a very powerful approach to simulate the fully nonlinear water wave problems