Numerical simulation of nonlinear viscous wavefields generated by piston-type wavemaker

A numerical method for the simulation of nonlinear wavefields generated by a piston-type wavemaker has been developed by solving the unsteady, two-dimensional Navier-Stokes equations and the exact free surface boundary conditions. The Stanford University modified marker and cell method for treating the free surface has been modified to permit more accurate extrapolation of the velocity components at the free surface. Both small- and large-amplitude waves generated by a piston-type wavemaker can be simulated by the present numerical scheme, and the process of wave formation can be examined in detail. To verify the accuracy of the numerical results, the wave profiles generated by the numerical method are compared with both theoretical and experimental results. For small wave steepness, the numerical results coincide well with theoretical and experimental results. For large wave steepness, the numerical wave heights are slightly lower than the experimental ones. The characteristics of the wavefields, including the velocity fields in the how domain, are also discussed in detail.