Internal wave-maker for Navier-Stokes equations models

The flow motion of incompressible fluid can be described by Navier-Stokes e quations with the continuity equation, which requires zero divergence of th e velocity vector (i.e., partial derivative u(i)partial derivative x(i) = 0 ). A new method is developed to generate specific wave trains by using desi gned mass source functions for the equation of mass conservation, i.e., par tial derivative u(i)partial derivative x(i) f(x, t), in the internal flow r egion. The new method removes the difficulty in specifying incident waves t hrough an inflow boundary with the presence of strong wave reflection. Inst ead, only the open (radiation) boundary condition is needed in the simulati on. By using different source functions, the writers are able to generate v arious wave trains, including the linear monochromatic wave, irregular wave , Stokes wave, solitary wave, and cnoidal wave. By comparing numerical resu lts with analytical solutions, the writers have shown that the proposed met hod can accurately generate not only small amplitude waves but also nonline ar waves in both intermediate and shallow water. This method has important applications of simulating wave-current interaction, wave shoaling on a rel atively steep slope, and wave-structure interaction where wave reflection i s significant.