A new depth-integrated non-hydrostatic model for free surface flows

A new depth-integrated model deploying a non-hydrostatic pressure distribution is presented.With the pressure divided into hydrostatic and dynamic components,the horizontal momentum equations were obtained by integrating the Navier-Stokes equations from the bottom to the free surface.The vertical momentum equation,in which the convective and viscosity terms were omitted,was approximated by the Keller-box scheme.The model has two steps.First,the dynamic pressure gradient terms were discretized semi-implicitly and the other terms were in explicit scheme.Second,the velocities expressed as the unknown dynamic pressure were substituted into the continuity equation,resulting in a five-diagonal symmetric matrix linear system that was solved by the conjugate gradient method.The model was validated with the propagation of a solitary wave and sinusoidal wave,indicating that it can predict free surface flows well.