Abstract
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.
Published Version
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