A Non‐conforming Finite‐element Method for Solving Non‐hydrostatic Free‐surface Flow Problems

In this paper, we develop a two-dimensional vertical numerical model for simulating unsteady free-surface flows, using a non-hydrostatic pressure distribution. A fractional step numerical procedure is employed. The governing differential equations are discretized using the finite-element method. The velocity and salinity fields are approximated using the so-called linear non-conforming p(1)(NC) element, and pressure and free-surface elevation are discretized using linear continuous P, approximations. This procedure is very efficient and Could also be applied to hydrostatic flow problems. Our numerical scheme is validated by three test cases, namely a deepwater standing wave, the propagation of a solitary wave in a long channel and the density-driven flow. Copyright (C) 2007 John Wiley & Sons, Ltd.