Aimed at providing a simple yet stable method to deal with moving boundary problem, a simplified treatment is proposed and is implemented in the Marine Environmental Committee (MEC) ocean model, which combines the 3-D hydrodynamic multi-layers with a shallow water layer. Tidal current around general geometries such as long shore and sinking-island can be simulated effectively.
In tidal simulations, most researchers take great efforts to deal with complicated geometries in order to get precise results. It will be even more difficult when there exists a quite long beach (long shore effect) whose length could be several kilometers in only a few meters'' tidal height, and/or very shallow water that exposes its bottom during a low tide to form an island that will be submerged during flood tide (island effect), where the topologies of meshes will be changed. It requires a numerical model to be precise and stable enough so as to simulate this kind of moving boundary problem. The above problem usually involves cells being flooded or dried during the calculation, which arises in a wide range of free-surface hydraulics problems, such as tidal floods, dam breaks and overland flow of precipitation. Techniques to handle these problems include deformable computational meshes, modified equations in very shallow regions (e.g. Meselhe and Holly, 1993) and shock capturing schemes (e.g. Tchamen and Kawahita, 1994). Akanabi and Katopodes (1987) gave a brief summary of problems encountered in the numerical simulation of flood waves propagating on the dry bed. Khan (2000) developed a finite element model for the flow over frictionless horizontal surface and smoothed and rough surface of horizontal and sloping laboratory channel and numerical oscillations at the front of surge were reported. Beffa and Connel (2001) reported numerical oscillations when cells switch from dry to wet or vice versa.
