A Three-dimensional Tidal Model in Boundary-fitted Curvilinear Grids

Abstract

In hydrodynamic models of marine and estuarine currents the use of boundary-fitted curvilinear grids not only makes the model grids fit to the coastline and bathymetry well, but also makes the kinetic boundary conditions simple and more accurate. Because of these advantages, a three-dimensional tidal model with boundary-fitted curvilinear grids has been developed to simulate both tide and current in estuarine and shelf water. The basic idea is to use a set of coupled σ-stretched and elliptic transformations to map the physical space into a corresponding transformed space such that all boundaries are coincident with co-ordinate lines and the transformed grids are rectangular. The hydrodynamic equations in the transformed space are solved in a rectangular mesh of the transformed grid system. The application of the model in the simulation of the M2,S2 , K1and O1tidal waves in the Bohai Sea, China, shows that the numerical results are in good agreement with the observations. The method of boundary-fitted curvilinear grids is effective for improving simulation accuracy of current in the estuarine and shallow seas, especially at the coastal regions where the current was usually impractical by a uniform Cartesian grid system with the shoreline and bathymetry represented by numerous stair-steps.