VAHM - A Vertically Averaged Hydrodynamic Model Using Boundary-Fitted Coordinates

A numerical model called VAHM for computing the vertically averaged hydrodynamics of a water body, including salinity effects, has been developed. The model employs the concept of boundary-fitted coordinates to allow for an accurate representation of the boundary of the region being modeled while retaining the simplicity of the finite difference method of solution. Although a general curvilinear coordinate system covers the physical domain, all computations to solve the governing fluid dynamic equations, as well as the computation of the boundary-fitted coordinate system, are performed in a transformed rectangular plane with square grid spacing. A combination implicit- explicit finite difference scheme has been employed to numerically solve the governing equations. With such a scheme, the water surface elevation is computed implicitly using the Accelerated Gauss-Seidel solution technique, whereas the velocity and salinity fields are solved in an explicit manner. The major advantage of such a scheme is that the speed of a surface gravity wave is removed from the stability criteria while many desirable features of an explicit scheme are retained. Although additional work on VAHM remains to be completed before the model can be considered fully operational, results from the three applications of river and ocean boundaries demonstrate that the basic model behaves properly. (Author)