A three dimensional boundary fitted coordinate hydrodynamic model, part I: Development and testing

A three dimensional hydrodynamic model has been developed in boundary fitted coordinates for application to shelf and coastal sea circulation. The momentum and continuity equations are solved on a space staggered grid system using a semi-implicit finite-difference solution algorithm for the exterior vertically averaged flow and an explicit procedure for the interior flow. The vertical coordinate, transformed by the local depth, is approximated by a series of permeable layers. The interior momentum equations are solved explicitly with the exception that the vertical diffusive terms employ an implicit specification to ease the time step restriction. The model has been tested in a two dimensional mode against analytic solutions for a standing wave in a closed basin, tidal flow in a annular basin with constant depth and wind driven flow in a elliptic cylindrical basin. Three dimensional tests of the code include wind and density forcing in a rectangular basin. All simulations show excellent agreement with the analytic solutions.