A two-dimensional finite volume hydrodynamic model for coastal areas: Model development and validation

Abstract

A two dimensional implicit finite volume scheme for solving the shallow-water equations is developed. The effects of the Coriolis force, surface wind stress, and waves are included. A non-uniform rectilinear forward staggered grid is used with Cartesian coordinates. The time integration is performed using the Euler implicit technique. The convective flux is treated using the deferred correction method. The viscous terms are discretized using a second order central difference approximation. The SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is used for coupling the velocity components and the water elevation gradient for the water level correction. The system of equations is solved sequentially using the Strongly Implicit Procedure (SIP). To simulate wave driven current, a phase averaged wave model is used first to simulate wave transformation and calculate radiation stresses. The performance of the developed model is validated for different sources of external forces and different combinations of boundary conditions. The validation cases include tidal circulation in a harbor and wave induced currents behind a breakwater parallel to the coastline. The model is finally applied to simulate the flow pattern in a closed artificial lagoon and along the coastline near Damietta Port located along the Northern coast of Egypt. Results of the developed model agree well with the published results for the considered cases.