Implicit solution for estuarine hydrodynamic modelling

Abstract

This is a two-dimensional, finite difference, vertically averaged hydrodynamic model for shallow water estuaries. It utilizes three time levels and solves for current components in alternating direction exclusively by an implicit scheme. The purpose of using the implicit approach is to minimize the instability problem by which the usual implicit-explicit alternating scheme is inherently plagued when grid size is small or when water depths are deep. This is due to the explicit scheme limitation, whose time step is governed by the Courant-Friedrich-Lewy criterion. By the implicit-implicit scheme, a large time step would greatly reduce the CPU time. An effort was also made to model the effects of canals in the estuarine system. A different grid system than Leendertse's was used to lessen the lateral smoothing in Chezy coefficients caused by the large gradient of water bottom features. This grid system has both water elevation and depth measured at the center of the grid and is especially applicable for uneven grid-size models. The computer program is written to ensure easy-to-use features so that this model can be readily applied to different estuaries.