Accuracy of an estuarine hydrodynamic model using smooth elements

Abstract

A finite element model which uses triangular, isoparametric elements with quadratic basis functions for the two velocity components and linear basis functions for water surface elevation is used in the computation of shallow water wave motions. Specifically addressed are two common uncertainties in this class of two‐dimensional hydrodynamic models: the treatment of the boundary conditions at open boundaries and the treatment of lateral boundary conditions. The accuracy of the models is tested with a set of numerical experiments in rectangular and curvilinear channels with constant and variable depth. The results indicate that errors in velocity at the open boundary can be significant when boundary conditions for water surface elevation are specified. Methods are suggested for minimizing these errors. The results also show that continuity is better maintained within the spatial domain of interest when ‘smooth’ curve‐sided elements are used at shoreline boundaries than when piecewise linear boundaries are used. Finally, a method for network development is described which is based upon a continuity criterion to gauge accuracy. A finite element network for San Francisco Bay, California, is used as an example.