Streamline Upwind Finite-Element Method for Overland Flow

Abstract

A streamline upwind, finite-element method is proposed to solve the two-dimensional (2D) kinematic wave and shallow water wave equations for overland flow problems. The spatial domain is discretized into a network of quadrilateral, bilinear finite elements, and time derivatives are treated by a three-point finite-difference scheme to increase numerical stability. Solutions computed by the streamline upwind method are compared to those of the Galerkin method. Streamline upwind and Galerkin solutions of the kinematic wave equation exhibited good agreement with an analytic solution for flow over an inverted cone. However, the Galerkin solution exhibited oscillations during the steady portion of the runoff hydrogaph. Galerkin solutions of the shallow water wave equations for inverted cone and bowl-shaped surfaces displayed oscillations in time and space, while the streamline upwind method exhibited no oscillatory behavior. Results generated by the streamline upwind method also agreed well with experimental data sets and simulations conducted with the MacCormick finite-difference method.