Mathematical Modeling of a River Stream Based on a Shallow Water Approach

Abstract

Flood control problems as well as problems connected with wastewater discharge into rivers are issues of current importance. Depth averaged shallow water equations are used to model flows where water depth is much less than the horizontal dimension of the computational area and the free surface greatly influences the flow. The present work is focused on developing the mathematical model, applying the unsteady 2D shallow water equations, and constructing a numerical method for computing the river flow in extensive spatial areas. A finite volume solver for turbulent shallow water equations is presented. Some computational examples were carried out to investigate the applicability of the model. The comparison between the numerical solution and experimental results shows that the depth averaged model correctly represents flow patterns in the cases described and nonlinear effects in a river flow.