Simulation of floods caused by overloaded sewer systems: extensions of shallow‐water equations

Abstract

AbstractThe outflow of water from a manhole onto a street is a typical flow problem within the simulation of floods in urban areas that are caused by overloaded sewer systems in the event of heavy rains. The reliable assessment of the flood risk for the connected houses requires accurate simulations of the water flow processes in the sewer system and in the street.The Navier–Stokes equations (NSEs) describe the free surface flow of the fluid water accurately, but since their numerical solution requires high CPU times and much memory, their application is not practical. However, their solutions for selected flow problems are applied as reference states to assess the results of other model approaches.The classical shallow‐water equations (SWEs) require only fractions (factor 1/100) of the NSEs' computational effort. They assume hydrostatic pressure distribution, depth‐averaged horizontal velocities and neglect vertical velocities. These shallow‐water assumptions are not fulfilled for the outflow of water from a manhole onto the street. Accordingly, calculations show differences between NSEs and SWEs solutions.The SWEs are extended in order to assess the flood risks in urban areas reliably within applicable computational efforts. Separating vortex regions from the main flow and approximating vertical velocities to involve their contributions into a pressure correction yield suitable results. Copyright © 2005 John Wiley & Sons, Ltd.