Flooding in urban drainage systems: coupling hyperbolic conservation laws for sewer systems and surface flow

• Published in: International journal for numerical methods in fluids Vol. 76; no. 11; pp. 789 - 810
• Main Authors: Borsche, R., Klar, A.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 20.12.2014; Wiley Subscription Services, Inc
• Subjects: finite volume; hydrodynamics; hyperbolic; Joining; Manholes; Mathematical analysis; Mathematical models; Networks; nonlinear dynamics; Numerical analysis; partial differential equations; Sewer systems; Sewers; shallow water
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.3957

SUMMARYIn this paper, we propose a model for a sewer network coupled to surface flow and investigate it numerically. In particular, we present a new model for the manholes in storm sewer systems. It is derived using the balance of the total energy in the complete network. The resulting system of equations contains, aside from hyperbolic conservation laws for the sewer network and algebraic relations for the coupling conditions, a system of ODEs governing the flow in the manholes. The manholes provide natural points for the interaction of the sewer system and the runoff on the urban surface modeled by shallow‐water equations. Finally, a numerical method for the coupled system is presented. In several numerical tests, we study the influence of the manhole model on the sewer system and the coupling with 2D surface flow. Copyright © 2014 John Wiley & Sons, Ltd. The coupling of urban surface flows with the underlying sewer network is considered. Therefore a well‐posed manhole model is developed. The coupled system of a network of hyperbolic PDEs, ODEs and a 2D balance law is investigated in several numerical examples.