# American Institute of Mathematical Sciences

June  2012, 2(2): 101-120. doi: 10.3934/mcrf.2012.2.101

## Numerical approximation of an optimization problem to reduce leakage in water distribution systems

 1 Institut de Mathématiques de Bordeaux IMB UMR 5251, Institut Polytechnique de Bordeaux, Université de Bordeaux, F-33405 Talence, France, France 2 Irstea, UR REBX, F-33612 Cestas Cedex, France, France

Received  April 2011 Revised  January 2012 Published  May 2012

Leakage represents a large part of the supplied water in Water Distribution Systems (WDS). Consequently, it is important to develop some efficient strategies to manage such a phenomenon. In this paper an improved formulation of the hydraulic network equations that incorporate pressure-dependent leakage, is presented and validated. The formulation is derived from the Navier-Stokes equations and solved using an adequate splitting method. Then, this formulation is used to study a constrained optimization problem with the objective to minimize the distributed water volume reducing the leakage. The problem is described and validated for academic case studies and real networks.
Citation: Pierre Fabrie, Elodie Jaumouillé, Iraj Mortazavi, Olivier Piller. Numerical approximation of an optimization problem to reduce leakage in water distribution systems. Mathematical Control & Related Fields, 2012, 2 (2) : 101-120. doi: 10.3934/mcrf.2012.2.101
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