2019/01/11 by Manish Kumar Singh, Singh, Manish K., Vassilis Kekatos +1
Engineering · Environmental Science · #FOS: Mathematics #Groundwater flow and contamination studies #Membrane Separation Technologies #Optimization and Control (math.OC) #Water Systems and Optimization
paper · pdf · doi:10.48550/arxiv.1901.03676
openalex publication_date 2019/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Increasing concerns on the security and quality of water distribution systems\n(WDS), call for computational tools with performance guarantees. To this end,\nthis work revisits the physical laws governing water flow and provides a\nhierarchy of solvers of complementary value. Given the water injection or\npressure at each WDS node, finding the water flows within pipes and pumps along\nwith the pressures at all WDS nodes constitutes the water flow (WF) problem.\nThe latter entails solving a set of (non)-linear equations. We extend\nuniqueness claims on the solution to the WF equations in setups with multiple\nfixed-pressure nodes and detailed pump models. For networks without pumps, the\nWF solution is already known to be the minimizer of a convex function. The\nlatter approach is extended to networks with pumps but not in cycles, through a\nstitching algorithm. For networks with non-overlapping cycles, a provably exact\nconvex relaxation of the pressure drop equations yields a mixed-integer\nquadratically-constrained quadratic program (MI-QCQP) solver. A hybrid scheme\ncombining the MI-QCQP with the stitching algorithm can handle WDS with\noverlapping cycles, but without pumps on them. Each solver is guaranteed to\nconverge regardless of initialization, as numerically validated on a benchmark\nWDS.\n