Method to Cope with Zero Flows in Newton Solvers for Water Distribution Systems

Abstract

This paper presents and discusses a simple method to deal with zero flows in Newton solvers for water distribution systems, in particular in a previously published global gradient algorithm. The method consists in replacing the Hazen-Williams head loss–flow relationship for flows below a certain threshold with a linear relationship, which coincides with Hazen-Williams’ at zero, but has a nonzero derivative at that point, thus avoiding computational troubles associated with zero flows. Manual and automatic random testing of example networks shows that the proposed method compares well with both the algorithm adopted in water distribution modeling software and the recently proposed regularization method in convergence rate while outperforming them in computational veracity and applicability range.