A Fixed-Point Iteration for Steady-State Analysis of Water Distribution Networks

TL;DR

This paper introduces a fixed-point iteration method for solving steady-state water flow equations in urban water networks, ensuring local convergence and solution uniqueness under certain conditions.

Contribution

It presents a novel fixed-point iteration approach based on turbulent flow assumptions and the Hazen-Williams formula for steady-state water network analysis.

Findings

Method converges locally when spectral radius condition is met

Provides estimates for convergence speed based on Jacobian spectral radius

Validated on a sample water network

Abstract

This paper develops a fixed-point iteration to solve the steady-state water flow equations in an urban water distribution network. The fixed-point iteration is derived upon the assumption of turbulent flow solutions and the validity of the Hazen-Williams head loss formula for water flow. Local convergence is ensured if the spectral radius of the Jacobian at the solution is smaller than one. The implication is that the solution is at least locally unique and that the spectral radius of the Jacobian provides an estimate of the convergence speed. A sample water network is provided to assert the application of the proposed method.