A Fixed-Point Iteration for Steady-State Analysis of Water Distribution Networks
Provides a new numerical method for steady-state analysis of water distribution networks, though the problem is well-studied and the approach is incremental.
The paper develops a fixed-point iteration for solving steady-state water flow equations in urban water distribution networks, proving local convergence under the Hazen-Williams formula. A sample network demonstrates the method's applicability.
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.