An efficient null space inexact Newton method for hydraulic simulation of water distribution networks

TL;DR

This paper introduces an efficient inexact Newton method utilizing partial updates and null space basis optimization for hydraulic simulation in water networks, improving computational efficiency and reliability.

Contribution

It proposes a novel inexact Newton algorithm with partial updates and optimized null space bases, reducing computational costs in hydraulic network analysis.

Findings

Reduced computational cost through single symbolic factorization

Improved numerical reliability with partial updates

Validated on medium to large-scale water networks

Abstract

Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes' frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters are studied to propose appropriate values. Different null space basis generation schemes are analysed to choose methods for sparse and well-conditioned null space bases resulting in a smaller update set. The Newton steps are computed in the null space by solving sparse, symmetric positive definite systems with sparse Cholesky factorizations. By using the constant structure of the null space system matrices, a single symbolic factorization in the Cholesky decomposition is used multiple times, reducing the computational cost of linear solves. The algorithms and analyses are validated using medium to large-scale water network models.