An efficient null space inexact Newton method for hydraulic simulation of water distribution networks
For engineers simulating water distribution networks, this method offers a more efficient solution to the nonlinear equations arising in hydraulic analysis.
The paper proposes an inexact Newton method for hydraulic simulation of water distribution networks that reduces computational cost by partially updating frictional headloss computations and reusing symbolic Cholesky factorizations. Validation on medium to large-scale networks shows improved efficiency while maintaining numerical reliability.
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.