Testing linear solvers for WDN models

Steady-state Water Distribution Network (WDN) modelling, which is normally performed as part of hydraulic system simulation, computes pipe flow rates and nodal heads for a given set of boundary conditions (i.e., tank levels, nodal demands, pipe hydraulic resistances, pump curves, minor losses, etc.). The problem is nonlinear based on solution of energy and mass conservation laws. The mathematical solution to such a problem is generally found by using global linearization techniques involving the simultaneous solution of all the system’s equations. The related algorithms use successive approximations in order to iteratively reach the solution of the original nonlinear mathematical system. This requires the solution of a linear system of equations at each iteration. The matrix of coefficient of that linear system is generally sparse, symmetric and positive definite, as for example in the global gradient algorithm (GGA). Thus, the robust and fast solution of such a linear problem is an important issue in order to achieve computational efficiency with respect to large size hydraulic systems. This work will study the two main strategies of linear system solvers, the direct and iterative methods, together with the most reliable and efficient ordering, factorization and pre-conditioning strategies in the context of steady-state WDN modelling. The results show that exists a direct method based on a specialized decomposition which is superior to all the other alternatives.