Efficient Method for Analyzing Pipe Networks

摘要

The governing equations for a general network are first set up, and then reformulated in terms of matrices. This is exploited to show that the choice of model for the flow equations are essential for the behaviour of the iterative method used to solve the problem: If the flow equations are formulated in terms of pipe discharges, then the energy heads can be eliminated, and we get a set of generalised loop equations; further, an iterative method as Newton-Raphson's method gives identical discharge-iteratives when applied to the full system or to the reduced system. Similarly, when the flow equations are expressed in terms of energy heads, then Newton-iterations gives identical iterates for energy heads when applied to the full or to reduced system. The behaviour of some iterative methods is compared in the initial phase with large errors. It is concluded that it is best to use the generalized loop equations, and a robust iterative strategy is suggested. (ERA citation 13:047144)