An implicit method for the analysis of transient flows in pipe networks

Existing methods for the analysis of transient flows in pipe networks are often geared towards certain types of flows such as gas flows vis-A-vis liquid flows or isothermal flows vis-A-vis non-isothermal flows. Also, simplifying assumptions are often made which introduce inaccuracies when the method is applied outside the domain for which it was originally intended. This paper describes an implicit finite difference method based on the simultaneous pressure correction approach which is valid for both liquid and gas flows, for both isothermal and non-isothermal flows and for both fast and slow transients. The problematic convective acceleration term in the momentum equation, often neglected in other methods, is retained but eliminated by casting the momentum equation in an alternative form. The accuracy and stability of the method, depending on a time-step weighing factor alpha, are illustrated by analysing fast transients in a pipeline and simple branching network. The proposed method compares very well with the second-order-method of characteristics and the two-step Lax-Wendroff method. The advantages of the present method is its speed over a range of problems including both fast and slow transients, its accuracy, its stability and its flexibility. Copyright (C) 2001 John Wiley Sons, Ltd.