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

Existing methods for the analysis of transient /ows in pipe networks are often geared towards certain types of /ows such as gas /ows vis-9a-vis liquid /ows or isothermal /ows vis-9a-vis non-isothermal /ows. Also, simplifying assumptions areofte n madewhich introduceinaccuracie s when theme thod is applied outside the domain for which it was originally intended. This paper describes an implicit =nite di>erence method based on the simultaneous pressure correction approach which is valid for both liquid and gas /ows, for both isothermal and non-isothermal /ows 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 , areillustrate d 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–Wendro> 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 /exibility