Runge-Kutta time-stepping schemes with TVD central differencing for the water hammer equations

In the present study, Runge-Kutta schemes are used to simulate unsteady flow in elastic pipes due to sudden valve closure. The spatial derivatives are discretized using a central difference scheme. Second-order dissipative terms are added in regions of high gradients while they are switched off in smooth flow regions using a total variation diminishing (TVD) switch. The method is applied to both one- and two-dimensional water hammer formulations. Both laminar and turbulent flow cases are simulated. Different turbulence models are tested including the Baldwin-Lomax and Cebeci-Smith models. The results of the present method are in good agreement with analytical results and with experimental data available in the literature. The two-dimensional model is shown to predict more accurately the frictional damping of the pressure transient. Moreover, through order of magnitude and dimensional analysis, a non-dimensional parameter is identified that controls the damping of pressure transients in elastic pipes. Copyright (c) 2006 John Wiley & Sons, Ltd.