This paper addresses the critically important issue regarding the appropriate size of the discretisation elements whilst ensuring stability and reasonable computational work loads for the numerical simulation of highly transient flows. The simulation of outflow following the puncture of a hypothetical 100 m pipeline at 21.6 bara (2160 kPa) and 293.15 K is used as a case example. The pipeline is assumed to contain different classes of hydrocarbons including permanent gases and liquids, two-phase mixtures and flashing liquids. The simulated outflow data for varying discretisation time and distance elements, expressed in terms of a Courant, Friedrichs and Lewy (CFL) factor indicate that in the case of permanent fluids and two-phase mixtures, a hyperbolic increase in the computational run time with decreasing CFL factor is obtained. There is no CFL factor dependency with the simulated outflow data. However in the case of flashing liquids and their mixtures, although similar trends in the computation run times are observed, the prescribed CFL stability condition at CFL factors of less than 0.4 does not result in convergence. (C) 2009 Elsevier Ltd. All rights reserved.