The authors have made a transition from the mass balance equations based on the Kirchhoff laws in network hydraulic simulation to discretization of continuity equation. For this purpose a control-volume finite-difference method has been applied. This paper introduces an extension of the developed control-volume method for time-dependent processes in hydraulic networks. This extension developed for slow time-varying conditions in the hydraulic networks and is not intended to calculate rapidly occurring local phenomena such as water hammer.
Skibin, A., & Volkov, V. (2014). Extending the control-volume method to unsteady network hydraulic simulations. In Procedia Engineering (Vol. 89, pp. 595–602). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2014.11.483