Water hammer simulation by implicit method of characteristic

An Implicit Method of Characteristics is proposed in this paper to alleviate the shortcomings and limitations of the mostly used conventional Method of Characteristics (MOC). An element-wise definition is used for all the devices that may be used in a pipeline system and the corresponding equations are derived in an element-wise manner. The proper equations defining the behavior of each device including pipes are derived and assembled to form the final system of equations to be solved for the unknown nodal heads and flows. Proposed method allows for any arbitrary combination of devices in the pipeline system. The method is used to solve two example problems of transient flow caused by closure of a valve and failure of a pump system and the results are presented and compared with those of the explicit MOC. The results show the ability of the proposed method to accurately predict the variations of head and flow in all cases considered.