Water hammer simulation of a series pipe system using the MacCormack time marching scheme

Transient simulation is very important to protect the water supply pipeline system from extreme pressures. In order to numerically simulate the transient response in a variable–property series pipe system, the water hammer model and matched boundary conditions are developed by introducing the MacCormack time marching scheme. Based on the proposed method, the transient pressure and flow velocity are numerically predicted for a variable–property series pipe, and then the results are compared to the classical method of characteristics (MOC). The improved method can yield a reasonable numerical solution for a closed pipe, and the solution agrees well with the MOC and existing experimental results. In the proposed model, the time step is no longer subjected to the length of the space step; consequently, it is more convenient in meshing and modifying the $x-t$ grid. Especially, it is very advantageous in establishing the simultaneous calculation in water hammer simulation for a variable–property series pipes system or complicated distribution networks.