A numerical approach to the standard model of water hammer with fluid-structure interaction

In the classic water hammer (WH) theory, 1D liquid flow in a quasi-rigid pipe is assumed. When the pipe is flexible or is fixed to the foundation with elastic supports, the dynamic fluid structure interaction (FSI) should be taken into account for more accurate modelling of the system behaviour. The standard model of WH-FSI for a straight pipe reach is governed by fourteen hyperbolic partial differential equations of the first order, two for 1D liquid flow and twelve for 3D motion of the pipe. This model is presented in the paper and an algorithm for its numerical solution based of the method of characteristics is proposed. Basic boundary conditions (BC) are shortly discussed. The important condition at the junction of two sub-pipes fixed to the foundation with a viscoelastic support is presented in details and a general method of its solution is proposed.