In this study, automatic modification of stresses in rigid parts of a pipe line system is modeled using the trial results of a second-order explicit Finite Volume (FV) Godunov type scheme for one-dimensional transient flow in pipes. The developed model for numerical analysis of transient pressure is based on Riemann solution of continuity equation coupled with the momentum Equation (including convective term). The implementation of boundary conditions such as reservoirs, valves, and pipe junctions in the Godunov approach is similar to that of the method of characteristics (MOC) approach. The computed pressure waves are compared with analytical solution as well as laboratory measurements for single pipes. The model is applied on two classic problems (systems consisting of a reservoir, a pipe and a valve). The second-order Godunov scheme is stable for Courant number less than or equal to unity, and therefore, can be applied for the problems with variable mesh spacing. In order to show the ability of the developed model to deal with such cases, the computed maximum pressure distribution along a pipeline with variable segment coordinates are used for trial modification of pipe thickness and stress distribution.

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