The main contribution of the paper is to incorporate pipe-wall viscoelastic and unsteady friction in the derivation of the water-hammer solutions of non-conservative hyperbolic systems with conserved quantities as variables. The system is solved using the Godunov finite volume scheme to obtain numerical solutions. This results in the appearance of a new term in the mass conservation equation of the classical governing system. This new numerical algorithm implements the Godunov approach to one-dimensional hyperbolic systems of conservation laws on a finite volume stencil. The viscoelastic pipe-wall response in the mass conservation part of the source term has been modeled using generalized Kelvin–Voigt theory. For the momentum part of the source term a fast, robust and accurate numerical scheme linked to the Lambert W-function for calculating the friction factor has been used. A case study has been used to illustrate the influence of the various formulations; a comparison between the classical solution, the numerical solution including quasi-steady friction, the numerical solution incorporating the viscoelastic effects, and measurements are presented. The inclusion of viscoelastic effects results in better agreement between the measured and solved values.
Incorporate the viscoelastic pipe and unsteady friction in water-hammer formulations
Present the solutions of non-conservative hyperbolic systems with conserved quantities as variables
Adapt the finite volume approach, which was developed for hyperbolic equations to tackle systems that are not in ‘proper’ conservation form
Give a new numerical algorithm in finite volume for study several variants;