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.

本文的主要贡献是在以守恒量为变量的非守恒双曲系统的水锤解的推导中，将管壁粘弹性和非定常摩擦纳入其中。使用Godunov有限体积方案对系统进行求解，以获得数值解。这导致在经典控制系统的质量守恒方程中出现新术语。这种新的数值算法将Godunov方法用于有限体积模板上的一维双曲守恒律系统。源项质量守恒部分中的粘弹性管壁响应已使用广义的Kelvin-Voigt理论建模。对于源项的动量部分，一个与Lambert W相关的快速，健壮和准确的数值方案-已使用用于计算摩擦系数的函数。通过案例研究来说明各种配方的影响。给出了经典解，包括准稳态摩擦的数值解，包含粘弹性效应的数值解和测量值之间的比较。包含粘弹性效应可以使测量值和求解值之间的一致性更好。