Abstract: For one-dimensional water hammer simulations, the weight-function unsteady friction model is considered to be the most accurate model compared with steady-state friction models, as it describes pressure attenuation accurately through fully considering the influence of the past velocity and acceleration on shear stress in hydraulic transients. Due to the complexity of convolution integral terms and the consideration that a first-order accurate solution is satisfactory for most of the problems, its previous solutions are based on the first-order methods of characteristics (MOC). To improve accuracy, this paper derives a second-order approximate solution of the MOC convolution integral, and verifies its accuracy against experimental data. Results show that the new scheme is second-order accurate and the first-order scheme leads to computational errors that increase with the increase in grid size, flow velocity and viscosity.

Key words: transient flow, water hammer, weight-function unsteady friction model, second-order approximate solution, calculation error