An accurate and efficient scheme involving unsteady friction for transient pipe flow

A robust prediction system should monitor all possible hydraulic transients, which is significant for the appropriate and safe operation of pipe systems. A second-order finite volume method (FVM) Godunov-type scheme (GTS) considering unsteady friction factors is introduced to simulate hydraulic transients, which was rarely involved in previous work. One explicit-solution source item approach developed in this work is crucial for the proposed GTS to easily incorporate various forms of the existing unsteady friction models, including original convolution-based models (Zielke model and Vardy–Brown model), simplified convolution-based model (Trikha–Vardy–Brown (TVB) model), and Brunone instantaneous acceleration-based model. Results achieved by the proposed models are compared with experimental data as well as predictions by the classic Method of Characteristics (MOC). Results show that the MOC scheme may produce severe numerical attenuation in the case of a low Courant number. The proposed second-order GTS unsteady friction models are accurate, efficient, and stable even for Courant numbers less than one and sparse grid, and only need much less grid number and computation time to reach the same numerical accuracy. The TVB convolution-based model and Brunone model in the second-order GTS are suggested for further applications in hydraulic transients due to their high accuracy and efficiency. HIGHLIGHTS A Godunov-type scheme involving unsteady pipe friction is developed.; An explicit-solution source item approach is introduced to incorporate unsteady friction.; The numerical models are validated by the experimental data.; The proposed models are accurate, efficient, and stable for transient pipe flow.; A Brunone unsteady friction model is more efficient than the convolution-based model.