Godunov-type solutions for free surface transient flow in pipeline incorporating unsteady friction

A finite-volume second-order Godunov-type scheme (GTS) combining the unsteady friction model (UFM) is introduced to simulate free surface flow in pipelines. The exact solution to the Riemann problem calculates the mass and momentum fluxes while considering the Brunone unsteady friction factor. One simple boundary treatment with double virtual cells is proposed to ensure the whole computation domain with second-order accuracy. Results of various transient free-surface flows achieved by the proposed models are compared with exact solution, experimental data, the four-point implicit Preissmann scheme solution, as well as predictions by the classic Method of Characteristics (MOC). Results show that the proposed second-order GTS UFMs are accurate, efficient, and stable even for Courant numbers less than one and sparse grid. The four-point implicit Preissmann scheme may produce severe numerical attenuation in the case of large time steps and unsuitable weighting factors, while the MOC scheme may produce severe numerical attenuation in the case of a low Courant number and could not maintain mass conservation. The numerical simulations considering the unsteady friction factor are closer to the measured water depth variations. The effect of unsteady friction becomes more important as the initial water depth difference increases significantly.