Pressure-balanced Saint–Venant equations for improved asymptotic modelling of pipe flow

Abstract

In urban drainage networks, steady free surface flows in circular-shaped pipes are commonly observed given low inflow discharges. Therefore, accurate computation of such steady states is of great practical significance, especially considering bent pipes. This requires numerical schemes to be capable of achieving a delicate balance between slope source terms and fluxes in the discrete framework. To this end, in the current study, a new method using pressure balanced Saint–Venant equations and positivity preserving Godunov-type finite volume scheme, is developed for 1D flow simulation in bent circular pipes. Using pressure balancing, a set of pre-balanced Saint–Venant equations is derived. The numerical discretization method uses an approximate Riemann solver and is capable of dealing with wetting–drying process stably in frictional pipes. As verified by several test cases, the proposed method shows better performances than existing methods in modelling the asymptotic flow behavior and preserving steady states in bent circular pipes.