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.

在城市排水管网中，由于流入流量较低，通常会观察到圆形管道中稳定的自由表面流。因此，准确计算这种稳态具有重要的实际意义，特别是考虑到弯曲的管道。这需要数值方案能够在离散框架中的斜率源项和通量之间实现微妙的平衡。为此，在当前的研究中，开发了一种使用压力平衡圣维南方程和正性保持 Godunov 型有限体积方案的新方法，用于弯曲圆形管道中的一维流动模拟。使用压力平衡，可以推导出一组预先平衡的圣维南方程。数值离散化方法使用近似黎曼求解器，能够稳定地处理摩擦管道中的干湿过程。