Accurate Numerical Modeling for 1D Open-Channel Flow with Varying Topography

Abstract

In this paper, an accurate numerical model is presented for one-dimensional open-channel flows with varying topographies; the model is specifically applied to rectangular channels with variable widths. A pressure term is introduced in the shallow water momentum equation to construct a new conservation term, and the resulting non-conservation term is included in the source term to characterize the actual topography changes in the open-channel flow. Based on a Harten Lax and van Leer (HLL) Riemann solver for a homogeneous system, an upwind scheme is introduced into the model in which the flux is determined via randomly selecting a local Riemann solution state. This two-step random choice method enables the scheme to reach second-order accuracy in space. A Runge–Kutta scheme is introduced into the discretization of the source term of the system to achieve second-order accuracy. The proposed model is validated via a selection of steady and transient hydraulic problems with reference solutions. When compared with published experimental results, the predictions of the proposed model show a high degree of accuracy.