Comparative Numerical Analysis on Momentum Flux Evaluation Schemes for Shallow Water Flows in Open Channel Networks

Abstract

Analyzing macroscopic dynamics of surface water flows is one of the most important issues in agricultural and environmental engineering. The dynamics of surface water is described using the cross-sectionally averaged one-dimensional shallow water equations (1-D SWEs) with the assumptions of the incompressibility of water and 10 hydrostatic pressure distribution. A typical surface water system involves an open channel network. To develop an accurate and efficient simulation method for the flows in open channel networks is therefore an important task. This paper proposes a new momentum flux evaluation scheme for the 1-D SWEs in locally 1-D open channel networks. The scheme evaluates the momentum flux considering the contact angles of the reaches at a junction as well as the discharge ratios, ensuring non-increase of the momentum variation. Numerical simulations of flows in an open channel network having a junction are carried out to compare the proposed scheme with the existing ones. Computational results of the discharge ratios show the validity of the proposed scheme, which in some cases is as accurate as the 2-D counterpart. Computational results of water surface profiles show the advantages of the proposed scheme over the existing ones, accurately reproducing the experimental flows that the latter cannot appropriately deal with.

Numerical comparison of shallow water models in multiply connected open channel networks

“…The 1-D SWEs that consist of the extended continuity equation 5and the momentum equation 2are numerically solved with the DFVM [21] equipped with one of the three IBCs, which are the IBC of Ishida et al [18], that of Unami and Alam [19], and that of Yoshioka et al [20]. The DFVMs with these IBCs are referred to as the M1-scheme, M2-scheme, and M3-scheme, respectively following Yoshioka et al [23].…”

“…is referred to as the momentum condition in this paper. According to the mathematical analysis [20], the IBC (8) satisfies the inequality 0 F (14) and the IBC (9) conditionally satisfies the momentum condition (13) subject to the constraint…”

“…The authors developed spatially staggered numerical schemes for solving the 1-D SWEs based on both the FEM and FVM techniques with the heuristic upwind methods for handling the momentum equation [18,19,20], which are referred to as the Finite Element/Volume Methods (FEVMs). There also exists an FVM counterpart of the FEVMs, which is referred to as the Dual-Finite Volume Method (DFVM) [21].…”

“…These numerical methods assume different IBCs in handling the momentum equation at junctions, which are considered to have significant impacts on simulated hydraulic processes. However, their qualitative and quantitative comparisons have not been performed so far except for Yoshioka et al [20] who focused on steady problems and Yoshioka et al [23] [18], that of Unami and Alam [19], and that of Yoshioka et al [20]. This paper is an extended version of Yoshioka et al [23] that focused only on applications of the numerical schemes to dam break flash floods.…”

“…This paper is an extended version of Yoshioka et al [23] that focused only on applications of the numerical schemes to dam break flash floods. Two real hydro-environmental problems are considered in this paper to demonstrate several advantages of the scheme proposed in [20]. The first problem is a surface water flow in a hydromorphic environment where the flow is driven by the lateral inflows due to rainfall and persistent seepage.…”