On the governing equations for horizontal and vertical coupling of one- and two-dimensional open channel flow models

Authors: SIMON, CESAR - University Of Pittsburgh; Langendoen, Eddy; ABAD, JORGE - University Of Pittsburgh; MENDOZA, ALEJANDRO - Metropolitan Autonomous University

Submitted to: Journal of Hydraulic Research IAHR
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 9/8/2017
Publication Date: 9/1/2020
Citation: Simon, C.A., Langendoen, E.J., Abad, J., Mendoza, A. 2020. On the governing equations for horizontal and vertical coupling of one- and two-dimensional open channel flow models. Journal of Hydraulic Research IAHR. 58(5):709-724. https://doi.org/10.1080/00221686.2019.1671507.
DOI: https://doi.org/10.1080/00221686.2019.1671507

Interpretive Summary: One-dimensional computer models of channel evolution are effective tools to quantify channel erosion and in-stream sediment loads. However, such models cannot adequately represent these processes when flow is overbank. These conditions occur for example when assessing reservoir rehabilitation or dam removal strategies. Scientists of the Watershed Physical Processes Research Unit, Oxford, MS and the University of Pittsburgh are jointly developing a computer model that uses one-dimensional (1D) computer models to simulate inbank processes and two-dimensional (2D) computer models to simulate overbank processes. This paper derives and quantifies the fluid mass and momentum fluxes that are present at the interface between 1D and 2D models for two different orientations of this interface, horizontal and vertical respectively. It was found that these fluxes are smaller for horizontally-oriented interfaces, and their approximation should therefore have a smaller impact on the overall model results than in the case of a vertically-oriented interface. These findings will help scientists in academia and research institutes to develop improved coupling strategies between 1D and 2D computer models, which are needed to study overbank flow processes, such as floods and reservoir rehabilitation.

Technical Abstract: Cross-section averaged, one-dimensional (1D) models of open-channel flow are computationally efficient for simulating in-channel hydrodynamics over long reaches and time periods, but cannot accurately simulate overbank flows and the transition from in-channel to overbank flow. Two-dimensional (2D), depth-averaged models can simulate such flows more accurately, however are computationally less efficient for long reaches and time periods. Further, 2D models cannot accurately represent the geometry of steep channel banks, which could impact the simulated near-bank flow during floods. Numerical models have been developed that laterally couple 1D channel and 2D overbank approaches to overcome the before-mentioned drawbacks. However, experimental investigations have shown that lateral coupling can produce significant errors in the computed discharge across the channel and floodplain. This paper presents a thorough derivation of the governing equations of horizontally (1D channel and 2D overbank regions) and vertically (1D in-channel and 2D overbank regions) coupled 1D and 2D hydrodynamic models, which introduces terms representing mass and both advective and diffusive momentum transfer between the various regions. A three-dimensional Reynolds-Averaged Navier-Stokes model was used to quantify these transfer terms for the case of an experimental meandering channel with overbank flow. The transfer terms that need to be approximated for the vertical coupling approach were smaller than those for the horizontal coupling approach, indicating that the vertical coupling method may therefore be more accurate. For both coupling methods and larger relative overbank flow depth, the advective momentum transfer exceeded the diffusive momentum transfer. The diffusive momentum transfer had similar magnitude for both coupling approaches, however the advective momentum transfer was an order of magnitude higher for the horizontal coupling method than for the vertical coupling method.