2017/01/10 by Chinedu Nwaigwe, Andreas Dedner, Nwaigwe, Chinedu +1
Earth and Planetary Sciences · Engineering · Environmental Science · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Flood Risk Assessment and Management #Fluid Dynamics and Turbulent Flows #Hydrology and Sediment Transport Processes #Hydrology and Watershed Management Studies #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1701.02577
openalex publication_date 2017/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One dimensional (1D) simulations of the flow and flooding of open channels\nare known to be inaccurate as the flow is multi-dimensional in nature,\nespecially at the flooded regions. However, multi-dimensional simulations, even\nin two dimensions (2D), are computationally expensive, hence the problem of\nefficiently coupling 2D and 1D simulations for the flow and flooding of open\nchannels has been the subject of much research and is investigated in this\npaper. We adopt a 1D model with coupling term for the channel flow and the 2D\nshallow water flow model for the floodplain. The 1D model with coupling term is\nderived by integrating the 3D Free Surface Euler equations but without imposing\nany restriction on the channel width variations. %leading to a new coupling\nterm. Finite volume methods are formulated for both the 2D and 1D models\nincluding a discrete coupling term in closed form. Coupling is achieved through\nthe discrete coupling term in the 1D model and the lateral numerical fluxes in\nthe 2D model. Since the lateral discharge in the channel cannot be guaranteed\nto be zero during flooding, we aim to recover the lateral variation by\ncomputing two lateral discharges over each cross section and propose to use an\nad-hoc model based on the y-discharge equation in the 2D model for this\npurpose. We then propose the numerical scheme for this ad-hoc model following\nthe hydrostatic reconstruction philosophy. Then, we show that the resulting\nmethod, named Horizontal Coupling Method (HCM), is well-balanced; we introduce\nthe no-numerical flooding property and also show that the method satisfies the\nproperty. Three numerical test cases are used to verify the performance of the\nmethod. The results show that the method performs well in both accuracy and\nefficiency and also approximates the channel lateral discharges with very good\naccuracy and little computational overhead.\n