Applicability of Zero-Inertia Approximation for Overland Flow Using a Generalized Mass-Conservative Implicit Finite Volume Framework
Publication: Journal of Hydrologic Engineering
Volume 29, Issue 1
Abstract
The zero-inertia approximation of the shallow water equations has been observed to provide reasonably accurate results for various flood propagation problems. The commonly adopted explicit time schemes in the numerical modeling of zero-inertia flows are computationally expensive and vulnerable to numerical instabilities. This paper presents a finite volume method-based zero-inertia overland flow model named surfaceFlowFOAM, developed using OpenFOAM framework with an implicit time discretization scheme. The nonlinear zero-inertia equation is linearized by applying the iterative Picard linearization technique. We have implemented a stabilized and adaptive time-stepping algorithm for controlling the convergence of Picard iterations to avoid numerical instability, thereby enhancing the overall computational efficiency. This study analyzes that the applicability of the zero-inertia approximation should be limited to low subcritical surface flow problems with Froude numbers less than 0.5. The analysis has been done by observing the effects of variations in bed-slope and rainfall intensity on the Froude number of flows developing over the overland surface. Furthermore, we have discussed the achieved mass balance accuracy of surfaceFlowFOAM in solving the considered test examples. The numerical results of surfaceFlowFOAM show excellent correspondence with the results presented in the literature for solved overland flow problems. The solution accuracy and the achieved computational efficiency ensure the potential applicability of surfaceFlowFOAM to solve the lower range (Froude number ) of two-dimensional subcritical flood flow problems.
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Data Availability Statement
Some or all data that support the findings of this study are available from the corresponding author upon reasonable request. However, the source code for surfaceFlowFOAM can be downloaded from the link: https://github.com/gwres/surfaceFlowFOAM.
Acknowledgments
All the simulations were performed utilizing the resources and supercomputing facilities of Param Shakti at the Indian Institute of Technology Kharagpur, established under the National Supercomputing Mission (NSM), supported by the Ministry of Electronics and Information Technology (MeitY) and Department of Science and Technology (DST), Government of India, and implemented by the Centre for Development of Advanced Computing (CDAC), Pune.
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Journal of Hydrologic Engineering
Volume 29 • Issue 1 • February 2024
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© 2023 American Society of Civil Engineers.
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Received: Feb 16, 2023
Accepted: Aug 9, 2023
Published online: Oct 24, 2023
Published in print: Feb 1, 2024
Discussion open until: Mar 24, 2024
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