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Finite Volume Models and Efficient Simulation Tools (EST) for Shallow Flows

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Advances in Fluid Mechanics

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

Abstract

Shallow-type mathematical models are built in the context of free surface flows over the main hypothesis that the flow layer depth is smaller than a relevant horizontal length scale. There is a wide range of physical situations in which these shallow-type formulations are applicable, such as open channels and rivers, tsunamis, floods, landslides or muddy slurries. Their numerical solution on the finite volume framework is governed by the dynamical properties of the flow, the uneven distribution of the bed level and also by the computational grid choice. The unified discretization of spatial flux derivatives and source terms has proven useful to ensure the properties of monotonicity, stability and conservation in the numerical solution. Surface shallow flows that occur in catchments and coasts usually require large space resolution over longer periods of time. The increasing complexity of the mathematical models, the advancements in numerical methods, as well as the increasing power of computation are making possible the physically-based simulation of these phenomena. The necessity of spatial resolution involves the use of a large number of elements, which increases the computational time when simulating realistic scenarios for a long time period. The resulting approach from the proper mathematical formulation, robust numerical resolution and efficient computational implementation of models (EST) can be very useful in the simulation of environmental surface processes with realistic temporal and spatial scales.

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Acknowledgements

This work is part of the PGC2018-094341-B-I00 research project funded by the Ministry of Science and Innovation/FEDER. Additionally, Mario Morales-Hernández was partially supported by the U.S. Air Force Numerical Weather Modeling Program.

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Authors and Affiliations

  1. Fluid Mechanics, University of Zaragoza, Zaragoza, Spain

    S. Martínez-Aranda, J. Fernández-Pato, I. Echeverribar, A. Navas-Montilla, M. Morales-Hernández, P. Brufau, J. Murillo & P. García-Navarro

  2. Hydronia-Europe S.L, Madrid, Spain

    J. Fernández-Pato & I. Echeverribar

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  1. S. Martínez-Aranda
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Correspondence to P. Brufau .

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  1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan

    Dia Zeidan

  2. Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

    Lucy T. Zhang

  3. ISAE-ENSMA, Institut Pprime, Chasseneuil-du-Poitou, France

    Eric Goncalves Da Silva

  4. MNZ, Leipzig University of Applied Sciences, Leipzig, Germany

    Jochen Merker

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Martínez-Aranda, S. et al. (2022). Finite Volume Models and Efficient Simulation Tools (EST) for Shallow Flows. In: Zeidan, D., Zhang, L.T., Da Silva, E.G., Merker, J. (eds) Advances in Fluid Mechanics. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-1438-6_3

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