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SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies

Authors

  • Olivier Delestre,

    Corresponding author
    1. Institut Jean Le Rond d'Alembert, CNRS & UPMC Université Paris 06, F-75005 Paris, France
    • MAPMO UMR CNRS 7349, Université d'Orléans, UFR Sciences, Bâtiment de mathématiques, F-45067 Orléans cedex 2, France
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  • Carine Lucas,

    1. MAPMO UMR CNRS 7349, Université d'Orléans, UFR Sciences, Bâtiment de mathématiques, F-45067 Orléans cedex 2, France
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  • Pierre-Antoine Ksinant,

    1. MAPMO UMR CNRS 7349, Université d'Orléans, UFR Sciences, Bâtiment de mathématiques, F-45067 Orléans cedex 2, France
    2. INRA, UR0272, UR Science du sol, Centre de recherche d'Orléans, CS 40001, F-45075 Orléans Cedex 2, France
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  • Frédéric Darboux,

    1. INRA, UR0272, UR Science du sol, Centre de recherche d'Orléans, CS 40001, F-45075 Orléans Cedex 2, France
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  • Christian Laguerre,

    1. MAPMO UMR CNRS 7349, Université d'Orléans, UFR Sciences, Bâtiment de mathématiques, F-45067 Orléans cedex 2, France
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  • T.-N.-Tuoi Vo,

    1. MAPMO UMR CNRS 7349, Université d'Orléans, UFR Sciences, Bâtiment de mathématiques, F-45067 Orléans cedex 2, France
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    • Presently at: Department of Applied Mathematics, National University of Ireland, Galway, Republic of Ireland.

  • François James,

    1. MAPMO UMR CNRS 7349, Université d'Orléans, UFR Sciences, Bâtiment de mathématiques, F-45067 Orléans cedex 2, France
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  • Stéphane Cordier

    1. MAPMO UMR CNRS 7349, Université d'Orléans, UFR Sciences, Bâtiment de mathématiques, F-45067 Orléans cedex 2, France
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Errata

This article is corrected by:

  1. Errata: SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies Volume 74, Issue 3, 229–230, Article first published online: 28 November 2013

Correspondence to: Olivier Delestre, Laboratoire de Mathématiques J.A. Dieudonné & Polytech Nice-Sophia, Université de Nice - Sophia Antipolis, Parc Valrose, 06108 Nice cedex 02, France.

E-mail: Delestre@unice.fr

SUMMARY

Numerous codes are being developed to solve shallow water equations. Because these are used in hydraulic and environmental studies, their capability to simulate flow dynamics properly is critical to guarantee infrastructure and human safety. Although validating these codes is an important issue, code validations are currently restricted because analytic solutions to the shallow water equations are rare and have been published on an individual basis over a period of more than five decades. This article aims at making analytic solutions to the shallow water equations easily available to code developers and users. It compiles a significant number of analytic solutions to the shallow water equations that are currently scattered through the literature of various scientific disciplines. The analytic solutions are described in a unified formalism to make a consistent set of test cases. These analytic solutions encompass a wide variety of flow conditions (supercritical, subcritical, shock, etc.), in one or two space dimensions, with or without rain and soil friction, for transitory flow or steady state. The corresponding source codes are made available to the community (http://www.univ-orleans.fr/mapmo/soft/SWASHES), so that users of shallow water-based models can easily find an adaptable benchmark library to validate their numerical methods. Copyright © 2012 John Wiley & Sons, Ltd.

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