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                <term xml:lang="en">Strickler</term>
                <term xml:lang="en">diffusion</term>
                <term xml:lang="en">friction</term>
                <term xml:lang="en">rain</term>
                <term xml:lang="en">Chézy</term>
                <term xml:lang="en">Darcy-Weisbach</term>
                <term xml:lang="en">Shallow Water equation</term>
                <term xml:lang="en">Manning</term>
                <term xml:lang="en">backwater curves</term>
                <term xml:lang="en">source terms</term>
                <term xml:lang="en">transitory flow</term>
                <term xml:lang="en">steady-state flow</term>
                <term xml:lang="en">validation of numerical methods</term>
                <term xml:lang="en">benchmarking</term>
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              <p>Numerous codes are being developed to solve Shallow Water equations. Because they are used in hydraulics and environmental studies, their capability to simulate properly flow dynamics is essential to guarantee infrastructure and human safety. Hence, validating these codes and the associated numerical methods is an important issue. Analytic solutions would be excellent benchmarks for these issues. However, analytic solutions to Shallow Water equations are rare. Moreover, they have been published on an individual basis over a period of more than five decades, making them scattered through the literature. In this paper, a significant number of analytic solutions to the Shallow Water equations is described in a unified formalism. They encompass a wide variety of flow conditions (supercritical, subcritical, shock ...), in 1 or 2 space dimensions, with or without rain and soil friction, for transitory flow or steady state. An original feature is that the corresponding source codes are made freely available to the community (https://www.idpoisson.fr/swashes/), so that users of Shallow Water based models can easily find an adaptable benchmark library to validate their numerical methods.</p>
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            <abstract xml:lang="fr">
              <p>De nombreux codes sont développés pour résoudre les équations des écoulements en eau peu profonde. Parce qu'ils sont utilisés en hydraulique et dans les études environnementales, leur capacité à simuler correctement la dynamique des écoulements est essentielle pour garantir la sécurité des infrastructures et des personnes. La validation de ces codes et des méthodes numériques associées est donc une question importante. Les solutions analytiques seraient d'excellents cas tests pour ces questions. Cependant, les solutions analytiques aux équations des écoulements en eau peu profonde sont rares. De plus, elles ont été publiées individuellement sur une période de plus de cinq décennies, ce qui fait qu'elles sont dispersées dans la littérature. Dans cet article, un nombre important de solutions analytiques aux équations des écoulements en eau peu profonde est décrit dans un formalisme unifié. Elles englobent une grande variété de conditions d'écoulement (supercritique, sous-critique, choc...), en 1 ou 2 dimensions spatiales, avec ou sans pluie et frottement du sol, pour un écoulement transitoire ou en régime permanent. Une caractéristique originale est que les codes sources correspondants sont mis gratuitement à la disposition de la communauté (https://www.idpoisson.fr/swashes/), de sorte que les utilisateurs de modèles d'écoulements en eau peu profonde peuvent facilement trouver une bibliothèque de référence adaptable pour valider leurs méthodes numériques.</p>
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