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SWASHES: a compilation of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies

By Olivier Delestre, Carine Lucas, Pierre-Antoine Ksinant, Frédéric Darboux, Christian Laguerre, Thi Ngoc Tuoi Vo, Francois James and Stephane Cordier


40 pages There are some errors in the published version. This is a corrected version.International audienceNumerous codes are being developed to solve Shallow Water equations. Because there are used in hydraulic and environmental studies, their capability to simulate properly flow dynamics is critical to guarantee infrastructure and human safety. While 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 1 or 2 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 (, so that users of Shallow Water-based models can easily find an adaptable benchmark library to validate their numerical methods

Topics: Shallow-Water, Saint-Venant, Analytic solutions, Benchmarking, Validation of numerical methods, Steady-state flow, Transitory flow, Source terms, Diffusion term, Friction term, Chezy, Manning, Strickler, Darcy-Weisbach, Rain, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics []/Fluids mechanics [physics.class-ph], [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph]
Publisher: Wiley
Year: 2013
DOI identifier: 10.1002/fld.3741
OAI identifier: oai:HAL:hal-00628246v6
Provided by: HAL-UNICE

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