SWASHES: A library for benchmarking in hydraulics / SWASHES : une   biblioth\`eque de bancs d'essai en hydraulique
  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 (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. 
Olivier Delestre (JAD), Carine Lucas (MAPMO), Pierre-Antoine Ksinant   (MAPMO, USS), Fr\'ed\'eric Darboux (USS), Christian L...
math.NA math.AP