A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validationEmmanuel Audusse, Marie-Odile Bristeau, Benoît Perthame and Jacques Sainte-MarieESAIM: M2AN, 45 1 (2011) 169-200DOI: https://doi.org/10.1051/m2an/2010036