\beamer@endinputifotherversion {3.36pt} \beamer@sectionintoc {1}{Introduction}{2}{0}{1} \beamer@subsectionintoc {1}{1}{Layerwise Discretized Shallow Water model}{2}{0}{1} \beamer@sectionintoc {2}{1D bilayer model}{8}{0}{2} \beamer@subsectionintoc {2}{1}{Hyperbolicity and waves patterns}{8}{0}{2} \beamer@subsectionintoc {2}{2}{The 1D Riemann problem}{9}{0}{2} \beamer@sectionintoc {3}{2D bilayer model}{11}{0}{3} \beamer@subsectionintoc {3}{1}{Hyperbolicity and waves patterns}{11}{0}{3} \beamer@subsectionintoc {3}{2}{Definition of the non-conservative products}{16}{0}{3} \beamer@subsectionintoc {3}{3}{The 2D Riemann problem}{25}{0}{3} \beamer@subsectionintoc {3}{4}{Some analytical solutions}{28}{0}{3} \beamer@sectionintoc {4}{Conclusions}{29}{0}{4}