Mixing and Mixtures in Geo- and Biophysical Flows: A Focus on Mathematical Theory and Numerical Methods

2D versus 1D models for thin film flows

Jean-Paul Vila

INSA Toulouse

By using Prandtl shift system of coordinate, the present contribution developed for the first time an efficient tool for computing simple asymptotic expansion of 3D flow of thin films over a general non flat topography. 2D systems of two equations are thus introduced and generalize those classically obtained on a plane surface. An asymptotic framework is also presented and enables to obtain simplified 1D systems with two (or 3) equations when the topography of the 2D models exhibits the characteristics of a 1 dimensional channel with general cross sections. In the special case of Shallow Water systems, we compare the new models to the classical one used in standard hydraulic flows.