LJKDeterministic Models and Algorithms: EDPMOISE Seminar

On Thursday April 2 2009 at 11h00 in Salle 1  Tour IRMA

Seminary of Mr Sébastien MARTIN (Université Paris Sud11, Orsay)

Vicoelastic fluids in a thin domain

Summary

We address the mathematical and numerical study of a large class of viscoelastic thin film flows described by an OlroydB model in which the Deborah number has the same order of magnitude than the thickness of the fluid. After scaling both equations and stress tensor in an adequate way, we are able to obtain an asymptotic 2D problem. Obtaining the asymptotic problem is partly an heuristic process, so we have to rigorously prove the solvability of this problem. This is the goal of the mathematical analysis which is divided in two parts for sake of clearness: i) the Newtonian case is first studied and a new way is proposed to obtain an existence and uniqueness result for the problem using the velocity as a leading unknown ; ii) such an approach can be easily generalized to the viscoelastic case by using a monotonicity property of the nonlinear term. Then, a new algorithm is presented and convergence results are given. At last, numerical comparison between various model are presented.
