Résolution des équations de Navier-Stokes et Détection des bifurcations stationnaires par une Méthode Asymptotique-Numérique

Abstract

Perturbation methods (asymptotic expansions) are usually considered as powerful methods for solving many kinds of non-linear problems. However, these methods are very often applied in a purely analytic framework, and the calculation is limited to the first few terms of the series. Since a few years, we have shown that the combination of perturbation techniques and finite element method can lead to a robust numerical method for some categories of non-linear problems. In this paper, we apply these techniques to compute branches of stationary solutions of Navier-Stokes equations and to detect stationary bifurcations.