Automatic detection and branch switching methods for steady bifurcation in fluid mechanics

This paper deals with the computation of steady bifurcations in the framework of 2D incompressible Navier–Stokes flow. We first propose a numerical method to accurately detect the critical Reynolds number where this kind of bifurcation appears. From this singular value, we introduce a numerical tool to compute all the steady bifurcated branches. All these algorithms are based on the Asymptotic Numerical Method [1,2]. The critical values are determined by using a bifurcation indicator [3–5] and the bifurcated branches are computed by using an augmented system which was first introduced in solid mechanics [4,6]. Several numerical examples from 2D Navier–Stokes show the reliability and the efficiency of the proposed methods.