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

Yann Guevel (1) , Hassan Boutyour (2) , Jean-Marc Cadou (1)

1 LIMATB - Laboratoire d'Ingénierie des Matériaux de Bretagne
2 Département de Physique Appliquée [Settat]

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. The critical values are determined by using a bifurcation indicator and the bifurcated branches are computed by using an augmented system which was first introduced in solid mechanics. Several numerical examples from 2D Navier-Stokes show the reliability and the efficiency of the proposed methods.

Mots clés: Branch switching; Stationary bifurcation; Navier-Stokes; Continuation method; Perturbation method

Domaines: Mécanique [physics.med-ph]

Yann Guevel, Hassan Boutyour, Jean-Marc Cadou. Automatic detection and branch switching methods for steady bifurcation in fluid mechanics. Journal of Computational Physics, 2011, 230 (9), pp.3614-3629. ⟨10.1016/j.jcp.2011.02.004⟩. ⟨hal-00715955⟩