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

作者：Guevel Y; Boutyour H; Cadou J M^*

来源：Journal of Computational Physics, 2011, 230(9): 3614-3629.

DOI：10.1016/j.jcp.2011.02.004

• Stationary bifurcation
• Navier-Stokes
• Branch switching
• Continuation method
• Perturbation method

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.

• 出版日期2011-5-1