Mesh‐free model for Hopf's bifurcation points in incompressible fluid flows problems. (16th May 2022)

• Record Type: Journal Article
• Authors: Rammane, Mohammed; Mesmoudi, Said; Tri, Abdeljalil; Braikat, Bouazza; Damil, Noureddine
• Is Part Of: International journal for numerical methods in fluids. Volume 94:Number 9(2022)
• Page Start: 1566
• Page End: 1581
• Publication Date: 2022-05-16
• Subjects: high order continuation -- Hopf bifurcation -- incompressible fluid flow -- moving least squares -- strong formulation -- transitory flow; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.5101
• Languages: English
• ISSNs: 0271-2091

Abstract

Abstract: In this article, a new numerical model is proposed to detect numerically the Hopf bifurcation point of incompressible fluid flows problems. The concept of this model consists to propose a Hopf bifurcation indicator which is solved by a high order mesh free algorithm (HO‐MFA) using the moving least squares (MLS) approximation. This numerical model is based on a strong formulation of Navier–Stokes equations. This procedure allowed us to recover the results of the literature in 3 D $$ 3D $$ using only a 2 D $$ 2D $$ modelization for low Reynolds number. This new model is tested on the classical flow around a cylindrical obstacle and the backward‐facing step flow to show the advantage and ability of the proposed model to detect the bifurcation points and to determinate the flow periodicity. Abstract : In this article, a new numerical model is proposed to detect numerically the Hopf bifurcation point of incompressible fluid flows problems. The concept of this model consists to propose a Hopf bifurcation indicator which is solved by a high order mesh free algorithm (HO‐MFA) using the moving least squares (MLS) approximation. This numerical model is based on a strong formulation of Navier–Stokes equations. This procedure allowed us to recover the results of the literature in 3D using only a 2D modelization.