Filter-matrix lattice Boltzmann simulation of lid-driven deep-cavity flows, Part II - Flow bifurcation

Following the first part of this study, the filter-matrix lattice Boltzmann (FMLB) model is now applied to the investigation of the bifurcation behavior in the lid-driven deep-cavity flow. In this second part, the first Hopf bifurcations in the lid-driven cavity flow patterns with aspect ratios of 1-5 are examined in detail, revealing that the critical Reynolds number converges to a constant value with the increase of the cavity depth, and that the time-dependent vortex structures are periodic or quasi-periodic once this critical Reynolds number is exceeded. Through comparison against the relevant numerical results reported in the available literature, the present FMLB approach demonstrates its effectiveness and usefulness in studying the bifurcation phenomena arising in complex lid-driven deep-cavity flows.

[1]  Roger Pierre,et al.  Localization of Hopf bifurcations in fluid flow problems , 1997 .

[2]  Yih-Ferng Peng,et al.  Transition in a 2-D lid-driven cavity flow , 2003 .

[3]  K. C. Hung,et al.  Vortex structure of steady flow in a rectangular cavity , 2006 .

[4]  Chao-An Lin,et al.  Multi relaxation time lattice Boltzmann simulations of transition in deep 2D lid driven cavity using GPU , 2013 .

[5]  Jitesh S. B. Gajjar,et al.  Global flow instability in a lid‐driven cavity , 2009 .

[6]  P. N. Shankar,et al.  The eddy structure in Stokes flow in a cavity , 1993, Journal of Fluid Mechanics.

[7]  R. Pierre,et al.  A neutral stability curve for incompressible flows in a rectangular driven cavity , 2003 .

[8]  Nicola Parolini,et al.  Numerical investigation on the stability of singular driven cavity flow , 2002 .

[9]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[10]  Shiyi Chen,et al.  Simulation of Cavity Flow by the Lattice Boltzmann Method , 1994, comp-gas/9401003.

[11]  A. Acrivos,et al.  Steady flows in rectangular cavities , 1967, Journal of Fluid Mechanics.

[12]  Chao-An Lin,et al.  Multi relaxation time lattice Boltzmann simulations of deep lid driven cavity flows at different aspect ratios , 2011 .

[13]  C. Bruneau,et al.  The 2D lid-driven cavity problem revisited , 2006 .

[14]  M. D. Deshpande,et al.  FLUID MECHANICS IN THE DRIVEN CAVITY , 2000 .

[15]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[16]  E. Erturk,et al.  Numerical solutions of 2‐D steady incompressible driven cavity flow at high Reynolds numbers , 2004, ArXiv.

[17]  B. Rogg,et al.  Lattice Boltzmann simulation of lid-driven flow in deep cavities , 2006 .

[18]  Cyrus K. Aidun,et al.  Lattice-Boltzmann Method for Complex Flows , 2010 .

[19]  Arthur Veldman,et al.  Proper orthogonal decomposition and low-dimensional models for driven cavity flows , 1998 .

[20]  S. García,et al.  The lid-driven square cavity flow : From stationary to time periodic and chaotic , 2007 .

[21]  Mehmet Sahin,et al.  A novel fully‐implicit finite volume method applied to the lid‐driven cavity problem—Part II: Linear stability analysis , 2003 .

[22]  Jun Cao,et al.  Filter-matrix lattice Boltzmann simulation of lid-driven deep-cavity flows, Part I - Steady flows , 2013, Comput. Math. Appl..