Global 2D stability analysis of the cross lid-driven cavity flow with a streamfunction-vorticity approach

References

• P. Roache, Computational Fluid Dynamics. Hermosa Press, New Mexico, 1972.
   Google Scholar
• D.A. Anderson, J.C. Tannehil, and R.H. Pletcher, Computational Fluid Mechanics and Heat Transfer, Hemisphere Publishing Corporation, New York, 1984.
   Google Scholar
• L. Quartapelle, Numerical Solution of the Incompressible Navier-Stokes Equations, Birkhauser Verlag, Basel, Switzerland, 1993.
   Google Scholar
• Jr. J.D. Anderson, Computational Fluid Dynamics, McGraw-Hill, Inc., New York, 1995.
   Google Scholar
• C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM Publications, Philadelphia, PA, 1995.
   Google Scholar
• S. Albensoeder and H.C. Kuhlmann, Accurate Three-Dimensional Lid-Driven Cavity Flow, J. Comput. Phys., vol. 206, pp. 536–558, 2005.
   Web of Science ®Google Scholar
• D.C. Lo, K. Murugesan, and D.L. Young, Numerical Solution of Three-Dimensional Velocity-Vorticity Navier-Stokes Equations by Finite Difference Method, Int. J. Numer. Methods Fluids, vol. 47, pp. 1469–1487, 2005.
   Web of Science ®Google Scholar
• B.N. Jiang, T.N. Lin, and L.A. Povinelli, Large-Scale Computation of Incompressible Viscous Flow by Least-Squares Finite Element Method, Comput. Methods Appl. Mech. Engrg., vol. 114, pp. 213–231, 1994.
   Web of Science ®Google Scholar
• Y.F. Peng, Y.H. Shiau, and R.R. Hwang, Transition in a 2-D Lid-Driven Cavity Flow, Comput. Fluids, Vol. 32, pp. 337–352, 2003.
   Web of Science ®Google Scholar
• E.M. Wahba, Steady Flow Simulations Inside a Driven Cavity up to Reynolds Number 35,000, Comput. Fluids, vol. 66, pp. 85–97, 2012.
   Web of Science ®Google Scholar
• E. Erturk, Discussions on Driven Cavity Flow, Int. J. Numer. Methods Fluids, vol. 60, pp. 275–294, 2009.
   Web of Science ®Google Scholar
• C.H. Bruneau, and M. Saad, The 2D Lid-Driven Cavity Problem Revisited, Comput. Fluids, vol. 35, pp. 326–348, 2006.
   Web of Science ®Google Scholar
• C.K. Aidun, N.G. Triantafillopoulos, and J.D. Benson, Global Stability of a Lid-Driven Cavity with Through-Flow: Flow Visualization Studies, Phys. Fluids A, vol. 3, pp. 2081, 1991.
   Web of Science ®Google Scholar
• N. Alleborn, H. Raszillier, and F. Durst, Lid-Driven Cavity With Heat and Mass Transport, Int. J. Heat Mass Transfer, vol. 42, pp. 833–853, 1999.
   Web of Science ®Google Scholar
• O.R. Burggraf, Analytical and Numerical Studies of the Structure of Steady Separated Flows, J. Fluid Mech., Vol. 24, pp. 113–151, 1966.
   Web of Science ®Google Scholar
• F. Pan, and A. Acrivos, Steady Flows in Rectangular Cavities, J. Fluid Mech., vol. 28, pp. 643–655, 1967.
   Web of Science ®Google Scholar
• M. Cheng, and K.C. Hung, Vortex Structure of Steady Flow in a Rectangular Cavity, Comput. Fluids, vol. 35, pp. 1046–1062, 2006.
   Web of Science ®Google Scholar
• U. Ghia, K.N. Ghia, and C.T. Shin, High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equation and a Multigrid Method, J. Comput. Phys., vol. 48, pp. 387–411, 1982.
   Web of Science ®Google Scholar
• H.C. Kuhlmann, M. Wanschura, and H.J. Rath, Flow in Two-Sided Lid-Driven Cavities: Non-Uniqueness, Instability, and Cellular Structures, J. Comput. Phys., vol. 336, pp. 267–299, 1997.
   Google Scholar
• C.H. Blohm, and H.C. Kuhlmann, The Two-Sided Lid-Driven Cavity: Experiments on Stationary and Time-Dependent Flows, J. Fluid Mech., vol. 450, pp. 67–95, 2002.
   Web of Science ®Google Scholar
• W.F. Spotz, and G.F. Carey, High Order Compact Finite Difference Methods with Applications to Viscous Flows, Tech. Rept. 94-03, Texas Institute of Computational and Applied Mechanics, The University of Texas at Austin, Texas, 1994.
   Google Scholar
• J.C. Kalita, D.C. Dalal, and A.K. Dass, A Class of Higher Order Compact Schemes for the Unsteady Two-Dimensional Convection-Diffusion Equation with Variable Convection Coefficients, Int. J. Numer. Methods Fluids, vol. 38, pp. 1111–1131, 2002.
   Web of Science ®Google Scholar
• J.C. Kalita, D.C. Dalal, and A.K. Dass, Fully Compact Higher-Order Computation of Steady-State Natural Convection in a Square Cavity, Physical Review E, vol. 64 no. 6, pp. 066703(1–13), 2001.
   Google Scholar
• J.C. Kalita, and A.K. Dass, Higher Order Compact Simulation of Double-Diffusive Natural Convection in a Vertical Porous Annulus, Eng. Appl. Comp. Fluid, vol. 5 no. 3, pp. 357–371, 2011.
   Google Scholar
• S.K. Pandit, J.C. Kalita, and D.C. Dalal, A Fourth-Order Accurate Compact Scheme for the Solution of Steady Navier-Stokes Equations on Non-Uniform Grids, Comput. Fluids, vol. 37 no. 2, pp. 121–134, 2007.
   Web of Science ®Google Scholar
• J. Zhang, Numerical Simulation of 2D Square Driven Cavity Using Fourth-Order Compact Finite Difference Schemes, Comput. Math. Appl., vol. 45, pp. 43–52, 2003.
   Web of Science ®Google Scholar
• J. Zhang, G. Lixin, and J. Kouatchou, A Two Colorable Fourth-Order Compact Difference Scheme and Parallel Iterative Solution for the 3-D Convection-Diffusion Equation, Math. Comput. Simulat., vol. 54, pp. 65–80, 2000.
   Web of Science ®Google Scholar
• S.E. Sherer, and J.N. Scott, High-Order Compact Finite-Difference Methods on General Overset Grids, J. Comput. Phys., vol. 210 no. 2, pp. 459–496, 2005.
   Web of Science ®Google Scholar
• G. Sutmann, and B. Steffen, High-Order Compact Solvers for the Three-Dimensional Poisson Equations, J. Comput. Appl. Math., vol. 187 no. 2, pp. 142–170, 2006.
   Web of Science ®Google Scholar
• J.C. Kalita, A.K. Dass, and D.C. Dalal, A Transformation-Free HOC Scheme for Steady Convection-Diffusion Equation on Non-Uniform Grids, Int. J. Numer. Meth. Fl., vol. 44, pp. 33–53, 2004.
   Web of Science ®Google Scholar
• J.C. Kalita, and P. Chhabra, An Improved (9, 5) Higher Order Compact Scheme for the Transient Two-Dimensional Convection Diffusion Equation, Int. J. Numer. Methods Fluids, vol. 51, pp. 703–717, 2006.
   Web of Science ®Google Scholar
• J.C. Kalita, and S. Sen, The (9, 5) HOC Formulation for the Transient Navier Stokes Equations in Primitive Variable, Int. J. Numer. Methods Fluids, vol. 55, pp. 387–406, 2007.
   Web of Science ®Google Scholar
• J.C. Kalita, and M.M. Gupta, A Stream Function Velocity Approach for 2D Transient Incompressible Viscous Flows, Int. J. Numer. Methods Fluids, vol. 62 no. 3, pp. 237–266, 2010.
   Web of Science ®Google Scholar
• M. Poliashenko, and C.K. Aidun, A Direct Method for Computation of Simple Bifurcations, J. Comput. Phys., vol. 121 no. 2, pp. 246–260, 1995.
   Web of Science ®Google Scholar
• A. Fortin, M. Jardak, J.J. Gervais, and R. Pierre, Localization of Hopf Bifurcations in Fluid Flow Problems, Int. J. Numer. Methods Fluids, vol. 24 no. 11, pp. 1185-1-210, 1997.
   Web of Science ®Google Scholar
• G. Tiesinga, F.W. Wubs, and A.E.P. Veldmen, Bifurcation Analysis of Incompressible Flow in a Driven Cavity by the Newton-Picard Method, J. Comput. Appl. Math., vol. 140, pp. 751–772, 2002.
   Web of Science ®Google Scholar
• J.M. Cadou, M. Potier-Ferry, and B. Cochelin, A Numerical Method for the Computation of Bifurcation Point in Fluid Mechanics, Eur. J. Mech. Fluid, vol. 25, pp. 234–254, 2006.
   Web of Science ®Google Scholar
• M. Sahin, and R.G. Owens, A Novel Fully-Implicit Finite Volume Method Applied to the Lid-Driven Cavity Problem, Part II, Linear Stability Analysis, Int. J. Numer. Methods Fluids, vol. 42, pp. 79–88, 2003.
   Web of Science ®Google Scholar
• J.C. Kalita, and B.B. Gogoi, Global Two-Dimensional Stability of the Staggered Cavity Flow with an HOC Approach, Comput. Math. Appl., vol. 67 no. 3, pp. 569–590, 2014.
   Web of Science ®Google Scholar
• J. de Vicente, D. Rodrguez, V. Theofilis, and E. Valero, Stability Analysis in Spanwise-Periodic Double-Sided Lid-Driven Cavity Flows with Complex Cross-Sectional Profiles, Comput. Fluids, vol. 43, pp. 143–153, 2011.
   Web of Science ®Google Scholar
• R.B. Lehoucq, D.C. Sorensen, and C. Yang, ARPACK User’s Guide, Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, 1997, Available at: http://www.caam.rice.edu/software/ARPACK/.
   Google Scholar
• Y.C. Zhou, B.S.V. Patnaik, D.C. Wan, and W. Wei, DSC Solution for Flow in a Staggered Double Lid Driven Cavity, Int. J. Numer. Meth. Eng., vol. 57, pp. 211–234, 2003.
   Web of Science ®Google Scholar
• F. Auteri, N. Parolini, and L. Quartapelle, Numerical Investigation on the Stability of Singular Driven Cavity Flow, J. Comput. Phys., vol. 183, pp. 1–25, 2002.
   Web of Science ®Google Scholar
• X. Merle, F. Alizard, and J.-H. Robinet, Finite Difference Methods for Viscous Incompressible Global Stability Analysis, Comput. Fluids, vol. 39, pp. 911–925, 2010.
   Web of Science ®Google Scholar
• J. Sanchez, F. Marques, and J.M. Lopez, A Continuation and Bifurcation Technique for Navier-Stokes Flows, J. Comput. Phys., vol. 180, pp. 78–98, 2002.
   Web of Science ®Google Scholar
• J.D. Hoffmann, Numerical Methods for Engineers and Scientists, Marcel Dekker Inc, New York, 2001.
   Google Scholar
• Y. Feldman, and A.Y. Gelfgat, Oscillatory Instability of a Three-Dimensional Lid-Driven Flow in a Cube, Phys. Fluids, vol. 22, pp. 093602, 2010.
   Google Scholar