Benchmark Solution for Time-Dependent Natural Convection Flows with an Accelerated Full-Multigrid Method

REFERENCES

• R. Peyret and T. D. Taylor , Methods for Fluid Flow , Springer-Verlag , Berlin , 1983 .
   Google Scholar
• Y. Achdou and J. L. Guermond , Convergence Analysis of a Finite Element Projection/Lagrange-Galerkin Method for the Incompressible Naviers-Stokes Equations , SIAM J. Numer. Anal. , vol. 37 , pp. 799 – 826 , 2000 .
   Web of Science ®Google Scholar
• M. J. Ni , S. Komori , and N. Morley , Projection Methods for the Calculation of Incompressible Unsteady Flows , Numer. Heat Transfer B , vol. 44 pp. 533 – 551 , 2003 .
   Web of Science ®Google Scholar
• W. Hackbusch , Multigrid Methods and Applications , Springer-Verlag , Berlin , 1985 .
   Google Scholar
• T. S. Park , Multigrid Method and Low-Reynolds-Number k–∊ Model for Turbulent Recirculating Flows , Numer. Heat Transfer B , vol. 36 , pp. 443 – 456 , 1999 .
   Web of Science ®Google Scholar
• X. Q. Chen , Multigrid Acceleration of Computations of Turbulent Particle-Laden Flows , Numer. Heat Transfer B , vol. 40 , pp. 139 – 162 , 2001 .
   Web of Science ®Google Scholar
• M. Hortmann , M. Peric , and G. Scheuerer , Finite Volume Multigrid Prediction of Laminar Natural Convection: Bench-Mark Solutions , Int. J. Numer. Meth. Fluids , vol. 11 , pp. 189 – 207 , 1990 .
   Web of Science ®Google Scholar
• E. Nobile , Simulation of Time-Dependent Flow in Cavities with the Additive-Correction Multigrid Method, Part I: Mathematical Formulation , Numer. Heat Transfer B , vol. 30 , pp. 341 – 350 , 1996 .
   Web of Science ®Google Scholar
• D. Braess , Towards Algebraic Multigrid for Elliptic Problems of Second Order , Computing , vol. 55 , pp. 379 – 393 , 1995 .
   Web of Science ®Google Scholar
• M. A. Christon , P. M. Gresho , and S. B. Sutton , Computational Predictability of Time-Dependent Natural Convection Flows in Enclosures (Including a Benchmark Solution) Int. J. Numer. Meth. Fluids , vol. 40 , pp. 953 – 980 , 2002 .
   Web of Science ®Google Scholar
• G. De Vahl Davis , Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution , Int. J. Numer. Meth. Fluids , vol. 3 , pp. 249 – 264 , 1983 .
   Web of Science ®Google Scholar
• D. C. Wan , B. S. V. Patnaik , and G. W. Wei , A New Benchmark Quality Solution for the Buoyancy-Driven Cavity by Discrete Singular Convolution , Numer. Heat Transfer B , vol. 40 , pp. 199 – 228 , 2001 .
   Web of Science ®Google Scholar
• P. Le Quéré , Accurate Solutions to the Square Thermally Driven Cavity at High Rayleigh Number , Comput. Fluids , vol. 20 , pp. 29 – 41 , 1991 .
   Web of Science ®Google Scholar
• H. N. Dixit and V. Babu , Simulation of High Rayleigh Number Natural Convection in a Square Cavity Using the Lattice Boltzmann Method , Int. J. Heat Mass Transfer , vol. 49 , pp. 727 – 739 , 2006 .
   Web of Science ®Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , McGraw-Hill , New York , 1980.
   Google Scholar
• B. P. Leonard , A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation , Comput. Meth. Appl. Mech. Eng. , vol. 19 , pp. 59 – 98 , 1979 .
   Web of Science ®Google Scholar
• S. Xin and P. Le Quéré , An Extended Chebyshev Pseudo-spectral Benchmark for the 8:1 Differentially Heated Cavity , Int. J. Numer. Meth. Fluids , vol. 40 , pp. 981 – 998 , 2002 .
   Web of Science ®Google Scholar
• S. Paolucci and D. R. Chenoweth , Transition to Chaos in a Differentially Heated Vertical Cavity , J. Fluid Mech. , vol. 201 , pp. 379 – 410 , 1989 .
   Web of Science ®Google Scholar
• R. J. A. Janssen and R. A. W. M. Henkes , Accuracy of Finite-Volume Discretizations for the Bifurcating Natural-Convection Flow in a Square Cavity , Numer. Heat Transfer B , vol. 24 , pp. 191 – 207 , 1993 .
   Web of Science ®Google Scholar
• E. Nobile , Simulation of Time-Dependent Flow in Cavities with the Additive-Correction Multigrid Method, Part II: Applications , Numer. Heat Transfer B , vol. 30 , pp. 351 – 370 , 1996 .
   Web of Science ®Google Scholar