Lattice Boltzmann Simulation of Two- and Three-Dimensional Incompressible Thermal Flows

REFERENCES

• De Vahl Davis , G. 1983 . Natural Convection of Air in a Square Cavity: A Bench Mark Solution . International Journal of Numerical Methods in Fluids , 3 : 249 – 264 .
   Web of Science ®Google Scholar
• Chenoweth , D. R. and Paolucci , S. 1986 . Natural Convection in an Enclosed Vertical Air Layer With Large Horizontal Temperature Differences . Journal of Fluid Mechanics , 169 : 173 – 210 .
   Web of Science ®Google Scholar
• Kalita , J. C. , Dalal , D. C. and Dass , A. K. 2001 . Fully Compact Higher-Order Computation of Steady-State Natural Convection in a Square Cavity . Physical Review E , 64 : 066703
   Web of Science ®Google Scholar
• Ball , K. S. and Kuo , D. C. 1994 . Spectral Simulation of Thermal Convection Using a Vorticity–Velocity Formulation . Journal of Heat Transfer , 2 : 313 – 320 .
   Google Scholar
• Ho , C. J. and Lin , F. H. 1997 . Simulation of Natural Convection in a Vertical Enclosure by Using a New Incompressible Flow Formulation-Pseudo Vorticity–Velocity Formulation . Numerical Heat Transfer Part A , 31 : 881 – 896 .
   Web of Science ®Google Scholar
• Peng , Y. , Shu , C. and Chew , Y. T. 2003 . Simplified Thermal Lattice Boltzmann Model for Compressible Thermal Flows . Physical Review E , 68 : 026701
   Web of Science ®Google Scholar
• Dixit , H. N. and Babu , V. 2006 . Simulation of High Rayleigh Number Natural Convection in a Square Cavity Using the Lattice Boltzmann Method . International Journal of Heat and Mass Transfer , 49 : 727 – 739 .
   Web of Science ®Google Scholar
• Shan , X. 2001 . Simulation of Rayleigh–Benard Convection Using a Lattice Boltzmann Method . Physical Review E , 55 : 2780 – 2788 .
   Web of Science ®Google Scholar
• Onishi , J. , Chen , Y. and Ohashi , H. 2001 . Lattice Boltzmann Simulation of Natural Convection in a Square Cavity . JSME International Journal, Series B , 44 : 53 – 62 .
   Web of Science ®Google Scholar
• Shu , C. , Peng , Y. and Chew , Y. T. 2002 . Simulation of Natural Convection in a Square Cavity by Taylor Series Expansion and Least Squares Based Lattice Boltzmann Method . International Journal of Modern Physics C , 13 : 1399 – 1414 .
   Web of Science ®Google Scholar
• Peng , Y. , Shu , C. and Chew , Y. T. 2003 . A 3D Incompressible Thermal Lattice Boltzmann Model and Application to Simulate Natural Convection in a Cubic Cavity . Journal of Computational Physics , 193 : 260 – 274 .
   Web of Science ®Google Scholar
• Mandal , J. C. , Agrawal , L. and Marathe , A. G. 2000 . Computation of Incompressible Flows With Natural Convection Using Pseudocompressibility Approach . Journal of Thermophysics , 14 : 606 – 612 .
   Web of Science ®Google Scholar
• Fusegi , T. , Hyun , J. M. , Kuwahara , H. and Farouk , B. 1991 . A Numerical Study of three- Dimensional natural convection in a Differentially Heated Cubical Enclosure . International Journal of Heat and Mass Transfer , 34 : 1543 – 1557 .
   Web of Science ®Google Scholar
• Tric , E. , Labrosse , G. and Betrouni , M. 2000 . A First Incursion Into the 3D Structure of Natural Convection of Air in a Differentially Heated Cubic Cavity, From Accurate Numerical Solutions . International Journal of Heat and Mass Transfer , 43 : 4043 – 4056 .
   Web of Science ®Google Scholar
• Mondal , B. and Mishra , S. C. 2008 . Simulation of Natural Convection in the Volumetric Radiation Using the Lattice Boltzmann Method . Numerical Heat Transfer Part A , 55 : 18 – 41 .
   Web of Science ®Google Scholar
• Barrios , G. , Rechtman , R. , Rojas , J. and Tovar , R. 2005 . The Lattice Boltzmann Equation for Natural Convection in a Two-Dimensional Cavity With a Partially Heated Wall . Journal of Fluid Mechanics , 522 : 91 – 100 .
   Web of Science ®Google Scholar
• Alexanders , F. , Chen , S. and Sterling , J. 1993 . Lattice-Boltzmann Thermo-Hydrodynamics . Physical Review E , 47 : R2249 – R2252 .
   PubMed Web of Science ®Google Scholar
• McNamara , G. , Garcia , A. L. and Alder , B. J. 1995 . Stabilization of Thermal Lattice Boltzmann Models . Journal of Statistical Physics , 91 : 395 – 408 .
   Web of Science ®Google Scholar
• Eggels , J. G. M. and Somers , J. A. 1995 . Numerical Simulation of Free Convective Flow Using the Lattice Boltzmann Scheme . International Journal of Heat and Fluid Flow , 16 : 357 – 364 .
   Web of Science ®Google Scholar
• He , X. , Chen , S. and Doolen , G. D. 1998 . A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit . Journal of Computational Physics , 146 : 282 – 300 .
   Web of Science ®Google Scholar
• Mei , R. , Shyy , W. , Yu , D. and Luo , L. S. 2000 . Lattice Boltzmann Method for 3-D Flows With Curved Boundary . Journal of Computational Physics , 161 : 680 – 689 .
   Web of Science ®Google Scholar