GDQ Method for Natural Convection in a Cubic Cavity Using Velocity–Vorticity Formulation

REFERENCES

• H. Fasel , Investigation of the Stability of Boundary Layers by a Finite-Difference Model of the Navier-Stokes Equations , J. Fluid Mech. , vol. 78 , pp. 355 – 383 , 1976 . [CSA]
   Web of Science ®Google Scholar
• M. Napolitano and L. A. Catalano , A Multigrid Solver for the Vorticity–Velocity Navier–Stokes Equations , Int. J. Numer. Meth. Fluids , vol. 13 , pp. 49 – 59 , 1993 . [CSA]
   Web of Science ®Google Scholar
• G. Guj and F. Stella , A Vorticity–Velocity Method for the Numerical Solution of 3D Incompressible Flows , J. Comput. Phys. , vol. 106 , pp. 286 – 298 , 1993 . [CSA]
   Web of Science ®Google Scholar
• C. Davis and P. W. Carpenter , A Novel Velocity–Vorticity Formulation of the Navier-Stokes Equations with Application to Boundary Layer Disturbance Evolution , J. Comput. Phys. , vol. 172 , pp. 119 – 165 , 2001 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• K. L. Wong and A. J. Baker , A 3D Incompressible Navier–Stokes Velocity–Vorticity Weak Form Finite Element Algorithm , Int. J. Numer. Meth. Fluids , vol. 38 , pp. 99 – 123 , 2002 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• G. D. Mallinson and G. de Vahl Davis , Three-Dimensional Natural Convection in a Box: A Numerical Study , J. Fluid Mech. , vol. 83 , pp. 1 – 31 , 1977 . [CSA]
   Web of Science ®Google Scholar
• O. Daube , Resolution of the 2D Navier-Stokes Equations in Velocity–Vorticity Form by Means of an Influence Matrix Technique , J. Comput. Phys. , vol. 103 , pp. 402 – 414 , 1992 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• M. S. Ingber and S. N. Kempka , A Galerkin Implementation of the Generalized Helmholtz Decomposition for Vorticity Formulations , J. Comput. Phys. , vol. 169 , pp. 215 – 237 , 2001 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• D. C. Lo and D. L. Young , Arbitrary Lagrangian-Eulerian Finite Element Analysis of Free Surface Flow Using a Velocity-Vorticity Formulation , J. Comput. Phys. , vol. 195 , pp. 175 – 201 , 2004 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• G. Guevremont , W. G. Habashi , and M. M. Hafez , Finite Element Solution of the Navier-Stokes Equations by a Velocity–Vorticity Method , Int. J. Numer. Meth. Fluids , vol. 10 , pp. 461 – 475 , 1990 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• R. E. Bellman , B. G. Kashef , and J. Casti , Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Equations , J. Comput. Phys. , vol. 10 , pp. 40 – 52 , 1972 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• C. Shu and B. E. Richards , Application of Generalized Differential Quadrature to Solve 2-Dimensional Incompressible Navier–Stokes Equations , Int. J. Numer. Meth. Fluids , vol. 15 , pp. 791 – 798 , 1992 . [CSA]
   Web of Science ®Google Scholar
• C. Shu , K. S. Yeo , and Q. Yao , An Efficient Approach to Simulate Natural Convection in Arbitrarily Eccentric Annuli by Vorticity-Stream Function Formulation , Numer. Heat Transfer A , vol. 38 , pp. 739 – 756 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• C. Shu , L. Wang , and Y. T. Chew , Numerical Computation of Three-Dimensional Incompressible Navier-Stokes Equations in Primitive Variable Form by DQ Method , Int. J. Numer. Meth. Fluids , vol. 43 , pp. 345 – 368 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• E. Tric , G. Labrosse , and M. Betrouni , A First Incursion into the 3D Structure of Natural Convection of Air in a Differentially Heated Cubic Cavity, from Accurate Numerical Solutions , Int. J. Heat Mass Transfer , vol. 43 , pp. 4043 – 4056 , 2000 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Y. Peng , C. Shu , and Y. T. Chew , A 3D Incompressible Thermal Lattice Boltzmann Model and its Application to Simulate Natural Convection in a Cubic Cavity , J. Comput. Phys. , vol. 193 , pp. 260 – 274 , 2003 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• T. Fusegi , J. M. Hyun , K. Kuwahara , and B. Farouk , A Numerical Study of Three-Dimensional Natural Convection in a Differentially Heated Cubical Enclosure, Int. J. Heat Mass Transfer , vol. 34, pp. 1543–1557, 1991. [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• S. Wakashima and T. S. Saitoh , Benchmark Solutions for Natural Convection in a Cubic Cavity Using the High-Order Time-Space Method , Int. J. Heat Mass Transfer , vol. 47 , pp. 853 – 864 , 2004 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• D. C. Lo , D. L. Young , and K. Murugesan , GDQ Method for Natural Convection in a Square Cavity Using a Velocity-Vorticity Formulation , Numer. Heat Transfer B , vol. 47 , pp. 321 – 341 , 2005 . [CSA]
   Web of Science ®Google Scholar
• C. Shu , Differential Quadrature and Its Application in Engineering , Springer-Verlag , London , UK , 2000 .
   Google Scholar