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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 48, 2005 - Issue 4
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Original Articles

Finite-Element Analysis of 3-D Viscous Flow and Mixed-Convection Problems by the Projection Method

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Pages 339-358 | Received 04 Dec 2004, Accepted 25 Jan 2005, Published online: 02 Sep 2006

REFERENCES

  • A. J. Chorin , Numerical Solution of the Navier-Stokes Equations , Math. Comput. , vol. 22 , pp. 745 – 762 , 1968 .
  • D. Brown , R. Cortez , and M. Minion , Accurate Projection Method for Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 168 , pp. 464 – 499 , 2001 . [CSA] [CROSSREF]
  • P. M. Gresho , On the Theory of Semi-implicit Projection Methods for Viscous Incompressible Flow and Its Implementation via a Finite Element Method that also Introduces a Ready Consistent Mass Matrix, Part 1: Theory , Int. J. Numer. Meth. Fluids , vol. 11 , pp. 587 – 620 , 1990 . [CSA]
  • J. Kim and P. Moin , Application of the Fractional-Step Method to the Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 59 , pp. 308 – 323 , 1985 . [CSA] [CROSSREF]
  • W. Chang , F. Giraldo , and B. Perot , Analysis of an Exact Fractional Step Method , J. Comput. Phys. , vol. 180 , pp. 183 – 199 , 2002 . [CSA] [CROSSREF]
  • S. V. Patankar and D. B. Spalding , A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows , Int. J. Heat Mass Transfer , vol. 15 , pp. 1787 – 1806 , 1972 . [CROSSREF]
  • B. R. Baliga and S. V. Patankar , A Control Volume Finite-Element Method for Two-Dimensional Fluid Flow and Heat Transfer , Numer. Heat Transfer , vol. 6 , pp. 245 – 261 , 1983 .
  • S. Jang , R. Jetly , and S. Acharya , Comparison of the PISO, SIMPLER and SIMPLEC Algorithms for the Treatment of the Pressure-Velocity Coupling in Steady Flow Problems , Numer. Heat Transfer , vol. 10 , pp. 209 – 228 , 1986 .
  • J. Dukpwica and J. Ramshaw , Tensor Viscosity Method for Convection in Numerical Fluid Dynamics, J. Comput. Phys. , vol. 32, pp. 71–91, 1979. [CSA] [CROSSREF]
  • P. M. Gresho , S. T. Chan , R. L. Lee , and C. D. Upson , A Modified Finite Element Method for Solving the Time-Dependent, Incompressible Navier-Stokes Equations, Part 1: Theory , Int. J. Numer. Meth. Fluids , vol. 4 , pp. 557 – 598 , 1984 . [CSA]
  • O. C. Zienkiewicz , R. Lohner , K. Morgan , and S. Nakazawa , Finite Elements in Fluid Mechanics—A Decade of Progress , in Finite Elements in Fluids , vol. 5 , pp. 1 – 26 , Wiley , New York , 1984 .
  • 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 .
  • 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]
  • 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]
  • 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]
  • R. Iwatsu , J. M. Hyun , and K. Kuwahara , Mixed Convection in a Driven Cavity with a Stable Vertical Temperature Gradient , Int. J. Heat Mass Transfer , vol. 36 , pp. 1601 – 1608 , 1993 . [CROSSREF]
  • R. Iwatsu and J. M. Hyun , Three-Dimensional Driven-Cavity Flows with a Vertical Temperature Gradient , Int. J. Heat Mass Transfer , vol. 38 , pp. 3319 – 3328 , 1995 . [CROSSREF]
  • A. K. Prasad and J. R. Koseff , Combined Forced and Natural Convection Heat Transfer in a Deep Lid-Driven Flow , Int. J. Heat Fluid Flow , vol. 17 , pp. 460 – 467 , 1996 . [CROSSREF]
  • H. F. Oztop and I. Dagtekin , Mixed Convection in Two-Sided Lid-Driven Differentially Heated Square Cavity , Int. J. Heat Mass Transfer , vol. 47 , pp. 1761 – 1769 , 2004 . [CSA] [CROSSREF]
  • J. Donea , S. Giuliani , and H. Lavel , Time-Accuracy Solution of Advection-Diffusion Problems by Finite Elements , Comput. Meth. Appl. Mech. Eng. , vol. 45 , pp. 123 – 145 , 1984 . [CSA] [CROSSREF]
  • W. H. Press , S. A. Teukolsky , W. T. Vetterling , and B. P. Flannery , Numerical Recipes in Fortran: The Art of Scientific Computing , 2nd ed. , Cambridge University Press , New York , 1992 .
  • B.-N. Jiang , T. L. Lin , and L. A. Povinelli , Large-Scale Computation of Incompressible Viscous Flow by Least-Square Finite Element Method , Comput. Meth. Appl. Mech. Eng. , vol. 114 , pp. 213 – 231 , 1994 . [CROSSREF]
  • B. F. Armaly , F. Durst , J. C. F. Pereira , and B. Schönung , Experimental and Theoretical Investigation of Backward-Facing Step Flow , J. Fluid Mech. , vol. 127 , pp. 473 – 496 , 1983 .

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