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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 30, 1996 - Issue 1
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Original Articles

FINITE-VOLUME MULTIGRID CALCULATION OF NATURAL-CONVECTION FLOWS ON UNSTRUCTURED GRIDS

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Pages 1-22 | Received 25 May 1995, Accepted 26 Jan 1996, Published online: 28 Mar 2007

References

  • G. de Vahl Davis , Natural Convection of Air in a Square Cavity A Bench Mark Numerical Solution , Int. Numer. Meth. Fluids , vol. 3 , pp. 249 – 264 , 1983 .
  • G. de Vahl Davis and I. P. Jones , Natural Convection in a Square Cavity A Comparison Exercise , Int. J. Numer. Meth. Fluids , vol. 3 , pp. 227 – 248 , 1983 .
  • C. Shu , B. C. Khoo , K. S. Yeo , and Y. T. Chew , Application of GDQ Scheme to Simulate Natural Convection in a Square Cavity , Int. Commun. Heat Mass Transfer , vol. 21 , pp. 809 – 817 , 1994 .
  • M. K. Ermakov , V. L. Gryaznov , S. A. Nikitin , D. S. Pavlovsky , and V. I. Polezhaev , A PC-Based System for Modeling of Convection in Enclosures on the Basis of the Navier-Stokes Equations , Int. J. Numer. Meth. Fluids , vol. 15 , pp. 975 – 984 , 1992 .
  • M. Hortmann , M. Peric , and G. Scheurer , Finite Volume Multigrid Prediction of Laminar Natural Convection Bench-Mark Solutions , Int. J. Numer. Mech. Fluids , vol. 11 , pp. 189 – 207 , 1990 .
  • E. Crespo del Arco and P. Bontoux , Numerical Solution and Analysis of Asymmetric Convection in a Vertical Cylinder An Effect of Prandtl Number , Phys. Fluids , vol. 1 , pp. 1348 – 1359 , 1989 .
  • C. Wagner , R. Friedrich , and R. Narayanan , Comments on the Numerical Investigation of Rayleigh and Marangoni Convection in a Vertical Circular Cylinder . Phys. Fluids , vol. 6 , pp. 1425 – 1433 , 1994 .
  • F. Moukalled and S. Acharya , Laminar Natural Convection Heat Transfer in an Eccentric Rhombic Annulus , Numer. Heat Transfer Part A , vol. 26 , pp. 551 – 568 , 1994 .
  • M. Peric , Natural Convection in Trapezoidal Cavities , Numer. Heat Transfer Part A , vol. 24 , pp. 213 – 219 , 1993 .
  • R. D. Flack , T. T. Konopnicki , and J. H. Rooke , The Measurement of Natural Convective Heat Transfer in Triangular Enclosures , J. Heat Transfer , vol. 101 , pp. 648 – 654 , 1979 .
  • R. D. Flack , The Experimental Measurement of Natural Convection Heat Transfer in Triangular Enclosures Heated or Cooled from Below , J. Heat Transfer , vol. 102 , pp. 770 – 772 , 1980 .
  • E. Martin and M. Sen , Analysis of Laminar Natural Convection in a Triangular Enclosure , Numer. Heat Transfer , vol. 13 , pp. 353 – 372 , 1988 .
  • E. Martin and M. Sen , Natural Convection in a Semielliptic Cavity , Numer. Heat Transfer , vol. 12 , pp. 101–119 , 1987 .
  • A. Jameson and D. J. Mavriplis , Finite Volume Solution of the Two Dimensional Euler Equations on a Regular Triangular Mesh , AIAA-85-0435 , 1985 .
  • Y. Jiang and A. J. Przekwas , Implicit, Pressure-Based Incompressible Navier-Stokes Equation Solver for Unstructured Meshes , AIAA-94-0305 , 1994 .
  • P. C. E. Jorgenson and R. H. Pletcher , An Implicit Numerical Scheme for the Simulation of Internal Viscous Flows, on Unstructured Grids , AIAA-94-0306 , 1994 .
  • R. Vilsmeier and D. Hänel , Adaptive Methods on Unstructured Grids for Euler and Navier-Stokes Equations , Comput. Fluids , vol. 22 , 485 – 499 , 1993 .
  • S. Ramadhyani , Solution of the Equations of Convective Heat, Mass and Momentum Transfer by Finite Element Method Using Quadrilateral Elements , Ph. D. thesis , University of Minnesota , Minneapolis , 1979 .
  • G. E. Schneider and M. J. Raw , Control-Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Collocated Variables-1. Computational Procedure , Numer. Heat Transfer , vol. 11 , pp. 363 – 390 , 1987 .
  • B. R. Baliga and S. V. Patankar , A New-Finite-Element Formulation for Convection-Diffusion Problems , Numer. Heat Transfer , vol. 3 , 393 – 409 , 1980 .
  • 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 .
  • C. Prakash and S. V. Patankar , A Control Volume-Based Finite-Element Method for Solving the Navier-Stokes Equations Using Equal-Order Velocity-Pressure Interpolation , Numer. Heat Transfer , vol. 8 , pp. 259 – 280 , 1985 .
  • C. Prakash , An Improved Control Volume Finite-Element Method for Heat and Mass Transfer, and for Fluid Flow Using Equal-Order Velocity-Pressure Interpolation , Numer. Heat Transfer , vol. 9 , pp. 253 – 276 , 1986 .
  • A. Brandt , Multi-Level Adaptive Solutions to Boundary-Value Problems , Math. Comput. , vol. 31 , pp. 333 – 390 , 1977 .
  • P. M. Sockol , Multigrid Solutions of the Navier-Stokes Equations on Highly Stretched Grids , Int. J. Numer. Meth. Fluids , vol. 8 , pp. 417 – 440 , 1993 .
  • B. Koobus , M. Lallemand , and A. Dervieux ,; Unstructured Volume-Agglomeration MG Solution of the Poisson Equation , Int. J. Numer. Meth. Fluids , vol. 18 , pp. 27 – 42 , 1994 .
  • D. J. Mavriplis and A. Jameson , Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes , ICASE Rep. 87 – 53 , 1987 .
  • D. J. Mavriplis , Multigrid Solution of the 2-D Euler Equations on Unstructured Triangular Meshes , AIAA J. , vol. 26 , pp. 824 – 831 , 1988 .
  • M. Lallemand , H. Steve , and A. Dervieux , Unstructured Multigridding by Volume Agglomeration Current Status , Comput. Fluids , vol. 21 , pp. 397 – 433 , 1992 .
  • V. Parthasarathy and Y. Kallinderis , A New Multigrid Approach for 3-D Unstructured, Adaptive Grids , AIAA-94-0078 , 1994 .
  • D. J. Mavriplis and A. Jameson , Multigrid Solution of the Navier-Stokes Equations on Triangular Meshes , AIAA J. , vol. 28 , pp. 1415 – 1425 , 1990 .
  • R. Jyotsna and S. P. Vanka , Multigrid Calculation of Steady, Viscous Flow in a Triangular Cavity , J. Comput. Phys. , vol. 122 , pp. 107 – 117 , 1995 .
  • S. V. Patankar , Numerical Heat Transfer , Hemisphere , Washington , DC , 1980 .
  • S. P. Vanka , Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables , J. Comput. Phys. , vol. 65 , pp. 138 – 158 , 1986 .
  • M. C. Thompson and J. H. Ferziger , An Adaptive Multigrid Technique for the Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 82 , pp. 94 – 121 , 1989 .
  • K. M. Smith , W. K. Cope , and S. P. Vanka , A Multigrid Procedure for Three-Dimensional Flows on Non-orthogonal Collocated Grids , Int. J. Numer. Meth. Fluids , vol. 17 , pp. 887 – 904 , 1993 .
  • R. Löhner and K. Morgan , An Unstructured Multigrid Method for Elliptic Problems , Int. J. Numer. Meth. Eng. , vol. 8 , pp. 417 – 440 , 1987 .
  • Address correspondence to Dr. S. Pratap Vanka, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 140 Mechanical Engineering Building, MC-244, 1206 W. Green Street, Urbana, IL 61801, USA.

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