Finite-volume multigrid calculation of natural-convection flows on unstructured grids

Numerical Heat Transfer, Part B: Fundamentals

Volumn 30, Issue 1, 1996, Pages 1-22

  Volker S ^a   Burton, T ^a   Vanka, S P ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF MOTION; FINITE VOLUME METHOD; PERFORMANCE;

FINITE VOLUME MULTIGRID CALCULATION; FLOW FIELDS; NATURAL CONVECTION FLOWS; PRESSURE BASED MULTIGRID PROCEDURE; RAYLEIGH NUMBERS; UNSTRUCTURED GRIDS;

NATURAL CONVECTION;

EID: 0030191622     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/10407799608915069     Document Type: Article

References (37)

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. M. Peric, Natural Convection in Trapezoidal Cavities, Numer. Heat Transfer Part A, vol. 24, pp. 213-219, 1993.
10. 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
11. 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.
12. E. Martin and M. Sen, Analysis of Laminar Natural Convection in a Triangular Enclosure, Numer. Heat Transfer, vol. 13, pp. 353-372, 1988.
13. E. Martin and M. Sen, Natural Convection in a Semielliptic Cavity, Numer. Heat Transfer, vol. 12, pp. 101-119,1987.
14. A. Jameson and D. J. Mavriplis, Finite Volume Solution of the Two Dimensional Euler Equations on a Regular Triangular Mesh, AIAA-85-0435,1985.
15. Y. Jiang and A. J. Przekwas, Implicit, Pressure-Based Incompressible Navier-Stokes Equation Solver for Unstructured Meshes, AIAA-94-0305,1994.
16. 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.
17. R. Vilsmeier and D. Hanel, Adaptive Methods on Unstructured Grids for Euler and Navier-Stokes Equations, Comput. Fluids, vol. 22, 485-499,1993.
18. 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.
19. 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.
20. B. R. Baliga and S. V. Patankar, A New-Finite-Element Formulation for Convection-Diffusion Problems, Numer. Heat Transfer, vol. 3, 393-409, 1980.
21. 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.
22. 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.
23. 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.
24. A. Brandt, Multi-Level Adaptive Solutions to Boundary-Value Problems, Math. Comput., vol. 31, pp. 333-390, 1977.
25. 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.
26. 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.
27. D. J. Mavriplis and A. Jameson, Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes, ICASE Rep. 87-53, 1987.
28. D. J. Mavriplis, Multigrid Solution of the 2-D Euler Equations on Unstructured Triangular Meshes, AIAA J., vol. 26, pp. 824-831, 1988.
29. M. Lallemand, H. Steve, and A. Dervieux, Unstructured Multigridding by Volume Agglomeration: Current Status, Comput. Fluids, vol. 21, pp. 397-433, 1992.
30. V. Parthasarathy and Y. Kallinderis, A New Multigrid Approach for 3-D Unstructured, Adaptive Grids, AIAA-94-0078,1994.
31. D. J. Mavriplis and A. Jameson, Multigrid Solution of the Navier-Stokes Equations on Triangular Meshes, AIAA J., vol. 28, pp. 1415-1425, 1990.
32. R. Jyotsna and S. P. Vanka, Multigrid Calculation of Steady, Viscous Flow in a Triangular Cavity, 3. Comput. Physvol. 122, pp. 107-117, 1995.
33. S. V. Patankar, Numerical Heat Transfer, Hemisphere, Washington, DC, 1980.
34. S. P. Vanka, Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables, J. Comput. Phys., vol. 65, pp. 138-158, 1986.
35. 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.
36. 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.
37. R. Löhner and K. Morgan, An Unstructured Multigrid Method for Elliptic Problems, Int. J. Numer. Meth. Eng., vol. 8, pp. 417-440, 1987.