A finite-volume method based on Voronoi discretization for fluid flow problems

Numerical Heat Transfer, Part B: Fundamentals

Volumn 45, Issue 4, 2004, Pages 319-342

  De Vasconcellos, João Flávio Vieira ^a   Maliska, Clovis R ^b  

^a STATE UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

BENCHMARKING; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL METHODS; FINITE VOLUME METHOD; HEAT TRANSFER; NATURAL CONVECTION; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

UNSTRUCTURED GRIDS; VORONOI DISCRETIZATION;

INCOMPRESSIBLE FLOW;

EID: 1942472574     PISSN: 10407790     EISSN: None     Source Type: Journal    
DOI: 10.1080/10407790490268869     Document Type: Article

References (30)

1. 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.
2. G. E. Schneider and M. J. Raw, A Skewed, Positive Influence Coefficient Upwinding Procedure for Control-Volume Based Finite-Element Convection-Diffusion Computation, Numer. Heat Transfer, vol. 9, pp. 1-26, 1985.
3. C. Prakash, An Improved Control Volume Finite-Element Method for Heat and Mass Transfer and Fluid Flow Using Equal-Order Velocity-Pressure Interpolation, Numer. Heat Transfer, vol. 9, pp. 253-276, 1986.
4. A. Jameson and D. Mavriplis, Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh, AIAA J., vol. 24, pp. 611-618, 1986.
5. D. Pan and J.-C. Cheng, Upwind Finite-Volume Navier-Stokes Computations on Unstructured Triangular Meshes, AIAA J., vol. 31, pp. 1618-1625, 1993.
6. D. Pan and J.-C. Cheng, A Second-Order Upwind Finite-Volume Method for Euler Solution on Unstructured Triangular Meshes, Int. J. Numer. Meth. Fluids, vol. 16, pp. 1079-1098, 1993.
7. C. J. Hwang and S. J. Wu, Adaptive Finite Volume Upwind Approach on Mixed Quadrilateral-Triangular Meshes, AIAA J., vol. 31, no. 1, pp. 61-67, 1993.
8. J. F. Thompson, F. C. Thames, and C. W. Mastin, Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate Systems for Field Containing Any Number of Arbitrary Two-Dimensional Bodies, J. Comput. Phys., vol. 15, pp. 299-319, 1974.
9. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980.
10. C. R. Maliska, Computational Heat Transfer and Fluid Mechanics, Livros Técnicos e Cientificos Editora, Rio de Janeiro, 1995.
11. N. Taniguchi and T. Kobayashi, Finite Volume Method on the Unstructured Grid System, Comput. Fluids, vol. 19, pp. 287-295, 1991.
12. N. Taniguchi, C. Arakawa, and T. Kobayashi, Construction of a Flow-Simulating Method with Finite Volume Based on a Voronoi Diagram, JSME Int. J., vol. 34, pp. 18-23, 1990.
13. P. C. E. Jorgenson and R. H. Pletcher, An Implicit Numerical Scheme for the Simulation of Internal Viscous Flow on Unstructured Grids, Comput. Fluids, vol. 25, pp. 447-466, 1996.
14. Y.-H. Hwang, Calculations of Incompressible Flow on a Staggered Triangular Grid, Part I: Mathematical Formulation, Numer. Heat Transfer B, vol. 27, pp. 323-336, 1995.
15. Y.-H. Hwang, Calculations of Incompressible Flow on a Staggered Triangular Grid, Part II: Applications, Numer. Heat Transfer B, vol. 27, pp. 337-353, 1995.
16. T. M. Shih, C. H. Tan, and B. C. Hwang, Effects of Grid Staggering on Numerical Schemes, Int. J. Numer. Meth. Fluids, vol. 9, pp. 193-212, 1989.
17. L. Davidson, A Pressure Correction Method for Unstructured Meshes with Arbitrary Control Volumes, Int. J. Numer. Meth. Fluids, vol. 22, pp. 265-281, 1996.
18. S. R. Mathur and J. Y. Murthy, A Pressure-Based Method for Unstructured Meshes, Numer. Heat Transfer B, vol. 31, pp. 195-215, 1997.
19. Y. G. Lai, An Unstructured Grid Method for Pressure-Based Flow and Heat Transfer Solver, Numer. Heat Transfer B, vol. 32, pp. 267-281, 1997.
20. G. D. Raithby and K. E. Torrence, Upstream-Weighted Differencing Schemes and Their Application to Elliptic Problems Involving Fluid Flow, Comput. Fluids, vol. 2, pp. 191-206, 1974.
21. F. C. Cardoso, A Finite Volume Scheme for the Solution of the Momentum Equations Using Voronoi Discretization, M.Sc. thesis, Federal University of Santa Catarina, Brazil, 1997.
22. J. P. Van Doormaal and G. D. Raithby, Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flow, Numer. Heat Transfer, vol. 7, pp. 147-163, 1984.
23. J. F. V. Vasconcellos, A Finite Volume Method Using Unstructured Grids for Flows with Moving Boundaries, Ph.D. thesis, Federal University of Santa Catarina, Brazil, 1999.
24. C. H. Marchi and C. R. Maliska, A Nonorthogonal Finite-Volume Method for Solution of All Speed Flows Using Co-located Variables, Numer. Heat Transfer B, vol. 26, pp. 293-311, 1994.
25. S. Balay, W. Gropp, L. C. McInnes, and B. Smith, PETSc 2.0 User Manual, Argonne National Laboratory, 1996.
26. O. R. Burggraf, Analytical and Numerical Studies of the Structure of Steady Separated Flows, J. Fluid Mech., vol. 24, pp. 113-151, 1966.
27. U. Guia, K. N. Guia, and C. T. Shin, High Reynolds Solution for Incompressible Flow Using the Navier-Stokes Equation and a Multigrid Method, J. Comput. Phys., vol. 48, pp. 387-411, 1982.
28. G. de Vahl Davis, Natural Convection of Air in a Square Cavity: A Benchmark Numerical Solution, Int. J. Numer. Meth. Fluids, vol. 3, pp. 249-264, 1983.
29. M. Hortmann, M. Peric, and G. Scheuerer, Finite Volume Multigrid Prediction of Laminar Natural Convection: Benchmark Solutions, Int. J. Numer. Meth. Fluids, vol. 11, pp. 189-207, 1990.
30. P. F. de Abreu, Modeling the Thermal Performance of Windows Using a Two-Dimensional Finite Volume Model, Ph.D. thesis, University of Waterloo, Waterloo, Canada, 1996.