Pressure-based finite-volume methods in computational fluid dynamics

Journal of Heat Transfer

Volumn 129, Issue 4, 2007, Pages 407-424

  Acharya, S ^a   Baliga, B R ^b   Karki, K ^c   Murthy, J Y ^d   Prakash, C ^e   Vanka, S P ^f  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b MCGILL UNIVERSITY   (Canada)

^c Innovative Research Inc   (United States)

^d PURDUE UNIVERSITY   (United States)

^e GE AVIATION   (United States)

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

Author keywords

Compressible; Finite volume; Fluid flow; Incompressible; Multigrid; Numerical methods; Pressure based

Indexed keywords

PRESSURE-BASED FINITE-VOLUME TECHNIQUES; PRESSURE-VELOCITY; SEGREGATED SOLUTION TECHNIQUES;

COMPRESSIBLE FLOW; COMPUTATIONAL FLUID DYNAMICS; FINITE VOLUME METHOD; MESH GENERATION; NUMERICAL METHODS;

INCOMPRESSIBLE FLOW;

COMPRESSIBLE FLOW; COMPUTATIONAL FLUID DYNAMICS; FINITE VOLUME METHOD; INCOMPRESSIBLE FLOW; MESH GENERATION; NUMERICAL METHODS;

EID: 34447642193     PISSN: 00221481     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2716419     Document Type: Review

References (144)

1. Harlow, F. H., and Fromm, J. E., 1965, "Computer Experiments in Fluid Dynamics," Sci. Am., 212, pp. 104-110.
2. Harlow, F. H., and Welch, J. E., 1965, "Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid With Free Surface," Phys. Fluids, 8, pp. 2182-2189.
3. Patankar, S. V., and Spalding, D. B., 1972, "A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows," Int. J. Heat Mass Transfer, 15, pp. 1767-1806.
4. Jameson, A., Baker, T. J., and Weatherill, N. P., 1986, "Calculation of Inviscid Flow over a Complete Aircraft," AIAA 24th Aerospace Sciences Meeting, Reno, Nevada, January 6-9, AIAA-86-0103.
5. Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Washington D.C.
6. Patankar, S. V., Pratap, V. S., and Spalding, D. B., 1974, "Prediction of Laminar Flow and Heat Transfer in Helically Coiled Pipes," J. Fluid Mech., 62, p. 539-551.
7. Patankar, S. V., Ivanovic, M., and Sparrow, E. M., 1979, "Analysis of Turbulent Flow and Heat Transfer in Internally Finned Tubes and Annuli," ASME J. Heat Transfer, 101, pp. 29-37.
8. Maliska, C. R., and Raithby, G. D., 1984, "A Method for Computing Three-Dimensional Flows Using Non-orthogonal Boundary-Fitted Coordinates," Int. J. Numer. Methods Fluids, 4, 519-537.
9. Shyy, W., Tong, S. S., and Correa, S. M., 1985, "Numerical Recirculating Flow Calculation Using a Body-Fitted Coordinate System," Numer. Heat Transfer, 8, pp. 99-113.
10. Karki, K. C., and Patankar, S. V., 1986, "Calculation Procedure for Viscous Incompressible Flows in Complex Geometries," Numer. Heat Transfer, 14, pp. 295-307.
11. Baliga, B. R., and Patankar, S. V., 1983, "A Control-Volume Finite Element Method for Two-Dimensional Incompressible Fluid Flow and Heat Transfer," Numer. Heat Transfer, 6, pp. 245-261.
12. Prakash, C., and Patankar, S. V., 1985, "A Control-Volume-Based Finite-Element Method for Solving the Navier-Stokes Equations Using Equal-Order Velocity-Pressure Interpolation," Numer. Heat Transfer, 8, pp. 259-280.
13. Schneider, G. E., and Raw, M. J., 1987, "Control-Volume Finite Element Method for Heat Transfer and Fluid Flow Using Co-Located Variables -1. Computational Procedures," Numer. Heat Transfer, 11, pp. 363-390.
14. Demirdzic, I., and Muzaferija, S., 1995, "Numerical Method for Coupled Fluid Flow, Heat Transfer and Stress Analysis Using Unstructured Moving Meshes With Cells of Arbitrary Topology," Comput. Methods Appl. Mech. Eng., 125, pp. 235-255.
15. Mathur, S. R., and Murthy, J. Y., 1997, "A Pressure-Based Method for Unstructured Meshes," Numer. Heat Transfer, Part A, 31, pp. 195-216.
16. Hsu, C. F., 1981, "A Curvilinear-Coordinate Method for Momentum, Heat and Mass Transfer in Domains of Irregular Geometry," Ph.D. thesis, University of Minnesota, Minneapolis.
17. Rhie, C. M., and Chow, W. L., 1983, "A Numerical Study of the Turbulent Flow Past an Isolated Airfoil With Trailing Edge Separation," AIAA J., 21, pp. 1525-1532.
18. Vanka, S. P., 1986, "Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables," J. Comput. Phys., 65, pp. 138-158.
19. Vanka, S. P, 1986, "Block-Implicit Multigrid Calculation of Two-Dimensional Recirculating Flows," Comput. Methods Appl. Mech. Eng., 59, pp. 29-48.
20. Smith, K. M., Cope, W. K., and Vanka, S. P., 1993, "Multigrid Procedure for Three-Dimensional Flows on Non-orthogonal Collocated Grids," Int. J. Numer. Methods Fluids, 17, pp. 887-904.
21. Jyotsna, R., and Vanka, S. P., 1995, "Multigrid Calculation of Steady, Viscous Flow in Triangular Cavity," J. Comput. Phys., 122, 107-117.
22. Patankar, S. V., 1971, "Calculation of Unsteady Compressible Flows Involving Shocks," Report No. UF/N/A/4, Imperial College, London.
23. Van Doormal, J. P., Raithby, G. D., and McDonald, B. H., 1987, "The Segregated Approach to Predicting Viscous Compressible Flows," ASME J. Turbomach., 109, pp. 268-277.
24. Karki, K. C., and Patankar, S. V., 1989, "Pressure Based Calculation Procedure for Viscous Flows at All Speeds in Arbitrary Configurations," AIAA J., 27, pp. 1167-1174.
25. Leonard, B. P., 1979, "A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation," Comput. Methods Appl. Mech. Eng., 19, pp. 59-98.
26. Hirsch, C., 1990, Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows, Wiley, New York.
27. Laney, C. B., 1998, Computational Gas Dynamics, Cambridge University Press, Cambridge, U.K.
28. Van Doormaal, J. P., and G. D. Raithby, 1984, "Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows," Numer. Heat Transfer, 7, pp. 147-163.
29. Issa, R. I., 1982, "Solution of the Implicit Discretized Fluid Flow Equations by Operator Splitting," Mechanical Engg. Report, FS/82/15, Imperial College, London.
30. Issa, R. I., Gosman, A. D., and Watkins, A, P., 1986, "The Computation of Compressible and Incompressible Recirculating Flows by a Non-Iterative Implicit Scheme," J. Comput. Phys., 62, pp. 66-82.
31. Jang, D. S., Jetli, R., and Acharya, S., 1986, "Comparison of the PISO, SIMPLER and SIMPLEC Algorithms for the Treatment of the Pressure-Velocity Coupling in Steady Flow Problems," Numer. Heat Transfer, 10(3), pp. 209-228.
32. Moukalled, F., and Acharya, S., 1989, "Improvements to Incompressible Flow Calculation on a Non-Staggered Curvilinear Grid," Numer. Heat Transfer, Part B, 15(2), pp. 131-152.
33. Prakash, C., 1981, "A Finite Element Method for Predicting Flow Through Ducts With Arbitrary Cross-Sections," Ph.D. thesis, University of Minnesota, Minneapolis.
34. Pope, S. B., 1978, "The Calculation of Turbulent Recirculating Flows in General Orthogonal Coordinates," J. Comput. Phys., 26, pp. 197-217.
35. Rastogi, A. K., 1984, "Hydrodynamics in Tubes Perturbed by Curvilinear Obstructions," ASME J. Fluids Eng., 106, pp. 262-269.
36. Raithby, G. D., Galpin, P. F., and Van Doormaal, J. P., 1986, "Prediction of Heat and Fluid Flow in Complex Geometries Using General Orthogonal Coordinates," Numer. Heat Transfer, 9, pp. 125-142.
37. Demirdzic, I., Gosman, A. D., Issa, R. I., and Peric, M., 1987, "A Calculation Procedure for Turbulent Flows in Complex Geometries," Comput. Fluids, 15, pp. 251-273.
38. Segal, A., Wesseling, P., Van Kan, J., Oosterlee, C. W., and Kassels, K., 1992, "Invariant Discretization of the Incompressible Navier-Stokes Equations in Boundary Fitted Co-ordinates," Int. J. Numer. Methods Fluids, 15, pp. 411-426.
39. Karki, K. C., 1986, "A Calculation Procedure for Viscous Flows at All Speeds in Complex Geometries," Ph.D. thesis, University of Minnesota, Minneapolis.
40. Davidson, L., and Hedberg, P., 1989, "Mathematical Derivation of a Finite-Volume Formulation for Laminar Flow in Complex Geometries," Int. J. Numer. Methods Fluids, 9, pp. 531-540.
41. Shyy, W., Tong, S. S., and Correa, S. M., 1985, "Numerical Recirculating Flow Calculation Using a Body-Fitted Coordinate System," Numer. Heat Transfer, 8, pp. 99-113.
42. Vanka, S. P., Chen, C.-J., and Sha, W. T., 1980, "A Semi-Implicit Calculation Procedure for Flow Described in Body-Fitted Coordinate Systems," Numer. Heat Transfer, 3, pp. 1-19.
43. Joshi, D. S., and Vanka, S. P., 1991, "Multigrid Calculation Procedure for Internal Flows in Complex Geometries," Numer. Heat Transfer, Part B, 20, pp. 61-80.
44. Kelkar, K. M., and Choudhury, D., 1993, "Numerical Method for the Computation of Flow and Scalar Transport Using Non-Orthogonal Boundary-Fitted Coordinates," Numer. Heat Transfer, Part B, 24, pp. 391-414.
45. He, P., and Salcudean, M., 1994, "A Numerical Method for 3D Viscous Incompressible Flows Using Non-Orthogonal Grids," Int. J. Numer. Methods Fluids, 18, pp. 449-469.
46. Melaen, M. C., 1992, "Calculation of Fluid Flows With Staggered and Non-staggered Curvilinear Nonorthogonal Grids - The Theory," Numer. Heat Transfer, Part B, 21, pp. 1-19.
47. Baliga, B. R., 1978, "A Control-Volume-Based Finite Element Method for Convective Heat and Mass Transfer," Ph.D. thesis, University of Minnesota, Minneapolis.
48. Baliga, B. R., and Patankar, S. V., 1980, "A New Finite Element Formulation for Convection-Diffusion Problems," Numer. Heat Transfer, 3, pp. 393-409.
49. Baliga, B. R., 1997, "Control-Volume Finite Element Methods for Fluid Flow and Heat Transfer," in Advances in Numerical Heat Transfer, J. W. Minkowycz and M. E. Sparrow, eds., Taylor & Francis, New York, Vol. 1, Chap. 3, pp. 97-135.
50. Zienkiewicz, O. C., and Taylor, R. L., 2000, The Finite Element Method Vol. 3 Fluid Dynamics, 5th ed., McGraw-Hill, London.
51. Peric, M., Kessler, R., and Scheuerer, G., 1998, "Comparison of Finite-Volume Numerical Methods With Staggered and Co-Located Grids," Comput. Fluids, 16, pp. 389-403.
52. Baliga, B. R., and Atabaki, N., 2006, "Control-Volume-Based Finite-Difference and Finite-Element Methods," in Handbook of Numerical Heat Transfer, 2nd ed., J. W. Minkowycz, M. E. Sparrow, and Y. J. Murthy eds., John Wiley & Sons, New York, Chap. 6.
53. Venditti, D. A., 1998, "An h-Adaptive Control-Volume Finite Element Method for Steady, Two-Dimensional Fluid Flow and Heat Transfer," M.Eng. thesis, McGill University, Montreal, Quebec, Canada.
54. Spalding, D. B., 1972, "A Novel Finite-Difference Formulation for Differential Expressions Involving Both First and Second Derivatives," Int. J. Numer. Methods Eng., 4, pp. 551-559.
55. Raithby, G. D., 1976, "Skew Upstream Difference Schemes for Problems Involving Fluid Flow," Comput. Methods Appl. Mech. Eng., 9, pp. 153-164.
56. Masson, C., and Baliga, B. R., 1994, "A Control-Volume Finite Element for Dilute Gas-Solid Particle Flows," Comput. Fluids, 23, pp. 1073-1096.
57. Schneider, G. E., and Raw, M. J., 1986, "A Skewed Positive Influence Coefficient Upwind Procedure for Control-Volume-Based Finite Element Convection-Diffusion Computation," Numer. Heat Transfer, 9, pp. 1-26.
58. Saabas, H. J., and Baliga, B. R., 1994, "A Co-Located Equal-Order Control-Volume Finite Element Method for Multidimensional, Incompressible Fluid Flow - Part I: Formulation," Numer. Heat Transfer, Part B, 26, pp. 381-407.
59. Tran, L. D., Masson, C., and Smaïli, A., 2006, "A Stable Second-Order Mass-Weighted Upwind Scheme for Unstructured Meshes," Int. J. Numer. Methods Fluids, 51, pp. 749-771.
60. Elias, S. R., Stubley, G. D., and Raithby, G. D., 1997, "An Adaptive Agglomeration Method for Additive Correction Multigrid," Int. J. Numer. Methods Eng., 40, pp. 887-903.
61. Masson, C., and Baliga, B. R., 1998, "Simulation of Gas-Solid Particle Flows Over a Wide Range of Concentration," Int. J. Numer. Methods Fluids, 28, pp. 1441-1479.
62. Ledain-Muir, B., and Baliga, B. R., 1988, "Solution of Three-Dimensional Convection-Diffusion Problems Using Tetrahedral Elements and Flow-Oriented Upwind Interpolation," Numer. Heat Transfer, 9, pp. 253-272.
63. Costa, V. A. F., Oliveira, L. A., and Figueiredo, A. R., 1995, "A Control-Volume-Based Finite Element Method for Three-Dimensional Incompressible Turbulent Fluid Flow, Heat Transfer and Related Phenomena," Int. J. Numer. Methods Fluids, 21, pp. 591-613.
64. Mathur, S. R., and Murthy, J. Y., 2000, "Unstructured Finite Volume Methods for Multi-Mode Heat Transfer," in Advances in Heat Transfer, J. W. Minkowycz and M. E. Sparrow eds., Taylor and Francis, New York, Vol. II pp. 37-70.
65. Davidson, L., 1996; "A Pressure Correction Method for Unstructured Meshes With Arbitrary Control Volumes," Int. J. Numer. Methods Fluids, 22, pp. 265-281.
66. Murthy, J. Y., Minkowyez, W. J., Sparrow, E. M., and Mathur, S. R., 2006, "Survey of Numerical Methods," Handbook of Numerical Heat Transfer, 2nd ed., J. W. Minkowycz, M. E. Sparrow, and Y. J. Murthy eds., John Wiley & Sons, New York, Chap. 1.
67. Hutchinson, B. R., and Raithby, G. D., 1986, "A Multigrid Method Based on the Additive Correction Strategy," Numer. Heat Transfer, 9, pp. 511-537.
68. Van den Vorst, H. A., and Sonneveld, P., 1990, "CGSTAB: A More Smoothly Converging Variant of CGS," Technical Report, Delft University of Technology, Delft, The Netherlands.
69. Van den Vorst, H. A., 1992, "BI-CGSTAB: A Fast and Smoothly Converging Variant of BI-CG for the Solution of Non-Symmetric Linear Systems," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput., 13, pp. 631-644.
70. Saad, Y., and Schultz, M. H., 1986, "GMRES: A Generalized Residual Algorithm for Solving Non-Symmetric Linear Systems," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput., 7, pp. 856-869.
71. Demirdzic, I., Lilek, Z., and Peric, M., 1992, "Fluid Flow and Heat Transfer Test Problems for Non-Orthogonal Grids," Int. J. Numer. Methods Fluids, 15, pp. 329-354.
72. Murthy, J. Y., and Mathur, S. R., 2001, "Unstructured Mesh Methods for Combustion Problems, in CFD in Industrial Combustion, E. C. Baukal and X. Li, eds., CRC Press, Boca Raton, FL, pp. 61-94.
73. Murthy, J. Y., and Mathur, S. R., 1998, "Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes," J. Thermophys. Heat Transfer, 12(3), pp. 313-321.
74. Beam, R. M., and Warming, R. F., 1978, "An Implicit Factored Scheme for Compressible Navier-Stokes Equations," AIAA J., 16, pp. 393-402.
75. MacCormack, R. W., 1982, "A Numerical Method for Solving Equations of Compressible Viscous Flows," AIAA J., 20, pp. 1275-1281.
76. Ni, R. H., 1982, "A Multiple Grid Scheme for Solving the Enter Equations," AIAA J., 20, pp. 1565-1571.
77. Choi, D., and Merkle, C. L., 1985, "Application of Time-Iterative Schemes to Incompressible Flows," AIAA J., 23, 1518-1524.
78. Kwak, D., Chang, J. L. C., Shanks, S. P., and Chakravarthy, S. R., 1986, "A Three-Dimensional Incompressible Navier-Stokes Flow Solver Using Primitive Variables," AIAA J., 24, 390-396.
79. Issa, R. I., and Javareshkian, M. H., 1998, "Pressure-Based Compressible Calculation Method Utilizing Total Variation Diminishing Schemes," AIAA J., 36, pp. 1652-1657.
80. Moukalled, F., and Darwish, M., 2001, "A High-Resolution Pressure Based Algorithm for Fluid Flow at All Speeds," J. Comput. Phys., 168, pp. 101-133.
81. Demirdzic, I., Lilek, Z., and Peric, M., 1993, "A Collocated Finite Volume Method for Predicting Flows at All Speeds," Int. J. Numer. Methods Fluids, 16, 1029-1050.
82. Marchi, C. H., and Maliska, C. R., 1994, "A Nonorthogonal Finite-Volume Method for the Solution of All Speed Flows Using Co-located Variables," Numer. Heat Transfer, Part B, 26, pp. 293-311.
83. Shyy, W., and Chen, M. H., 1992, "Pressure-Based Multigrid Algorithm for Flow at All Speeds," AIAA J., 30, pp. 2660-2669.
84. Rincon, J., and Elder, R., 1997, "A High-Resolution Pressure-Based Method for Compressible Flows," Comput. Fluids, 26 pp. 217-231.
85. Demirdzic, I., Issa, R. I., and Lilek, Z., 1990, "Solution Method for Viscous Flows at All Speeds in Complex Domains," in Notes on Numerical Fluid Mechanics, P. Wesseling ed., Vieweg, Braunschweig, Vol. 29.
86. Mathur, S. R., and Murthy, J. Y., 1999, "All Speed Flows on Unstructured Meshes Using a Pressure Correction Approach," AIAA Paper No. 99-3365.
87. Lien, F. S., 2000, "A Pressure-Based Unstructured Grid Method for All-Speed Flows," Int. J. Numer. Methods Fluids, 33, pp. 355-374.
88. Karimian, S. M. H., and Schneider, G. E., 1994, "Pressure-Based Computational Method for Compressible and Incompressible Flows," J. Thermophys. Heat Transfer, 8, pp. 267-274.
89. Darbandi, M., and Schneider, G. E., 1997, "Momentum Variable Procedure for Solving Compressible and Incompressible Flows," AIAA J., 35, 1801-1805.
90. Lien, F. S., and Leschziner, M. A., 1993, "A Pressure-Velocity Solution Strategy for Compressible Flow and Its Application to Shock/ Boundary-Layer Interaction Using Second-Moment Turbulence Closure," ASME J. Fluids Eng., 115, pp. 717-125.
91. McGuirk, J. J., and Page, G. J., 1990, "Shock Capturing Using a Pressure Correction Method," AIAA J., 29, pp. 1751-1757.
92. Hafez, M., South, J., and Murman, E., 1979, "Artificial Compressibility Methods for Numerical Solutions of Transonic Full Potential Equations," AIAA J., 17, pp. 838-844.
93. Wornom, S. F., and Hafez, M. M., 1986, "Calculation of Quasi-One Dimensional Flows With Shocks," Comput. Fluids, 14, pp. 131-140.
94. Ferziger, J. H., and Peric, M., 1996, Computational Methods for Fluid Dynamics, Springer Verlag, Berlin.
95. Hackbusch, W., and Trottenberg, U., 1982, Multigrid Methods, Springer Verlag, Berlin.
96. Stuben, K., and Trottenberg, U., 1982, Multigrid Methods: Fundamental Algorithms, Model Problems, Analysis and Applications, in Lecture Notes in Mathematics No. 960, pp. 1-176, Springer Verlag, Berlin.
97. Brandt, A., 1984, Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, GMD Bonn, GMD-Studien Nr. 85.
98. MGNET: Multigrid Bibliography, maintained by C. C. Douglas, Yale University.
99. Trottenberg, U., and Oosterlee, C. W., and Schuller, A., 2001, Multigrid, Academic Press, New York.
100. Sivaloganathan, S., and Shaw, G, J., 1988, "A Multigrid Method for Recirculating Flows," Int. J. Numer. Methods Fluids, 8(4), p 417-440.
101. Shyy, W., Chen, M-H., and Sun, C-S., 1992, "Pressure-based Multigrid Algorithm for Flow at all Speeds," AIAA J., 30(11), pp. 2660-2669.
102. Hortmann, M., Peric, M., and Scheurer, G., 1990, "Finite Volume Multigrid Method for the Prediction of Incompressible Flows," Int. J. Numer. Methods Fluids, 11, pp. 189-207.
103. Lange, C. F., Schafer, M., and Durst, F., 2002, "Local Block Refinement With a Multigrid Flow Solver," Int. J. Numer. Methods Fluids, 38, pp. 21-41.
104. Brandt, A., 1977, "Multilevel Adaptive Solutions to Boundary-Value Problems," Math. Comput., 31, pp. 333-390.
105. Henson, V. E., 2003, "Multigrid Methods for Nonlinear Problems: An Overview," Proc. SPIE, 5016(1), pp. 36-48.
106. Vanka, S. P., 1986, "A Calculation Procedure for Three-Dimensional Recirculating Flows," Comput. Methods Appl. Mech. Eng., 55, pp. 321-338.
107. Vanka, S. P., 1986, "Performance of a Multigrid Calculation Procedure in Three-Dimensional Sudden Expansion Flows," Int. J. Numer. Methods Fluids, 6, pp. 459-477.
108. Joshi, D. S., and Vanka, S. P., 1991, "Multigrid Calculation Procedure for Internal Flows in Complex Geometries," Numer. Heat Transfer, Part B, 20, pp. 61-80.
109. Caretto, L. S., Gosman, A. D., Patankar, S. V., and Spalding, D. B., 1973, "Two Calculation Procedures for Steady, Three-Dimensional Flows With Re-circulation," Proceedings of the 3rd International Conference on Numerical Methods in Fluid Mechanics. II, pp. 60-68.
110. Galpin, P. F., Van Doormaal, J. P., and Raithby, G. D., 1985, "Solution of the Incompressible Mass and Momentum Equations by Application of a Coupled Equation Line Solver," Int. J. Numer. Methods Fluids, 5(7), pp. 615-625.
111. He, P., Salcudean, M., Gartshore, I. S., and Nowak, P., 1996, "Multigrid Calculation of Fluid Flows in Complex 3D Geometries Using Curvilinear Grids," Comput. Fluids, 25(4), pp. 395-419.
112. Shyy, W., Sun, C.-S., Chen, M.-H., and Chang, K. C., 1993, "Multigrid Computation for Turbulent Recirculating Flows in Complex Geometries," Numer. Heat Transfer, Part A, 23(1), pp. 79-98.
113. Jyotsna, R., and Vanka, S. P., 1995, "A Pressure-Based Multigrid Procedure for the Navier-Stokes Equations on Unstructured Grids," Proceedings of the 1995 Copper Mountain Conference on Multigrid Methods, Copper Mountain, Co.
114. Lin, F. B., and Sotiropoulos, F., 1997, "Strongly-Coupled Multigrid Method for 3-D Incompressible Flows Using Near-Wall Turbulence Closures," ASME J. Fluids Eng., 119(2), pp. 314-324.
115. Zheng, X., Liao, C., Liu, C., Sung, C. H., and Huang, T. T., 1997, "Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models, Part I-Numerical Method," ASME J. Fluids Eng., 119(4), pp. 893-899.
116. Vanka, S. P., Krazinski, J. L., and Nejad, A. S., 1989, "Efficient Computational Tool for Ramjet Combustor Research," J. Propul. Power, 5(4), pp. 431-437.
117. Wang, G., 1994, "Numerical Simulations of STOVL Hot Gas Ingestion in Ground Proximity Using a Multigrid Solution Procedure," MS thesis, University of Illinois at Urbana-Champaign, IL.
118. Koobus, B., Lallemand, M. H., and Dervieux, A., 1994, "Unstructured Volume Agglomeration MG: Solution of the Poisson Equation," Int. J. Numer. Methods Fluids, 18, pp. 27-42.
119. Mavriplis, D. J., and Venkatakrishnan, V., 1995, "A 3D Agglomeration Multigrid Solver for the Reynolds-Averaged Navier-Stokes Equations on Unstructured Meshes," 33rd Aerospace Sciences Meeting and Exhibit, Jan. 9-12, Reno, NV.
120. Mavriplis, D. J., 2006, "Viscous Flow Analysis Using a Parallel Unstructured Multigrid Solver," AIAA J., 38(11), pp. 2067-2076.
121. Mavriplis, D. J., 1999, "Directional Agglomeration Multigrid Techniques for High-Reynolds-Number Viscous Flows," AIAA J., 37(10), pp. 1222-1230.
122. Lambropoulos, N. K., Koubogiannis, D. G., and Giannakoglou, K. C., 2004, "Acceleration of a Navier-Stokes Equation Solver for Unstructured Grids Using Agglomeration Multigrid and Parallel Processing," Comput. Methods Appl. Mech. Eng., 193, pp. 781-803.
123. Hwang, Y. H., 1995, "Unstructured Additive Correction Multigrid Method for the Solution of Matrix Equations," Numer. Heat Transfer, Part B, 27, pp. 195-212.
124. Sathyamurthy, P. S., and Patankar, S. V., 1994, "Block-Correction-Based Multigrid Method for Fluid Flow Problems," Numer. Heat Transfer, Part B, 25(4), pp. 375-394.
125. Brandt, A., McCormick, S. F., and Ruge, J., 1984, "Algebraic Multigrid (AMG) for Sparse Matrix Equations," Sparsity and its Applications, D. J. Evans, ed., Cambridge University Press, Cambridge, pp. 257-284.
126. Webster, R., 1994, "An Algebraic Multigrid Solver for Navier-Stokes Problems," Int. J. Numer. Methods Fluids, 18, pp. 761-780.
127. Webster, R., 1996, "An Algebraic Multigrid Solver for Navier-Stokes Problems in the Discrete Second Order Approximation," Int. J. Numer. Methods Fluids, 22, pp. 1103-1123.
128. Vanka, S. P., 1985, "Block-Implicit Calculation of Steady Turbulent Recirculating Flows," Int. J. Heat Mass Transfer, 28(11), pp. 2093-2103.
129. Yu, C.-C., and Heinrich, J. C., 1986, "Petrov-Galerkin Methods for Time-Dependent Convective Transport Equation," Int. J. Numer. Methods Eng., 23, pp. 883-901.
130. Ortega, J. M., and Rheinboldt, W. C., 1980, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York.
131. Haroutunian, V. H., Engelman, M. S., and Hasbani, I., 1993, "Segregated Finite Element Algorithms for the Numerical Solution of Large-Scale Incompressible Flow Problems," Int. J. Numer. Methods Fluids, 17, pp. 323-348.
132. Hughes, T. J. R., Franca, L. P., and Becestra, M., 1986, "A New Finite Element Formulation for Computational Fluid Dynamics, V: Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of the Stokes Problem Accomodating Equal-Order Interpolations," Comput. Methods Appl. Mech. Eng., 59, pp. 85-99.
133. Tezduyar, T. E., Shih, R., Mittal, S., and Ray, S. E., 1990, "Incompressible Flow Computation With Stabilized Bi-Linear and Linear Equal-Order Interpolation Velocity-Pressure Elements," Technical Report, University of Minnesota Supercomputing Institute Research Report UMSI90/165.
134. Amon, C. H., 2000, "Spectral Element Methods for Unsteady Fluid Flow and Heat Transfer in Complex Geometries: Methodology and Applications," Advances in Numerical Heat Transfer, W. J. Minkowycz and E. M. Sparrow, eds., Taylor and Francis, New York, Vol. 2, Chap. 3, pp. 71-108.
135. Belytschko, T., Lu, Y. Y., and Gu, L., 1994, "Element-Free Galerkin Methods," Int. J. Numer. Methods Eng., 37, pp. 229-256.
136. Duarte, C. A., and Oden, J. T., 1996, "An Hp Adaptive Method Using Clouds," Comput. Methods Appl. Mech. Eng., 139, pp. 237-262.
137. Liu, G. R., 2002, Mesh Free Methods: Moving Beyond the Finite Element Method, CRC Press, Boca Raton, FL.
138. Atluri, S. N., and Zhu, T., 1998, "A New Meshless Local Petrov-Galerkin (MPLG) Approach in Computational Mechanics," Comput. Mech., 22, pp. 117-127.
139. Pepper, D. W., 2006, "Meshless Methods," Handbook of Numerical Heat Transfer, 2nd ed., W. J. Minkowycz, E. M. Sparrow, and J. Y. Murthy, eds., John Wiley and Sons, New York, pp. 225-247.
140. Raithby, G. D., and Chui, E. H., 1990, "A Finite-Volume Method for Predicting Radiant Heat Transfer in Enclosures With Participating Media," ASME J. Heat Transfer, 112, pp. 415-423.
141. Chai, J. S., Lee, H. S., and Patankar, S. V., 1994, "Finite-Volume Method for Radiation Heat Transfer," J. Thermophys. Heat Transfer, 8(3), pp. 419-425.
142. Murthy, J. Y., and Mathur, S. R., 1998, "Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes," J. Thermophys. Heat Transfer, 12(3), pp. 313-321.
143. Wang, Z. J., Przekwas, A. J., and Liu, Y., 2002, "A FV-TD Electromagnetic Solver Using Adaptive Cartesian Grids," Comput. Phys. Common., 148, pp. 17-29.
144. Murthy, J. Y., and Mathur, S. R., 2002, "Computation of Sub-Micron Thermal Transport Using an Unstructured Finite Volume Method," ASME J. Heat Transfer, 124(6), pp. 1176-1181.