Perspective on unstructured grid flow solvers

AIAA Journal

Volumn 34, Issue 3, 1996, Pages 533-547

  Venkatakrishnan, V ^a,b,c,d  

^a NASA LANGLEY RESEARCH CENTER   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

^c RUTGERS UNIVERSITY   (United States)

^d NASA AMES RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; FINITE VOLUME METHOD; NAVIER STOKES EQUATIONS; REVIEWS;

ADAPTIVE METHOD; COMPRESSIBLE FLUID; DISCRETIZATION METHOD; MODELING; MULTIGRID; PARALLEL PROCESSING; TURBULENCE STRUCTURE;

COMPUTATIONAL FLUID DYNAMICS;

COMPUTATIONAL FLUID DYNAMICS; GRIDS; UNSTRUCTURED FLOW SOLVERS;

EID: 0029656535     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/3.13101     Document Type: Review

References (189)

1. Anon., "Special Course on Unstructured Grid Methods for Advection Dominated Flows," AGARD Rept. 787, AGARD, 1992.
2. Abgrall, R., "On Essentially Non-Oscillatory Schemes on Unstructured Meshes: Analysis and Implementation," Journal of Computational Physics, Vol. 114, 1994, pp. 45-58.
3. Aftosmis, M., Gaitonde, D., and Tavares, T. S., "Behavior of Linear Reconstruction Techniques on Unstructured Meshes," AIAA Journal, Vol. 33, No. 11, 1995, pp. 2038-2049.
4. Alonso, J., and Jameson, A., "Fully-Implicit Time-Marching Aeroelastic Solution," AIAA Paper 94-0056, Jan. 1994.
5. Anderson, W. K., "A Grid Generation and Flow Solution Method for the Euler Equations of Unstructured Grids," Journal of Computational Physics, Vol. 110, 1994, pp. 23-38.
6. Anderson, W. K., and Bonhaus, D. L., McGhee, R. J., and Walker, B. S., "Navier-Stokes Computations and Experimental Comparisons for Multielement Airfoil Configurations," Journal of Aircraft, Vol. 32, No. 6, 1995, pp. 1246-1253.
7. Anderson, W. K., and Bonhaus, D. L., "An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids," Computers and Fluids, Vol. 23, 1994, pp. 1-21.
8. Angrand, F., and Dervieux, A., "Some Explicit Triangular Finite Element Schemes for the Euler Equations," International Journal for Numerical Methods in Fluids, Vol. 4, 1984, pp. 749-764.
9. Arminjon, P., and Dervieux, A., "Construction of TVD-Like Artificial Viscosities on Two-Dimensional Arbitrary FEM Grids," Journal of Computational Physics, Vol. 106, 1993, pp. 176-198.
10. Baldwin, B. S., and Barth, T. J., "A One-Equation Turbulence Transport Model for High Reynolds Wall-Bounded Flows," NASA TM 102847, Aug. 1990.
11. Baldwin, B. S., and Barth, T. J., "A One-Equation Turbulence Transport Model for High Reynolds Wall-Bounded Flows," AIAA Paper 91-0610, Jan. 1991.
12. Baldwin, B. S., and Lomax, H. J., "Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows," AIAA Paper 78-257, Jan. 1978.
13. Barth, T. J., "Numerical Aspects of Computing Viscous High Reynolds Number Flows on Unstructured Meshes," AIAA Paper 91-0721, Jan. 1991.
14. Barth, T. J., "A Three-Dimensional Upwind Euler Solver for Unstructured Meshes," Proceedings of the AIAA 10th Computational Fluid Dynamics Conference (Honolulu, HI), AIAA, Washington, DC, 1995, pp. 228-238.
15. Barth, T. J., "Recent Developments in High Order k-Exact Reconstruction on Unstructured Meshes," AIAA Paper 93-0668, Jan. 1993.
16. Barth, T. J., and Fredrickson, P. O., "Higher Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction," AIAA Paper 90-0013, Jan. 1990.
17. Barth, T. J., and Jespersen, D. C., "The Design and Application of Upwind Schemes on Unstructured Meshes," AIAA Paper 89-0366, Jan. 1989.
18. Batina, J. T., "Implicit Flux-Split Euler Scheme for Unsteady Aerodynamic Analysis Involving Unstructured Dynamic Meshes," AIAA Journal, Vol. 29, No. 7, 1991, pp. 1836-1843.
19. Batina, J. T., "Implicit Upwind Solution Algorithms for Three-Dimensional Unstructured Meshes, AIAA Journal, Vol. 31, No. 5, 1993, pp. 801-805.
20. Baum, J. D., Luo, H., and Löhner, R., "A New ALE Adaptive Unstructured Methodology for the Simulation of Moving Bodies," AIAA Paper 94-0414, Jan. 1994.
21. Benek, J. A., Buning, P. G., and Steger, J. L., "A 3-D Chimera Grid Embedding Technique," AIAA Paper 85-1523, July 1985.
22. Berger, M. J., and Colella, P., "Local Adaptive Mesh Refinement for Shock Hydrodynamics," Journal of Computational Physics, Vol. 82, 1989, pp. 67-84.
23. Berger, M. J., and Leveque, R. J., "An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries," AIAA Paper 89-1930, June 1989.
24. Bey, K. S., and Oden, J. T., "A Runge-Kutta Local Projection P1-Discontinuous Galerkin Finite Element Method for High Speed Flows," Proceedings of the AIAA 10th Computational Fluid Dynamics Conference (Honolulu, HI), AIAA, Washington, DC, 1991, pp. 541-555.
25. Bokhari, S., Crockett, T. W., and Nichol, D. M., "Parametric Nested Dissection," ICASE, NASA Langley Research Center, ICASE Rept. 93-39, Hampton, VA, July 1993.
26. Bonhaus, D. L., "An Upwind Multigrid Method for Solving Viscous Flows on Unstructured Triangular Meshes," M.S. Thesis, George Washington Univ., Washington, DC, 1993.
27. Boris, J. P., and Book, D. L., "Flux Corrected Transport, 1 SHASTA, A Fluid Transport Algorithm That Works," Journal of Computational Physics, Vol. 11, 1973, pp. 38-69.
28. Braaten, M. E., and Connell, S. D., "A 3-D Unstructured Adaptive Multigrid Scheme for the Navier-Stokes Equations," GE Research and Development Center, TR 94CRD146, Schenectady, NY, Aug. 1994.
29. Brennis, A., and Eberle, A., "Application of an Implicit Relaxation Method Solving the Euler Equations for Time-Accurate Unsteady Problems," Journal of Fluids Engineering, Vol. 112, 1990, pp. 510-520.
30. Bristeau, M. O., Glowinski, R., Dimoyat, B., Periaux, J., Perrier, P., and Prionneau, O., "Finite Element Methods for the Compressible Navier-Stokes Equations," AIAA Paper 83-1890, July 1983.
31. Brown, P. N., and Saad, Y., "Hybrid Krylov Methods for Nonlinear Systems of Equations," SIAM Journal on Scientific and Statistical Computing, Vol. 11, 1990, pp. 450-481.
32. Cai, X. C., Gropp, W. D., Keyes, D. E., and Tidriri, M. D., "NewtonKrylov-Schwarz Methods in CFD," Proceedings of the International Workshop on Numerical Methods for the Navier-Stokes Equations, Vol. 47, Notes in Numerical Fluid Mechanics, Vieweg Verlag, Brunswick/Wiesbaden, Germany, 1994.
33. Chakravarthy, S., Szema, K. Y., Ramakrishnan, S., Burman, R., and Schultz, R., "Inviscid CFD for Store Separation Using Unified Boundary Conditions," AIAA Paper 93-3404, Aug. 1993.
34. Chalot, F., Mallet, M., and Ravachol, M., "A Comprehensive Finite Element Navier-Stokes Solver for Low and High-Speed Aircraft Design," AIAA Paper 94-0814, Jan. 1994.
35. Cockburn, B., Hou, S., and Shu, C., "TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws IV: The Multidimensional Case," Mathematics of Computation, Vol. 54, 1990, pp. 545-581.
36. Connell, S. D., and Braaten, M. E., "Semi-Structured Mesh Generation for Three-Dimensional Navier-Stokes Calculations," AIAA Journal, Vol. 33, No. 6, 1995, pp. 1017-1024.
37. Connell, S. D., and Holmes, D. G., "A 3d Unstructured Adaptive Multigrid Scheme for the Euler Equations," AIAA Journal, Vol. 32, No. 8, 1994, pp. 1626-1632.
38. Davis, G. A., and Bendiksen, O. O., "Unsteady Transonic Two-Dimensional Euler Solutions Using Finite Elements," AIAA Journal, Vol. 31, No. 6, 1993, pp. 1051-1059.
39. De Zeeuw, D., and Powell, K. G., "An Adaptively Refined Cartesian Mesh Solver for the Euler Equations," Journal of Computational Physics, Vol. 104, 1993, pp. 56-69.
40. Deconinck, H., Hirsch, C., and Peuteman, J., "Characteristic Decomposition Methods for the Multidimensional Euler Equations," Lecture Notes in Physics, Vol. 264, 1986, pp. 216-221.
41. Deconinck, H., Paillere, H., Struijs, R., and Roe, P. L., "Multidimensional Upwind Schemes Based on Fluctuation-Splitting of Conservation Laws," Computational Mechanics, Vol. 11, 1993, pp. 323-340.
42. Desideri, J. A., and Dervieux, A., Compressible Flow Solvers Using Unstructured Grids, VKI Lecture Series, 1988-05, van Kármán Inst. for Fluid Dynamics, Rhôde St. Genèse, Belgium, 1988, pp. 1-115.
43. Donea, J., "A Taylor-Galerkin Method for Convective Transport Problems," International Journal for Numerical Methods in Engineering, Vol. 20, 1984, pp. 101-119.
44. Durlofsky, L. J., Engquist, B., and Osher, S., "Triangle-Based Adaptive Stencils for the Solution of Hyperbolic Conservation Laws," Journal of Computational Physics, Vol. 98, 1992, pp. 64-73.
45. Farhat, C., Fezoui, L., and Lanteri, S., "Two-Dimensional Viscous Flow Computation on the Connection Machine: Unstructured Meshes, Upwind Schemes and Parallel Computation," Computational Methods in Applied Mechanics and Engineering, Vol. 102, 1993, pp. 61-88.
46. Farhat, C., and Lesoinne, M., "Automatic Partitioning of Unstructured Meshes for the Parallel Solution of Problems in Computational Mechanics," International Journal for Numerical Methods in Engineering, Vol. 36, 1993, pp. 745-764.
47. Fezoui, L., and Stoufflet, B., "A Class of Implicit Upwind Schemes for Euler Simulations with Unstructured Meshes," Journal of Computational Physics, Vol. 84, 1989, pp. 174-206.
48. Freund, R. W., Golub, G. H., and Nachtigal, N. M., "Iterative Solutions of Linear Systems," Acta Numerica, Vol. 1, 1992, pp. 57-100.
49. Frink, N. T., "Upwind Scheme for Solving the Euler Equations on Unstructured Tetrahedral Meshes," AIAA Journal, Vol. 30, No. 1, 1992, pp. 70-77.
50. Frink, N. T., "Recent Progress Toward a Three-Dimensional Unstructured Navier-Stokes Flow Solver," AIAA Paper 94-0061, Jan. 1994.
51. Frink, N. T., Parikh, P., and Pirzadeh, S., "Aerodynamic Analysis of Complex Configurations Using Unstructured Grids," AIAA Paper 91-3292, Sept. 1991.
52. Garner, P. L., Meredith, P. T., and Stoner, R. C., "Areas for future CFD Development as Illustrated by Transport Aircraft Applications," Proceedings of the AIAA 10th Computational Fluid Dynamics Conference (Honolulu, HI), AIAA, Washington, DC, 1991, pp. 10-19.
53. Godfrey, A. G., Mitchell, C. R., and Walters, R. W., "Practical Aspects of Spatially High Accuracy Methods," AIAA Paper 92-0054, Jan. 1992.
54. Godunov, S. K., "A Difference Method for the Numerical Calculation of Discontinuous Solutions of the Hydrodynamic Equations," Mat.-Sb., Vol. 47, 1959.
55. Halt, D. W., and Agarwal, R. K., "Compact Higher Order Characteristic-Based Euler Solver for Unstructured Grids," AIAA Journal, Vol. 30, No. 8, 1992, pp. 1993-1999.
56. Harten, A., "On a Class of High-Resolution Total-Variation-Stable Finite Difference Schemes," SIAM Journal on Numerical Analysis, Vol. 21, 1984, pp. 1-23.
57. Harten, A., and Chakravarthy, S., "Multi-Dimensional ENO Schemes for General Geometries," ICASE, NASA Langley Research Center, ICASE Rept. 91-76, Hampton, VA, Sept. 1991.
58. Harten, A., Engquist, B., Osher, S., and Chakravarthy, S., "Uniformly High Order Accurate Essentially Non-Oscillatory Schemes III," Journal of Computational Physics, Vol. 71, 1987, pp. 231-303.
59. Hase, J. E., Anderson, D. A., and Parpia, I., "A Delaunay Triangulation Method and Euler Solver for Bodies in Relative Motion," Proceedings of the AIAA 10th Computational Fluid Dynamics Conference (Honolulu, HI), AIAA, Washington, DC, 1991, pp. 705-713.
60. Hasson, O., Morgan, K., and Peraire, J., "An Adaptive Implicit/Explicit Finite Element Scheme for Compressible High Speed Flows," AIAA Paper 89-0363, Jan. 1989.
61. Hassan, O., Morgan, K., and Peraire, J., "An Implicit Finite Element Method for High Speed Flows," AIAA Paper 90-0402, Jan. 1990.
62. Hawken, D. F., "Review of Some Adaptive Node-Movement Techniques in Finite-Element and Finite-Difference Solutions of Partial Differential Equations," Journal of Computational Physics, Vol. 95, 1991, pp. 254-302.
63. Holmes, D. G., and Connell, S. D., "Solution of the 2D NavierStokes Equations on Unstructured Adaptive Grids," AIAA Paper 89-1392, June 1989.
64. Hughes, T. J. R., "Recent Progress in the Development and Understanding of SUPG Methods with Special Reference to the Compressible Euler and Navier-Stokes Equations," International Journal for Numerical Methods in Fluids, Vol. 7, 1987, pp. 1261-1275.
65. Hughes, T. J. R., and Brooks, A., "A Multidimensional Upwind Scheme with No Crosswind Diffusion," Finite Element Methods for Convection Dominated Flows, edited by T. J. R. Hughes, American Society of Mechanical Engineers, New York, 1979.
66. Hughes, T. J. R., Franca, L. P., and Hulbert, G. M., "A New Finite Element Formulation for Computational Fluid Dynamics: VIII The Galerkin/Least-Squares Method for Adjective-Diffusion Systems," Computational Methods in Applied Mechanics and Engineering, Vol. 73, 1989, pp. 173-189.
67. Hughes, T. J. R., and Mallet, M., "A New Finite Element Formulation for CFD: IV A Discontinuity-Capturing Operator for Multi-Dimensional Adjective-Diffusive Systems," Computational Methods in Applied Mechanics and Engineering, Vol. 58, 1986, pp. 329-336.
68. Hummel, D., "On the Vortex Formulation over a Slender Wing at Large Angles of Incidence," AGARD CP-247, Paper 15, Feb. 1983.
69. Jarneson, A., "Solution of the Euler Equations by a Multigrid Method," Applied Mathematics and Computation, Vol. 13, 1983, pp. 327-356.
70. Jameson, A., "Time-Dependent Calculations Using Multigrid, with Applications to Unsteady Flows Past Airfoils and Wings," AIAA Paper 91-1596, July 1991.
71. Jameson, A., "Analysis and Design of Numerical Schemes for Gas Dynamics 1. Artificial Diffusion, Upwind Biasing, Limiters and Their Effect on Accuracy and Multigrid Convergence," International Journal of Computational Fluid Dynamics, Vol. 4, 1995, pp. 171-218.
72. Jameson, A., "Analysis and Design of Numerical Schemes for Gas Dynamics 2. Artificial Diffusion and Discrete Shock Structure," International Journal of Computational Fluid Dynamics (to be published).
73. Jameson, A., and Baker, T. J., "Improvements to the Aircraft Euler Method," AIAA Paper 87-0452, Jan. 1987.
74. Jameson, A., Baker, T. J., and Weatherill, N. P., "Calculationof Inviscid Transonic Flow over a Complete Aircraft," AIAA Paper 86-0103, Jan. 1986.
75. Jameson, A., and Mavriplis, D. J., "Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh," AIAA Journal, Vol.24, 1986, pp. 611-618.
76. Jameson, A., Schmidt, W., and Turkel, E., "Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes," AIAA Paper 81-1259, 1981.
77. Johan, Z., Hughes, T. J. R., Mathur, K. K., and Johnsson, S. L., "A Data Parallel Finite Element Method for Computational Fluid Dynamics on the Connection Machine System," Computational Methods in Applied Mechanics and Engineering, Vol. 99, 1992, pp. 113-124.
78. Johnson, C., Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge Univ. Press, New York, 1992.
79. Johnson, C., Nävert, U., and Pitkaranta, J., "Finite Element Methods for Linear Hyperbolic Problems," Computational Methods in Applied Mechanics and Engineering, Vol. 45, 1984, pp. 285-312.
80. Johnson, C., Szepessy, A., and Hansbo, P., "On the Convergence of Shock-Capturing Streamline-Diffusion Finite Element Methods for Hyperbolic Conservation Laws," Mathematics of Computation, Vol. 54, 1990, pp. 107-130.
81. Kallinderis, Y., "Algebraic Turbulence Modeling for Adative Unstructured Grids," AIAA Journal, Vol. 30, No. 3, 1992, pp. 631-639.
82. Kallinderis, Y., and Vijayan, P., "Adaptive Refinement-Coarsening Scheme for Three-Dimensional Unstructured Meshes," AIAA Journal, Vol. 31, No. 8, 1993, pp. 1440-1447.
83. Kallinderis, Y., and Ward, S., "Hybrid Prismatic/Tetrahedral Grid Generation of Complex Geometries," AIAA Paper 93-0669, Jan. 1993.
84. Kao, T. J., Su, T. Y, and Yu, N. J., "Navier-Stokes Calculations for Transport Wing-Body Configurations with Nacelles and Struts," AIAA Paper 93-2945, July 1993.
85. Kennon, S. R., Meyering, J. M., Berry, C. W., and Oden, J. T., "Geometry Based Delaunay Tetrahedralization and Mesh Movement Strategies for Multi-Body CFD," AIAA Paper 92-4575, Aug. 1992.
86. Kleb, W. L., Batina, J. T., and Williams, M. H., "Temporal Adaptive Euler/Navier-Stokes Algorithm Involving Unstructured Dynamic Meshes," AIAA Journal, Vol. 30, No. 8, 1992, pp. 1980-1985.
87. Knight, D. D., "A Fully Implicit Navier-Stokes Algorithm Using an Unstructured Grid and Flux-Difference Splitting," Applied and Numerical Mathematics: Transactions of IMACS, Vol. 16, No. 1/2, 1994, pp. 101-128.
88. Koobus, B., Lallemand, M. H., and Dervieux, A., "Unstructured Volume-Agglomeration MG: Solution of the Poisson Equation," INRIA Rept. 1946, June 1993.
89. LaBarre, R. E., "Computational Geometry Techniques for 2D and 3D Unstructured Mesh Generation with Application to the Solution of Divergence Form Partial Differential Equations," Ph.D. Thesis, Univ. of Connecticut, Storrs, CT, 1992.
90. Lallemand, M., Steve, H., and Dervieux, A., "Unstructured Multigridding by Volume Agglomeration: Current Status," Computers and Fluids, Vol. 21, 1992, pp. 397-433.
91. Lax, P., Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, 2nd ed., Vol. 11, SIAM Regional Series on Applied Mathematics, SIAM, Philadelphia, PA, 1973.
92. Lerat, A., and Sides, J., "Numerical Simulation of Unsteady Transonic Flows Using the Euler Equations in Integral Form," Israel Journal of Technology, Vol. 17, 1979, pp. 302-310.
93. Letniowski, F. W., "Three-Dimensional Delaunay Triangulations for Finite Element Approximations to a Second Order Diffusion Operator," SIAM Journal on Scientific and Statistical Computing, Vol. 13, 1992, pp. 765-770.
94. Leveque, R. J., Numerical Methods for Conservation Laws, Birhäuser, Germany, 1992.
95. Liou, M.-S., and Steffan, C. J., "A New Flux Splitting Scheme," Journal of Computational Physics, Vol. 107, 1993, pp. 23-39.
96. Löhner, R., "An Adaptive Finite Element Solver for Transient Problems with Moving Bodies," Computational Structures, Vol. 30, 1988, pp. 303-317.
97. Löhner, R., and Baum, J. D., "Adaptive H-Refinement on 3-D Unstructured Grids for Transient Problems," International Journal for Numerical Mathods in Fluids, Vol. 14, 1992, pp. 1407-1419.
98. Löhner, R., Morgan, K., Peraire, J., and Vahdati, M., "Finite Element Flux-Corrected Transport (FCT) for the Euler and Navier-Stokes Equations," Computational Methods in Applied Mechanics and Engineering, Vol.7, 1987, pp. 1093-1109.
99. Löhner, R., Morgan, K., and Zienkiewicz, O., "An Adaptive Finite Element Procedure for Compressible High Speed Flows, Computational Methods in Applied Mechanics and Engineering, Vol. 51, 1985, pp. 441-465.
100. Luo, H., Baum, J. D., and Löhner, R., "Edge-Based Finite Element Scheme for the Euler Equations," AIAA Journal, Vol. 32, No. 6, 1994, pp. 1183-1190.
101. Luo, H., Baum, J. D., Löhner, R., and Cabello, J., "Adaptive EdgeBased Finite Element Schemes for the Euler and Navier-Stokes Equations on Unstructured Grids," AIAA Paper 93-0336, Jan. 1993.
102. Luo, H., Baum, J. D., Löhner, R., and Cabello, J., "Implicit Schemes and Boundary Conditions for Compressible Flows on Unstructured Meshes," AIAA Paper 94-0816, Jan. 1994.
103. Marcum, D. L., and Agarwal, R. K., "Finite Element Navier-Stokes Solver for Unstructured Grids," AIAA Journal, Vol. 30, No. 3, 1992, pp. 648-654.
104. Mavriplis, D. J., "Three-Dimensional Multigrid Reynolds-Averaged Navier-Stokes Solver for Unstructured Meshes," AIAA Journal, Vol. 33, No. 3, 1995, pp. 445-453.
105. Mavriplis, D. J., "Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes," AIAA Journal, Vol. 28, No. 2, 1990, pp. 213-221.
106. Mavriplis, D. J., "Adaptive Mesh Generation for Viscous Flows Using Delaunay Triangulation," Journal of Computational Physics, Vol. 90, 1990, pp. 271-291.
107. Mavriplis, D. J., "Algebraic Turbulence Modeling for Unstructured and Adaptive Meshes," AIAA Journal, Vol. 29, No. 12, 1991, pp. 2086-2093.
108. Mavriplis, D. J., "Three-Dimensional Multigrid for the Euler Equations," AIAA Journal, Vol. 30, 1992, pp. 1753-1761.
109. Mavriplis, D. J., "Mesh Generation and Adaptivity for Complex Geometries," Handbook of Computational Fluid Mechanics, Academic, San Diego, CA, 1995.
110. Mavriplis, D. J., Das, R., Saltz, J., and Vermeland, R. E., "Implementation of a Parallel Unstructured Euler Solver on Shared and Distributed Memory Machines," Journal of Supercomputing, Vol. 8, No. 4, 1994, pp. 329-344.
111. Mavriplis, D. J., and Venkatakrishnan, V., "A 3D Agglomeration Multigrid Solver for the Reynolds-Averaged Navier-Stokes Equations on Unstructured Meshes," AIAA Paper 95-0345, Jan. 1995.
112. Mavriplis, D. J., and Venkatakrishnan, V., "Agglomeration Multigrid for Two-Dimensional Viscous Flows," Computers and Fluids, Vol. 24, 1995, pp. 553-570.
113. Meakin, R. L., "Moving Body Overset Grid Methods for Complete Aircraft Tiltrotor Simulations," Proceedings of the AIAA 11th Computational Fluid Dynamics Conference (Orlando, FL), AIAA, Washington, DC, 1993, pp. 576-588.
114. Meijerink, J. A., and van der Vorst, H. D., "Guidelines for the Usage of Incomplete Decompositions in Solving Sets of Linear Equations as They Occur in Practical Problems," Journal of Computational Physics, Vol. 44, 1981, pp. 134-155.
115. Melson, N. D., Sanetrik, M. D., and Atkins, H. L., "Time-Accurate Navier-Stokes Calculations with Multigrid Acceleration," 6th Copper Mountain Conference on Multigrid Methods, 1993, pp. 423-439.
116. Melton, J. E., Pandya, S. A., and Steger, J. L., "3D Euler Flow Solutions Using Unstructured Cartesian and Prismatic Grids," AIAA Paper 93-0331, Jan. 1993.
117. Miller, G. L., Teng, S.-H., Thurston, W., and Vavasis, S.A., "Automatic Mesh Partitioning," Graph Theory and Sparse Matrix Computation, edited by A. George, J. R. Gilbert, and J. W. H. Liu, IMA Volumes in Mathematics and Its Applications, Vol. 56, Springer-Verlag, 1993, pp. 57-84.
118. Mitchell, C. R., "Improved Reconstruction Schemes for the NavierStokes Equations on Unstructured Meshes," AIAA Paper 94-0642, Jan. 1994.
119. Mohammadi, B., "Complex Turbulent Compressible Flow Computation Using a Two-Layer Approach," International Journal for Numerical Methods in Fluids, Vol. 15, 1992, pp. 747-771.
120. Nakahashi, K., "A Finite-Element Method on Prismatic Elements for the Three-Dimensional Navier-Stokes Equations," Lecture Notes in Physics, Vol. 323, Springer-Verlag, 1989.
121. Nakahashi, K., and Egami, K., "An Automatic Euler Solver Using the Unstructured Upwind Method," Computers and Fluids, Vol. 19, 1991, pp. 273-286.
122. Ni, R. H., "A Multiple-Grid Scheme for Solving the Euler Equations," AIAA Journal, Vol. 20, No. 11, 1982, pp. 1565-1571.
123. Osher, S., "Riemann Solvers, the Entropy Condition and Difference Approximations," SIAM Journal on Numerical Analysis, Vol. 21, 1984, pp. 217-235.
124. Paillere, H., Deconinck, H., Struijs, R., Roe, P. L., Mesaros, L. M., and Muller, J. D., "Computations of Compressible Flows Using Fluctuation-Splitting on Triangular Meshes," Proceedings of the AIAA 11th Computational Fluid Dynamics Conference (Orlando, FL), AIAA, Washington, DC, 1993, pp. 36-50.
125. Palmerio, B., "An Attraction-Repulsion Mesh Adaption Model for Flow Solution on Unstructured Grids," Computers and Fluids, Vol. 23, 1994, pp. 487-506.
126. Paraschivoiu, M., Trepanier, J. Y., Reggio, M., and Camarero, R., "A Conservative Dynamic Discontinuity Tracking Algorithm for the Euler Equations," AIAA Paper 94-0081, Jan. 1994.
127. Parikh, P., Löhner, R., Gumbert, C., and Pirzadeh, S., "Numerical Solutions on a PATHFINDER and Other Configurations Using Unstructured Grids and a Finite Element Solver," AIAA Paper 89-0362, Jan. 1989.
128. Parpia, I., and Michalak, D. J., "Grid-Independent Upwind Scheme for Multidimensional Flows," AIAA Journal, Vol. 31, No. 4, 1993, pp. 646-651.
129. Parpia, I., and Parikh, P., "A Solution-Adaptive Mesh Generation Method with Cell-Face Orientation Control," AIAA Paper 94-0416, Jan. 1994.
130. Parthasarathy, V., and Kallinderis, Y., "New Multigrid Approach for Three-Dimensional Unstructured, Adaptive Grids," AIAA Journal, Vol. 32, No. 5, 1994, pp. 956-963.
131. Parthasarathy, V., Kallinderis, Y., and Nakajima, K., "Hybrid Adaptation Method and Directional Viscous Multigrid with Prismatic-Tetrahedral Meshes," AIAA Paper 95-0670, 1995.
132. Peraire, J., Peirö, J., and Morgan, K., "A 3d Finite-Element Multigrid Solver for the Euler Equations," AIAA Paper 92-0449, Jan. 1992.
133. Peraire, J., Peirö, J., and Morgan, K., "Adaptive Remeshing for Three-Dimensional Compressible Flow Computations," Journal of Computational Physics, Vol. 103, 1992, pp. 269-285.
134. Perez, E., "A 3d Finite-Element Multigrid Solver for the Euler Equations," INRIA Rept. 442, Sept. 1985.
135. Pirzadeh, S., "Three-Dimensional Unstructured Viscous Grids by the Advancing-Layers Method," AIAA Journal, Vol. 34, No. 1, 1996, pp. 43-49.
136. Pothen, A., Simon, H. D., and Liou, K. P., "Partitioning Sparse Matrices with Eigenvectors of Graphs," SIAM Journal on Matrix Analysis and Applications, Vol. 11, 1990, pp. 430-452.
137. Potsdam, M., Intemann, G., Frink, N. T., Campbell, R., Smith, L., and Pirzadeh, S., "Wing Pylon Fillet Design Using Unstructured Mesh Euler Solvers," AIAA Paper 93-3500, Aug. 1993.
138. Powell, K. G., Roe, P. L., and Quirk, J. J., "Adaptive-Mesh Algorithms for Computational Fluid Dynamics," Algorithmic Trends in Computational Fluid Dynamics, edited by M. Y. Hussaini, A. Kumar, and M. D. Salas, Springer-Verlag, New York, 1992, pp. 301-337.
139. Pulliam, T. H., "Time Accuracy and the Use of Implicit Schemes," Proceedings of the AIAA 11th Computational Fluid Dynamics Conference (Orlando, FL), AIAA, Washington, DC, 1993, pp. 685-701.
140. Quirk, J. J., "A Cartesian Approach with Hierarchical Refinement for Compressible Flows," Computational Fluid Dynamics, edited by S. Wagner, J. Periaux, and E. M. Hirshel, Wiley, New York, 1994, pp. 200-209.
141. Quirk, J. J., "Parallel Adaptive Grid Algorithm for Computational Shock Hydrodynamics," Applied Numerical Mathematics (to be published).
142. Rai, M. M., "Navier-Stokes Simulations of Blade-Vortex Interaction Using High-Order Accurate Upwind Schemes," AIAA Paper 87-0543, Jan. 1987.
143. Ramamurthi, R., Sandberg, W., and Löhner, R., "Evaluation of a Scalable 3-D Finite Element Incompressible Flow Solver," AIAA Paper 94-0756, Jan. 1994.
144. Rausch, R. D., Batina, J. T., and Yang, H. T. Y., "Spatial Adaptation of Unstructured Meshes for Unsteady Aerodynamic Flow Computations," AIAA Journal, Vol. 30, No. 5, 1992, pp. 1243-1251.
145. Roe, P. L., "Approximate Riemann Solvers, Parameter Vectors and Difference Schemes," Journal of Computational Physics, Vol. 43, 1981, pp. 357-372.
146. Roe, P. L., "Characteristic-Based Schemes for the Euler Equations," Annual Review of Fluid Mechanics, Vol. 18, 1986, pp. 337-365.
147. Roe, P. L., "Discrete Models for the Numerical Analysis of Time-Dependent Multidimensional Gas Dynamics," Journal of Computational Physics, Vol. 63, 1986, pp. 458-476.
148. Roe, P. L., "Finite-Volume Methods for the Compressible NavierStokes Equations," Numerical Methods for Laminar and Turbulent Flows, Pt. 2, edited by C. Taylor, W. G. Habashi, and M. M. Hafez, Pineridge, Montreal, PQ, Canada, 1987.
149. Roe, P. L., "Beyond the Riemann Problem, Part I," Algorithmic Trends in Computational Fluid Dynamics, edited by M. Y. Hussaini, A. Kumar, and M. D. Salas, Springer-Verlag, New York, 1992, pp. 341-367.
150. Rostand, P., and Stoufflet, B., "TVD Schemes to Compute Compressible Viscous Flows on Unstructured Meshes," Notes on Numerical Fluid Mechanics, Vol. 24, Vieweg Press, Brunswick, Germany, 1988.
151. Rumsey, C. L., van Leer, B., and Roe, P. L., "A Multidimensional Flux Function with Applications to the Euler and Navier-Stokes Equations," Journal of Computational Physics, Vol. 105, 1993, pp. 306-323.
152. Saad, Y., and Schultz, M. H., "GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems," SIAM Journal on Scientific and Statistical Computing, Vol. 7, 1986, pp. 856-869.
153. Selmin, V., "The Node-Centered Finite Volume Approach: Bridge Between Finite Differences and Finite Elements," Computational Methods in Applied Mechanics and Engineering, Vol. 102, 1993, pp. 107-138.
154. Shakib, F., Hughes, T. J. R., and Johan, Z., "A Multi-Element Group Preconditioned GMRES Algorithm for Nonsymmetric Problems Arising in Finite Element Analysis," Computational Methods in Applied Mechanics and Engineering, Vol. 87, 1989, pp. 415-456.
155. Shapiro, R. A., and Murman, E. M., "Higher-Order and 3-d Finite Element Methods for the Euler Equations," AIAA Paper 89-0655, Jan. 1989.
156. Shu, C., "TVB Uniformly High-Order Schemes for Conservation Laws," Mathematics of Computation, Vol. 49, 1987, pp. 105-121.
157. Sidilkover, D., "A Genuinely Multidimensional Upwind Scheme and Efficient Multigrid Solver for the Compressible Euler Equations," ICASE, NASA Langley Research Center, ICASE Rept. 94-84, Hampton, VA, Oct. 1994.
158. Sidilkover, D., and Roe, P. L., "Unification of Some Advection Schemes in Two Dimensions," ICASE, NASA Langley Research Center, ICASE Rept. 95-10, Hampton, VA, Feb. 1995.
159. Simon, H. D., "Partitioning of Unstructured Problems for Parallel Processing," Computing Systems in Engineering, Vol. 2, 1991, pp. 135-148.
160. Slack, D. C., Whitaker, D. L., and Walters, R. W., "Time Integration Algorithms for the Two-Dimensional Euler Equations on Unstructured Meshes," AIAA Journal, Vol. 32, No. 6, 1994, pp. 1158-1166.
161. Smith, W. A., "Multigrid Solution of Transonic Flow on Unstructured Grids," Recent Advances and Applications in Computational Fluid Dynamics, Proceedings of the ASME Winter Annual Meeting, edited by O. Baysal, Nov. 1990.
162. Spalart, S. R., and Allmaras, S. A., "A One-Equation Turbulence Model for Aerodynamic Flows, La Recherche Aérospatiale, 1994, pp. 5-21; see also AIAA Paper 92-0439, 1992.
163. Spekreijse, S. P., "Multigrid Discretization of Monotone Second-Order Discretizations of Hyperbolic Conservation Laws," Mathematics of Computation, Vol. 45, 1987, pp. 135-155.
164. Steger, J. L., "Implicit Finite-Difference Simulation of Flow About Arbitrary Two-Dimensional Geometries," AIAA Journal, Vol. 17, No. 7, 1978, pp. 679-686.
165. Tatsumi, S., Martinelli, L., and Jameson, A., "Flux-Limited Schemes for the Compressible Navier-Stokes Equations," AIAA Journal, Vol. 33, No. 2, 1995, pp. 252-261.
166. Thareja, R. R., Stewart, J. R., Hassan, O., Morgan, K., and Peraire, J., "A Point Implicit Unstructured Grid Solver for the Euler and Navier-Stokes Equations," AIAA Paper 88-0036, Jan. 1988.
167. Thomas, J. L., Taylor, S. L., and Anderson, W. K., "Navier-Stokes Computations of Vortical Flows Over Low Aspect Ratio Wings," AIAA Paper 87-0207, Jan. 1987.
168. Thomas, P. D., and Lombard, C. K., "Geometric Conservation Law and Its Applications to Flow Computations on Moving Grids," AIAA Journal, Vol. 17, No. 10, 1979, pp. 1030-1037.
169. Thompson, J. F., and Weatherill, N. P., "Aspects of Numerical Grid Generation: Current Science and Art," AIAA Paper 93-3539,1993.
170. Trepanier, J. Y., Zhang, H., Reggio, M., and Camarero, R., "Adaptive and Moving Meshes for the Computation of Unsteady Compressible Flows," Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, edited by A. S. Arcilla, J. Hauser, P. R. Eiseman, and J. F. Thompson, North-Holland, New York, 1991, pp. 43-54.
171. Valerzo, W. O., and Mavriplis, D. J., "Navier-Stokes Applications to High-Lift Airfoil Analysis," Journal of Aircraft, Vol. 32, No. 3, 1995, pp. 618-624.
172. Van Leer, B., "Towards the Ultimate Conservative Difference Scheme V. A Second Order Sequel to Godunov's Method," Journal of Computational Physics, Vol. 32, 1979, pp. 101-136.
173. Van Leer, B., Tai, C. H., and Powell, K. G., "Design of Optimally-Smoothing Multi-Stage Schemes for the Euler Equations," AIAA Paper 89-1933, June 1989.
174. Van Rosendale, J., "Floating Shock Fitting vis Lagrangian Adaptive Meshes," AIAA Paper 95-1721, June 1995.
175. Vassberg, J. C., "A Fast, Implicit Unstructured-Mesh Euler Method," AIAA Paper 92-2693, 1992.
176. Vatsa, V. N., Sanetrik, M. D., and Parlette, E. B., "Development of a Flexible and Efficient Multigrid-Based Multi-Block Flow Solver," AIAA Paper 93-0677, 1993.
177. Venkatakrishnan, V., "Parallel Implicit Unstructured Grid Euler Solvers," AIAA Journal, Vol. 32, No. 10, 1994, pp. 1985-1991.
178. Venkatakrishnan, V., "Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters," Journal of Computational Physics, Vol. 118, 1995, pp. 120-130.
179. Venkatakrishnan, V., and Barth, T. J., "Application of Direct Solvers to Unstructured Meshes for the Euler and Navier-Stokes Equations Using Upwind Schemes," AIAA Paper 89-0364, Jan. 1989.
180. Venkatakrishnan, V., and Mavriplis, D. J., "Implicit Solvers for Unstructured Meshes," Journal of Computational Physics, Vol. 105, 1993, pp. 83-91.
181. Venkatakrishnan, V., and Mavriplis, D. J., "Agglomeration Multigrid for the Three-Dimensional Euler Equations," AIAA Journal, Vol. 33, No. 4, 1995, pp. 633-640.
182. Venkatakrishnan, V., and Mavriplis, D. J., "Implicit Method for the Computation of Unsteady Flows on Unstructured Grids," Proceedings of the AIAA 12th Computational Fluid Dynamics Conference (San Diego, CA), AIAA, Washington, DC, 1995, pp. 675-686.
183. Venkatakrishnan, V., Simon, H. D., and Barth, T. J., "A MIMD Implementation of a Parallel Euler Solver for Unstructured Grids," Journal of Supercomputing, Vol. 6, 1992, pp. 117-137.
184. Vilsmeier R., and Hänel, D., "Adaptive Methods on Unstructured Grids for Euler and Navier-Stokes Equations," Computers and Fluids, Vol. 22, 1993, pp. 485-499.
185. Warren, G. P., Anderson, W. K., Thomas, J. L., and Krist, S. L., "Grid Convergence for Adaptive Methods," Proceedings of the AIAA 10th Computational Fluid Dynamics Conference (Honolulu, HI), AIAA, Washington, DC, 1991, pp. 729-741.
186. Watson, D. F., "Computing the n-Dimensional Delaunay Tessellation with Application to Voronoi Polytopes," Computer Journal, Vol. 24, 1981, pp. 167-172.
187. Whitaker, D. L., "Three-Dimensional Unstructured Grid Euler Computations Using a Fully-Implicit, Upwind Method," Proceedings of the AIAA 11th Computational Fluid Dynamics Conference (Orlando, FL), AIAA, Washington, DC, 1993, pp. 448-461.
188. Whitaker, D. L., Grossman, B., and Löhner, R., "Two-Dimensional Euler Computations on a Triangular Mesh Using an Upwind Finite-Volume Scheme," AIAA Paper 89-0470, Jan. 1989.
189. Zhang, H., Reggio, M., Trepanier, J. Y., and Camarero, R., "Discrete Form of the GCL for Moving Meshes and Its Implementation in CFD Schemes," Computers and Fluids, Vol. 22, 1993, pp. 9-23.