Unstructured mesh discretizations and solvers for computational aerodynamics

Collection of Technical Papers - 18th AIAA Computational Fluid Dynamics Conference

Volumn 1, Issue , 2007, Pages 499-526

  Mavriplis, Dimitri J ^a,b  

^a UNIVERSITY OF WYOMING   (United States)

^b AIAA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL AERODYNAMICS; OVERSET MESH METHODS; TRANSONIC FLOW CALCULATIONS; UNSTRUCTURED MESH TECHNOLOGY;

COMPUTATIONAL FLUID DYNAMICS; FLOW MEASUREMENT; PROBLEM SOLVING; VISCOUS FLOW;

AERODYNAMICS;

EID: 35748978541     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (94)

1. O. C. Zienkiewicz and R. L. Taylor. The Finite-Element Method for Solid and Structural Mechanics; 6th Edition. John Wiley and Sons, New York, NY, 2005.
2. M. O. Bristeau, O. Pironneau, R. Glowinski, J. Periaux, P. Perrier, and G. Poirier. On the numerical solution of non-linear problems in fluid dynamics by least squares and finite-element methods (II), applications to transonic flow simulations. Comput. Methods Appl. Mech. Engrg, 51:363-394, 1985.
3. A. Jameson and D. J. Mavriplis. Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh. AIAA J., 24(4):611-618, 1986.
4. A. Jameson, T. J. Baker, and N. P. Weatherill. Calculation of inviscid transonic flow over a complete aircraft. AIAA Paper 86-0103, January 1986.
5. J. A. Desideri and A. Dervieux. Compressible flow solvers using unstructured grids. VKI Lecture Series, 1988-05:1-115, 1988.
6. T. J. Barth and D. C. Jespersen. The design and application of upwind schemes on unstructured meshes. AIAA Paper 89-0366, January 1989.
7. D. J. Mavriplis. Solution of the Two-Dimensional Euler Equations on Unstructured Triangular Meshes. PhD thesis, Princeton University, MAE Department, 1987.
8. D. J. Mavriplis. Three-dimensional multigrid for the Euler equations. AIAA Journal, 30(7):1753-1761, July 1992.
9. J. Peraire, J. Peirö, and K. Morgan. A 3D finite-element multigrid solver for the Euler equations. AIAA Paper 92-0449, January 1992.
10. W. K. Anderson. A grid generation and flow solution method for the Euler equations on unstructured grids. Journal of Computational Physics, 110(1):23-38, January 1994.
11. T. Gerhold, M. Galle, O. Friedrich, and J. Evans. Calculation of complex three-dimensional configurations employing the DLR-Tau code. AIAA Paper 97-0167, January 1997.
12. D. J. Mavriplis. Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes. AIAA J., 28(2):213-221, 1990.
13. D. J. Mavriplis. Adaptive mesh generation for viscous flows using Delaunay triangulation. J. Comp. Phys., 90(2):271-291, 1990.
14. S. D. Connell and D. G. Holmes. A 3D unstructured adaptive multigrid scheme for the Euler equations. AIAA J., 32(8):1626-1632, 1994.
15. R. Löhner and J. D. Baum. Adaptive H-refinement on 3-D unstructured grids for transient problems. Int. J. Num. Meth. Fluids, 14:1407-1419, 1992.
16. Y. Kallinderis and P. Vijayan. Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes. AIAA J., 31(8):1440-1447, 1993.
17. J. Y. Trepanier, H. Zhang, M. Reggio, and R. Camarero. Adaptive and moving meshes for the computation of unsteady compressible flows. In A. S. Arcilla, J. Hauser, P. R. Eiseman, and J. F. Thompson, editors, Numerical grid generation in Computational Fluid dynamics and related fields, pages 43-54, New York, 1991. North-Holland.
18. G. P. Warren, W. K. Anderson, J. L. Thomas, and S. L. Krist. Grid convergence for adaptive methods. AIAA Paper 91-1592CP, July 1991.
19. W. K. Anderson. Private communication. 1994.
20. J. Peraire. Private communication. 1992.
21. D. J. Mavriplis. Aerodynamic drag prediction using unstructured mesh solvers. In CFD-Based Drag Prediction and Reduction, eds. H. Deconoinck, K. Sermus and C. van Dam, VKI Lecture Series 2003-02, von Karman Institute for Fluid Dynamics, Rhode St-Genese, Belgium, March 2003.
22. D. W. Levy and M. D. Thacker. Comparison of unstructured cell- and node-based schemes for the Euler equations. AIAA Paper 99-3185, June 1999.
23. D. W. Levy, T. Zickuhr, J. Vassberg, S. Agrawal, R. A. Wahls, S. Pirzadeh, and M. J. Hemsch. Summary of data from the first AIAA CFD drag prediction workshop. AIAA Paper 2002-0841, January 2002.
24. K. Laflin, O. Brodersen, M. Rakowitz, J. Vassberg, R. Wahls, and J. Morrison. Summary of data from the second AIAA CFD drag prediction workshop. AIAA Paper 2004-0555, January 2004.
25. J. C. Vassberg, E. N. Tinoco, M. Mani, O. P. Brodersen, B. Eisfeld, R. A. Wahls, J. H. Morrison, T. Zickuhr, K. R. Laflin, and D. J. Mavriplis. Summary of the third AIAA CFD drag prediction workshop. AIAA Paper 2007-0260, January 2007.
26. D. J. Mavriplis and D. W. Levy. Transonic drag prediction using an unstructured multigrid solver. AIAA Journal of Aircraft, 42(4):887-893, 2003.
27. S. Z. Pirzadeh and N. T. Frink. Assessment of the unstructured grid software TetrUSS for drag prediction of the DLR-F4 configuration. AIAA Paper 2002-0839, January 2002.
28. T. J. R. Hughes. Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations. Intl. J. for Numer. Meth. in Fluids, 7:1261-1275, 1987.
29. B. Cockburn, G. E. Karniadakis, and C. W. Shu. Discontinuous Galerkin Methods: Theory, Computation and Applications. Springer, 2000.
30. M. Aftosmis, D. Gaitonde, and T. S. Tavares. On the accuracy, stability and monotonicity of various reconstruction algorithms for unstructured meshes. AIAA Paper 94-0415, January 1994.
31. T. J. Barth. Parallel CFD algorithms on unstructured meshes. In Special Course on Parallel Computing in CFD, pages 7-1,7-41, May 1995. AGARD Report-807.
32. H. Luo, J. D. Baum, R. Löhner, and J. Cabello. Adaptive edge-based finite element schemes for the Euler and Navier-Stokes equations on unstructured grids. AIAA Paper 93-0336, January 1993.
33. D. Sidilkover. A genuinely multidimensional upwind scheme and efficient multigrid solver for the compressible Euler equations. ICASE Report 94-84, October 1994.
34. H. Deconinck, H. Paillere, R. Struijs, and P. L. Roe. Multidimensional upwind schemes based on fluctuation-splitting of conservation laws. Comp. Mechanics, 11(5/6):323-340, 1993.
35. K. Nakahashi. A finite-element method on prismatic elements for the three-dimensional Navier-Stokes equations. In Lecture Notes in Physics, volume 323. Springer Verlag, 1989.
36. Y. Kallinderis and S. Ward. Hybrid prismatic/tetrahedral grid generation for complex geometries. AIAA Paper 93-0669, January 1993.
37. S. Pirzadeh. Three-dimensional unstructured viscous grids by the advancing-layers method. AIAA Journal, 34(1):43-49, 1996.
38. D. J. Mavriplis. Unstructured mesh generation and adaptivity. In VKI Lecture Series VKI-LS 1995-02, March 1995.
39. M. Paraschivoiu, J. Y. Trepanier, M. Reggio, and R. Camarero. A conservative dynamic discontinuity tracking algorithm for the Euler equations. AIAA Paper 94-0081, January 1994.
40. J. van Rosendale. Floating shock fitting via lagrangian adaptive meshes. In Proceedings of the 12th AIAA CFD Conference, San Diego CA, June 1995. AIAA Paper 95-1721-CP.
41. A. Jameson. Analysis and design of numerical schemes for gas dynamics 1, artificial diffusion, upwind biasing, limiters and their effect on multigrid convergence. Int. J. of Comp. Fluid Dyn., 4:171-218, 1995.
42. T. J. Barth. Numerical aspects of computing viscous high Reynolds number flows on unstructured meshes. AIAA Paper 91-0721, January 1991.
43. W. K. Anderson and D. L. Bonhaus. An implicit upwind algorithm for computing turbulent flows on unstructured grids. Computers Fluids, 23(1):1-21, 1994.
44. A. Haselbacherand J. Blazek. Accurate and efficient discretization of NavierStokes equations on mixed grids. AIAA Journal, 38(11):2094-2102, 2000.
45. D. J. Mavriplis. Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes. AIAA-Paper 2003-3986, June 2003.
46. N. B. Petrovskaya. The impact of grid cell geometry on the least-squares gradient reconstruction. Technical Report No. 21, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, April 2003.
47. V. Venkatakrishnan. On the accuracy of limiters and convergence to steady state solutions. J. Comp. Phys., 118:120-130, 1995.
48. A Harten, P. D. Lax, and B Van Leer. On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25(1):35-61, 1983.
49. P. L. Roe. Approximate Riemann solvers, parameter vectors and difference schemes. J. Comp. Phys., 43(2):357-372, 1981.
50. A. Harten. High resolution schemes for hyperbolic conservation laws. J. Comp. Phys., 135(2):260-278, 1997.
51. W. K. Anderson. A grid generation and flow solution method for the Euler equations on unstructured grids. J. Comp. Phys., 110(1):23-38, 1994.
52. I. Babushka and A. K. Aziz. On the angle condition in the finite-element method. SIAM Journal of Numerical Analysis, 13(6), 1976.
53. A. Haselbacher, J. McGuirk, and G. Page. Finite-volume discretization aspects for viscous flows on unstructured meshes. AIAA Journal, 37(2):177-184, 1999.
54. R. Lohner, H. Luo, and J. D. Baum. Selective edge removal for unstructured grids with cartesian cores. Journal of Computational Physics, 206(1):208-226, 2005.
55. S. D. Connell and M. E. Braaten. Semi-structured mesh generation for three-dimensional Navier-Stokes calculations. AIAA J., 33(6):1017-1024, June 1995.
56. R. Lohner. Matching semi-structured and unstructured grids for Navier-Stokes calculations. AIAA paper 93-3348, July 1993.
57. D. J. Mavriplis. A three-dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes. AIAA Journal, 33(3):445-4531, March 1995.
58. K. Xu, C. A. Kim, L. Martinelli, and A. Jameson. BGK-based schemes for the simulation of compressible flow. Int. J. Computational Fluid Dynamics, 7:213-235, 1996.
59. G. May and A. Jameson. Improved gaskinetic multigrid method for three-dimensional computation of viscous flow. AIAA Paper 2005-5106, June 2005.
60. N. T. Frink. Upwind scheme for solving the Euler equations on unstructured tetrahedral meshes. AIAA J., 30(1):70-77, 1992.
61. V. Venkatakrishnan and T. J. Barth. Application of direct solvers to unstructured meshes for the Euler and Navier-Stokes equations using upwind schemes. AIAA Paper 89-0364, January 1989.
62. J. T. Batina. Implicit upwind solution algorithms for three-dimensional unstructured meshes. AIAA J., 31(5):801-805, May 1993.
63. R. R. Thareja, J. R. Stewart, O. Hassan, K. Morgan, and J. Peraire. A point implicit unstructured grid solver for the Euler and Navier-Stokes equations. AIAA Paper 88-0036, January 1988.
64. V. Venkatakrishnan and D. J. Mavriplis. Implicit method for the computation of unsteady flows on unstructured grids. In Proceedings of the 12th AIAA CFD Conference, San Diego CA, June 1995. AIAA Paper 95-1705-CP.
65. H. Guillard. Node nested multigrid with Delaunay coarsening. INRIA Report No. 1898, 1993.
66. M. E. Braaten and S. D. Connell. Three dimensional unstructured adaptive multigrid scheme for the Navier-Stokes equations. AIAA J., 34(2):281-290, February 1996.
67. B. R. Hutchinson, P. F. Galpin, and G. D. Raithby. Application of additive correction multigrid to the coupled fluid flow equations. Numerical Heat Transfer, 13:133-147, 1988.
68. W. A. Smith. Multigrid solution of transonic flow on unstructured grids. In Recent Advances and Applications in Computational Fluid Dynamics, November 1990. Proceedings of the ASME Winter Annual Meeting, Ed. O. Baysal.
69. M. Lallemand, H. Steve, and A. Dervieux. Unstructured multigridding by volume agglomeration: Current status. Computers and Fluids, 21(3)397-433, 1992.
70. V. Venkatakrishnan and D. J. Mavriplis. Agglomeration multigrid for the three-dimensional Euler equations. AIAA Journal, 33(4):633-640, April 1995.
71. D. J. Mavriplis and V. Venkatakrishnan. A unified multigrid solver for the Navier-Stokes equations on mixed element meshes. International Journal for Computational Fluid Dynamics, 8:247-263, 1997.
72. R. S. Tuminaro and C. Tong. Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines. Proceedings of the 2000 ACM/IEEE conference on Supercomputing, November 2000.
73. D. Martin and Löhner. An implicit linelet-based solver for incompressible flows. AIAA Paper 92-0668, January 1992.
74. D. J. Mavriplis. Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes. Journal of Computational Physics, 145(1):141-165, September 1998.
75. D. J. Mavriplis. Directional agglomeration multigrid techniques for high-Reynolds number viscous flow solvers. AIAA Journal, 37(10):1222-1230, October 1999.
76. E. J. Nielsen, J. Lu, M. A. Park, and D. L. Darmofal. An implicit exact dual adjoint solution method for turbulent flows on unstructured grids. Computers and Fluids, 33(9):1131-1155, November 2004.
77. I. Nompelis, T. Drayna, and G. Candler. A parallel unstructured implicit solver for hypersonic reacting flow simulation. AIAA Paper 2005-4867, June 2005.
78. S. Balay, K. Buschelman, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. Mclnnes, B. F. Smith, and H. Zhang. PETSc user's manual. ANL-95/11 -Revision 2.1.5,Argonne National Laboratory, 2004.
79. D. J. Mavriplis, M. Aftosmis, and M. Berger. High-resolution aerospace applications using the NASA Columbia supercomputer. Paper presented at the 2005 Supercomputing Conference, Seattle, WA. Tied for Best paper award at SC05., November 2005.
80. G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1):359-392, 1999.
81. D. J. Mavriplis. A CFD package for multi-element airfoil high-lift analysis. NSU2D User's Manual (Revision 4.0), December 1996.
82. P. R. Spalart and S. R. Allmaras. A one-equation turbulence model for aerodynamic flows. La Recherche Aérospatiale, 1:5-21, 1994.
83. F. M. White. Viscous Fluid Flow. McGraw-Hill, New York, NY, 1991.
84. W. K. Anderson, D. L. Bonhaus, R. J. McGhee, and B. S. Walker. Navier-Stokes computations and experimental comparisons for multielement airfoil configurations. AIAA J. of Aircraft, 32(6):1246-1253, 1995.
85. E. M. Lee-Rausch, P. B. Buning, D. J. Mavriplis, J. H. Morrison, M. A. Park, S. M. Rivers, and C. L. Rumsey. CFD sensitivity analysis of a drag prediction workshop wing/body transport configuration. AIAA Paper 2003-3400, June 2003.
86. E. M. Lee-Rausch, N. T. Frink, D. J. Mavriplis, R. D. Rausch, and W. E. Milholen. Transonic drag prediction on a DLR-F6 transport configuration using unstructured grid solvers. AIAA Paper 2004-0554, January 2004.
87. D. J. Mavriplis. Grid resolution study of a drag prediction workshop configuration using the NSU3D unstructured mesh solver. AIAA-Paper 2005-4729, June 2005.
88. S. Pirzadeh. Private communication. 2005.
89. E. M. Lee-Rausch, M. Park, E. Nielsen, W. Jones, and D. Hammond. Parallel adjoint-based error estimation and anisotropic grid adaptation for three-dimensional aerospace applications. AIAA Paper 2005-4842, June 2005.
90. P. Gnoffo and J. A. White. Computational aerothermodynamic simulation issues on unstructured grids. AIAA Paper 2004-2371, June 2004.
91. M. Aftosmis M. Berger and J. Melton. Robust and efficient cartesian mesh generation for component-based geometry. AIAA Paper 97-0196, January 1997.
92. S. Murman, M. Aftosmis, and M. Berger. Numerical simulation of rolling airframes using a multi-level cartesian method. AIAA Paper 2002-2798, June 2002.
93. S. Z. Tu and S. M. Ruffin. Solution adaptive, unstructured Cartesian-grid methodology for chemically reacting flow. AIAA Paper 2002-3097, June 2002.
94. K. Fidkowski and D. Darmofal. An adaptive simplex cut-cell method for discontinuous galerkin discretizations of the navier- stokes equations. AIAA Paper 2007-3941, June 2007.