Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes

13th Computational Fluid Dynamics Conference

Volumn , Issue , 1997, Pages 659-675

  Mavriplis, D J ^a  

^a NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; COARSENING; COMPUTATIONAL FLUID DYNAMICS; FLUID DYNAMICS; MACH NUMBER; MESH GENERATION; REYNOLDS NUMBER; TWO PHASE FLOW; VISCOUS FLOW;

ALTERNATE APPROACHES; DIRECTIONAL COARSENING; HIGH REYNOLDS NUMBER; LOW MACH NUMBER PRECONDITIONING; MULTI-GRID ALGORITHMS; MULTIGRID TECHNIQUE; SPEED OF CONVERGENCE; UNSTRUCTURED MESHES;

FLOW SIMULATION;

EID: 84983180727     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (45)

1. W. A. Mulder. A high resolution Euler solver based on multigrid semi-coarsening and defect correction. Journal of Computational Physics, 100: 91-104, 1992.
2. W. K. Anderson, R. Rausch and D. Bonhaus. Implicit multigrid algorithms for incompressible turbulent flows on unstructured grids. In Proceedings of the 12th AIAA CFD Conference, San Diego CA, June 1995. AIAA Paper 95-1740-CP.
3. D. Sidilkover. A genuinely multidimensional upwind scheme and efficient multigrid solver for the compressible Euler equations. ICASE Report 94-84, October 1994.
4. D. J. Mavriplis. Three-dimensional multigrid for the Euler equations. AIAA Journal, 30(7): 1753-1761, July 1992.
5. C. Ollivier-Gooch. Towards problem-independent multigrid cnvergence rates for unstructured mesh methods i: Inviscid and laminar flows. In Proceedings of the 6th International Symposium on CFD, Lake Tahoe, NV, September 1995.
6. N. Pierce and M. Giles. Preconditioning on stretched meshes. AIAA paper 96-0889, January 1996.
7. A. Brandt. Multigrid techniques with applications to fluid dynamics: 1984 guide. In VKI Lecture Series, pages 1-176, March 1984.
8. W. A. Mulder. A new multigrid approach to convection problems. Journal of Computational Physics, 83(2): 303-323, August 1989.
9. R. Radespiel and R. C. Swanson. Progress with multigrid schemes for hypersonic flow problems. Journal of Computational Physics, 116: 103-122, 1995.
10. S. R. Allmaras. Analysis of semi-implicit preconditioners for multigrid solution of the 2d compressible navier-stokes equations. In Proceedings of the 12th AIAA CFD Conference, San Diego CA, June 1995. AIAA Paper 95-1651-CP.
11. J. W. Ruge and K. Stiiben. Algebraic multigrid. In S. F. McCormick, editor, Multigrid Methods, SIAM Frontiers in Applied Mathematics, pages 73-131, Philadelphia, 1987. SIAM.
12. E. Morano, D. J. Mavriplis and V. Venkatakrishnan. Coarsening strategies for unstructured multigrid techniques with application to anisotropic problems. In 7th Copper Mountain Conf. on Multigrid Methods, pages 591-606, April 1995. NASA Conference Publication 3339.
13. J. Francescatto. Resolution de 1’equation de Poisson sur des maillages etires par une method multigrille. INRIA Report No. 2712, November 1995.
14. M. Raw. Robustness of coupled algebraic multigrid for the Navier-Stokes equations. AIAA paper 96-0297, January 1996.
15. D. J. Mavriplis and V. Venkatakrishnan. A unified multigrid solver for the Navier-Stokes equations on mixed element meshes. AIAA Paper 95-1666, June 1995.
16. T. J. Earth and S. W. Linton. An unstructured mesh newton solver for compressible fluid flow and its parallel implementation. AIAA paper 95-0221, January 1995.
17. P. L. Roe. Approximate Riemann solvers, parameter vectors and difference schemes. J. Comp. Phys., 43(2): 357-372, 1981.
18. V. Venkatakrishnan. On the accuracy of limiters and convergence to steady state solutions. J. Comp. Phys., 118: 120-130, 1995.
19. A. Jameson, W. Schmidt, and E. Turkel. Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes. AIAA Paper 81-1259, 1981.
20. B. van Leer, C. H. Tai, and K. G. Powell. Design of optimally-smoothing multi-stage schemes for the Euler equations. AIAA Paper 89-1933, June 1989.
21. K. Riemslagh and E. Dick. A multigrid method for steady Euler equations on unstructured adaptive grids. In 6th Copper Mountain Conf. on Multigrid Methods, NASA conference publication 3224, pages 527-542, 1993.
22. E. Morano and A. Dervieux. Looking for O(N) Navier-Stokes solutions on non-structured meshes. In 6th Copper Mountain Conf. on Multigrid Methods, pages 449-464, 1993. NASA Conference Publication 3224.
23. B. van Leer, W. T. Lee and P. Roe. Characteristic time-stepping or local preconditioning of the Euler equations. In Proceedings of the 10th AIAA CFD Conference, Honolulu, Hawaii, pages 260-282, June 1991. AIAA Paper 91-1552-CP.
24. P. R. Spalart and S. R. Allmaras. A one-equation turbulence model for aerodynamic flows. La Recherche Aerospatiale, 1: 5-21, 1994.
25. 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.
26. M. Lallemand, H. Steve, and A. Dervieux. Unstructured multigridding by volume agglomeration: Current status. Computers and Fluids, 21(3): 397-433, 1992.
27. D. J. Mavriplis and V. Venkatakrishnan. Agglomeration multigrid for two dimensional viscous flows. Computers and Fluids, 24(5): 553-570, May 1995.
28. D. J. Mavriplis. An advancing-front Delaunay triangulation algorithm designed for robustness. AIAA paper 93-0671, January 1993.
29. D. J. Mavriplis. Unstructured mesh generation and adaptivity. In 26th VKI Lecture Series on Computational Fluid Dynamics, Lecture Series 1995-02, March 1995.
30. O. Hassan, K. Morgan, and J. Peraire. An adaptive implicit/explicit finite element scheme for compressible high speed flows. AIAA Paper 89-0363, January 1989.
31. D. Martin and Lohner. An implicit linelet-based solver for incompressible flows. AIAA Paper 92-0668, January 1992.
32. L. Martinelli and A. Jameson. Validation of a multigrid method for the Reynolds-averaged Navier-Stokes Equations. AIAA Paper 88-0414, January 1988.
33. R. Radespiel and R. C. Swanson. An investigation of cell-centered and cell-vertex multigrid schemes for the Navier-Stokes equations. AIAA paper 89-053, January 1989.
34. E. Turkel. Preconditioning methods for solving the incompressible and low speed compressible equations. J. Comp. Phys., 72: 277-298, 1987.
35. Y. Choi and C. Merkle. The application of preconditioning to viscous flows. J. Comp. Phys., 105, 1993.
36. J. M. Weiss and W. A Smith. Preconditioning appb’ed to variable and constant density timeaccurate flows on unstructured meshes. AIAA Paper 94-2209, June 1994.
37. J. F. Lynn and B. van Leer. A semi-coarsened multigrid solver for the euler and navier-stokes equations with local preconditioning. In Proceedings of the 12th AIAA CFD Conference, San Diego, CA, pages 242-252, June 1995. AIAA Paper 95-1667-CP.
38. E. Turkel, V. N. Vatsa and R. Radespiel. Preconditioning methods for low speed flow. AIAA Paper 96-2460, 1996.
39. D. Jespersen, T. Pulliam and P. Buning. Recent enhancements to OVERFLOW. AIAA Paper 97-0644, January 1997.
40. Y. Saad and M. H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Cornput., 7(3): 856-869, 1986.
41. L. B. Wigton, N. J. Yu and D. P. Young. GMRES acceleration of computational fluid dynamic codes. In Proceedings of the 7th AIAA CFD Conference, pages 67-74, July 1985. AIAA Paper 85-1494-CP.
42. D. J. Mavriplis and V. Venkatakrishnan. A 3D agglomeration multigrid solver for the Reynoldsaveraged Navier-Stokes equations on unstructured meshes. International Journal for Numerical Methods in Fluids, 23(6): 527-544, 1996.
43. G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. Technical Report Technical Report 95-035, University of Minnesota, 1995. A short version appears in Intl. Conf. on Parallel Processing 1995.
44. B. van Leer, E. Turkel, C. H. Tai and L. Mesaros. Local preconditioning in a stagnation point. In Proceedings of the 12th AIAA CFD Conference, San Diego, CA, pages 88-101, June 1995. AIAA Paper 95-1654-CP.
45. D. L. Darmofal and P. J. Schmid. The importance of eigenvectors for local preconditioners of the euler equations. In Proceedings of the 12th AIAA CFD Conference, San Diego, CA, pages 102-117, June 1995. AIAA Paper 95-1655-CP.