Preconditioned multigrid methods for compressible flow calculations on stretched meshes

Journal of Computational Physics

Volumn 136, Issue 2, 1997, Pages 425-445

  Pierce, Niles A ^a   Giles, Michael B ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC THERMODYNAMICS; COARSENING; FOURIER SERIES; JACOBIAN MATRICES; NAVIER STOKES EQUATIONS; RUNGE KUTTA METHODS;

CELL STRETCHING; COMPUTATIONAL SAVINGS; FLOW CALCULATIONS; FOURIER; JACOBI MATRIX; MULTIGRID METHODS; MULTIGRIDS; PRECONDITIONERS; RUNGE KUTTA TIME STEPPING SCHEME; STRETCHED MESH;

BOUNDARY LAYERS;

EID: 0031572068     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5772     Document Type: Article

References (50)

1. Fedorenko R. P. The speed of convergence of one iterative process. Zh. Vychisl. Mat. Mat. Fiz. 4:1964;559.
2. Bakhvalov N. S. On the convergence of a relaxation method with natural constraints of the elliptic operator. Zh. Vychisl. Mat. Mat. Fiz. 6:1966;861.
3. 2. Math. Comp. 31:1977;892.
4. Brandt A. Multi-level adaptive solutions to boundary-value problems. Math. Comp. 31:1977;333.
5. Hackbusch W. On the multi-grid method applied to difference equations. Computing. 20:1978;291.
6. Ni R.-H. A multiple-grid scheme for solving the Euler equations. AIAA J. 20:1982;1565.
7. Jameson A. Solution of the Euler equations by a multigrid method. Appl. Math. Comput. 13:1983;327.
8. Jameson A. Multigrid algorithms for compressible flow calculations. Second European Conference on Multigrid Methods, Cologne, 1985. Lecture Notes in Mathematics. 1228:1986;Springer-Verlag, Berlin. p. 166-.
9. Jameson A., Schmidt W., Turkel E. Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes. AIAA Paper. 81-1259:1981.
10. van Leer B., Lee W.-T., Roe P. L., Tai C.-H. Design of optimally smoothing multi-stage schemes for the Euler equations. J. Appl. Numer. Math. 1991.
11. Li C. P. Numerical solution of the viscous reacting blunt body flows of a multicomponent mixture. AIAA Paper. 73-202:1973.
12. 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. Int. J. Comput. Fluid Dyn. 4:1995;171.
13. Liu F., Zheng X. A strongly coupled time-marching method for solving the Navier-Stokes andk. J. Comput. Phys. 128:1996;289.
14. N. A. Pierce, M. B. Giles, 1996, Preconditioning compressible flow calculations on stretched meshes, 34th Aerospace Sciences Meeting and Exhibit, Reno, NV, 1996.
15. Chorin A. J. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2:1967;12.
16. Turkel E. Fast solutions to the steady state compressible and incompressible fluid dynamics equations. Ninth Int. Conf. Num. Meth. Fluid Dyn. Lect. Notes in Physics. 218:1984;Springer-Verlag, New York/Berlin. p. 571-.
17. Viviand H. Pseudo-unsteady systems for steady inviscid flow calculations. Angrand F. Numerical Methods for the Euler Equations of Fluid Dynamics. 1985;334 SIAM, Philadelphia.
18. van Leer B., Lee W.-T., Roe P. L. Characteristic time-stepping or local preconditioning of the Euler equations. AIAA Paper. 91-1552-CP:1991.
19. Morano E., Lallemand M.-H., Leclercq M.-P., Steve H., Stoufflet B., Dervieux A. Local iterative upwind methods for steady compressible flows. Third European Conference on Multigrid Methods, Bonn, 1990. 1991;Springer-Verlag, Berlin. p. 227-.
20. Turkel E. Review of preconditioning methods for fluid dynamics. Apl. Num. Math. 12:1993;257.
21. S. Allmaras, 1993, Analysis of a local matrix preconditioner for the 2-D Navier-Stokes equations, 11th Computational Fluid Dynamics Conference, Orlando, FL, 1993.
22. N. A. Pierce, M. B. Giles, 1995, Preconditioning on stretched meshes, 12th AIAA CFD Conference, San Diego, CA, 1995.
23. Turkel E. Preconditioned methods for solving the incompressible and low speed compressible equations. J. Comput. Phys. 72:1987;277.
24. Choi Y.-H., Merkle C. L. The application of preconditioning in viscous flows. J. Comput. Phys. 105:1993;207.
25. Turkel E., Fiterman A., van Leer B. Preconditioning and the limit of the compressible to the incompressible flow equations for finite difference schemes. Caughey D. A., Hafez M. M. Frontiers of Computational Fluid Dynamics. 1994;215.
26. S. Allmaras, 1995, Analysis of semi-implicit preconditioners for multigrid solution of the 2-D compressible Navier-Stokes equations, 12th Computational Fluid Dynamics Conference, San Diego, CA, 1995.
27. Mulder W. A. A new multigrid approach to convection problems. J. Comput. Phys. 83:1989;303.
28. Buelow P. E. O., Venkateswaran S., Merkle C. L. Effect of grid aspect ratio on convergence. AIAA J. 32:1994;2401.
29. S. Venkataswaran, J. M. Weiss, C. L. Merkle, Y.-H. Choi, 1992, Propulsion-related flowfields using the preconditioned Navier-Stokes equation, AIAA Paper, 92-3437.
30. N. A. Pierce, M. B. Giles, A. Jameson, L. Martinelli, 1997, Accelerating three-dimensional Navier-Stokes calculations, AIAA Paper, 97-1953.
31. Jameson A. Aerodynamic design via control theory. J. Sci. Comput. 3:1988;233.
32. A. Jameson, N. A. Pierce, L. Martinelli, 1997, Optimum aerodynamic design using the Navier-Stokes equations, AIAA 35th Aerospace Sciences Meeting, Reno, NV, 1997.
33. A. Jameson, 1991, Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings, 10th Computational Fluid Dynamics Conference, Honolulu, HI, 1991.
34. N. A. Pierce, J. J. Alonso, 1997, A preconditioned implicit multigrid algorithm for parallel computation of unsteady aeroelastic compressible flows, 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, 1997.
35. N. A. Pierce, J. J. Alonso, Efficient computation of unsteady viscous flows by an implicit preconditioned multigrid method, AIAA J.
36. Roe P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
37. Swanson R. C., Turkel E. On central-difference and upwind schemes. J. Comput. Phys. 101:1991;292.
38. L. Martinelli, 1987, Calculations of Viscous Flows with a Multigrid Method, Princeton University.
39. N. A. Pierce, 1997, Preconditioned Multigrid Methods for Compressible Flow Calculations on Stretched Meshes, Oxford University.
40. J. A. Benek, P. G. Buning, J. L. Steger, 1985, A 3-D Chimera grid imbedding technique, 7th AIAA CFD Conference, Cincinatti, OH, 1985.
41. P. I. Crumpton, M. B. Giles, 1995, Implicit time accurate solutions on unstructured grids, 12th AIAA CFD Conference, San Diego, CA, 1995.
42. P. I. Crumpton, P. Moinier, M. B. Giles, July, 1997, Calculation of turbulent flow on unstructured grids with high aspect ratio, Proc. 10th International Conference on Numerical Methods for Laminar and Turbulent Flow, Swansea, UK.
43. W. A. Smith, Nov. 1990, Multigrid solution of transonic flow on unstructured grids, Recent Advances and Applications Computational Fluid Dynamics.
44. Mavriplis D. J., Venkatakrishnan V. Multigrid techniques for unstructured meshes. ICASE Report. 95-30:1995.
45. B. van Leer, W.-T. Lee, K. G. Powell, 1989, Sonic-point capturing, AIAA 9th Computational Fluid Dynamics Conference, 1989.
46. Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49:1983;357.
47. B. Baldwin, H. Lomax, 1978, Thin layer approximation and algebraic model for separated turbulent flows, AIAA Paper, 78-257.
48. Spalart P. R., Allmaras S. R. A one-equation turbulence model for aerodynamic flows. Rech. Aerosp. 1:1994;5.
49. C. F. Ollivier-Gooch, 1995, Towards problem-independent multigrid convergence rates for unstructured methods I: Inviscid and laminar viscous flows, Sixth International Symposium on Computational Fluid Dynamics, 913, Lake Tahoe, NY.
50. Cook P. H., McDonald M. A., Firmin M. C. P. Aerofoil RAE2822 pressure distributions, boundary layer and wake measurements. AGARD Advisory Report. 138:1979.