GMRES physics-based preconditioner for all reynolds and mach numbers: Numerical examples

International Journal for Numerical Methods in Fluids

Volumn 25, Issue 12, 1997, Pages 1347-1371

  Nigro, N ^a   Storti, M ^a   Idelsohn, S ^a  

^a UNIVERSIDAD NACIONAL DEL LITORAL   (Argentina)

Author keywords

3D finite element method by SUPG; Euler and Navier Stokes equations; Explicit and implicit solver; Preconditioning mass matrix; Steady state compressible and incompressible flow; Vector code

Indexed keywords

COMPUTER SOFTWARE; LAMINAR FLOW; MATHEMATICAL MODELS; MATRIX ALGEBRA; NAVIER STOKES EQUATIONS; NEWTONIAN LIQUIDS; NONLINEAR EQUATIONS; REYNOLDS NUMBER; VARIATIONAL TECHNIQUES; VECTORS; VISCOUS FLOW;

EULER CODES; MACH NUMBERS; PRECONDITIONING MASS MATRIX;

FINITE ELEMENT METHOD;

EULER FLOW; FINITE ELEMENT METHOD; LAMINAR FLOW; NAVIER-STOKES EQUATIONS; NEWTONIAN FLUID;

FINITE ELEMENT METHOD; FLUID FLOW; LAMINAR FLOW; NAVIER-STOKES EQUATIONS;

EID: 0031412129     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(19971230)25:12<1347::AID-FLD608>3.0.CO;2-C     Document Type: Article

References (35)

1. N. Nigro, M. Storti, S. Idelsohn and T. Tezduyar, 'Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations', Comput. Methods Appl. Mech. Eng., in press (1997).
2. S. Aliabadi, 'Parallel finite element computations in aerospace applications', Ph.D. Thesis, Department of Aerospace Engineering and Mechanics, University of Minnesota, 1994.
3. S. Aliabadi, S. Ray and T. Tezduyar, 'SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations', Comput. Mech., 11, 300-312 (1993).
4. C. Baumann, M. Storti and S. Idelsohn, 'A Petrov-Galerkin technique for the solution of transonic and supersonic flows', Comput. Methods Appl. Mech. Eng., 95, 49-70 (1992).
5. A. Brooks and T. Hughes, 'Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations', Comput. Methods Appl. Mech. Eng., 32, 199-259 (1982).
6. T. Hughes, M. Mallet and A. Mizukami, 'A new finite element method for CFD: II. Beyond SUPG', Comput. Methods Appl. Mech. Eng., 54, 341-355 (1986).
7. T. Hughes and M. Mallet, 'A new finite element method for CFD: III. The generalised streamline operator for multidimensional advection-diffusion systems', Comput. Methods Appl. Mech. Eng., 58, 305-328 (1986).
8. T. Hughes and M. Mallet, 'A new finite element method for CFD: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems', Comput. Methods Appl. Mech. Eng., 58, 329-336 (1986).
9. G. Le Beau, S. Ray, S. Aliabadi and T. Tezduyar, 'SUPG finite element computation of compressible flows with the entropy and conservation variables formulations', Comput. Methods Appl. Mech. Eng., in press.
10. M. Mallet, 'A finite element method for CFD', Ph.D. Thesis, Department of Civil Engineering, Stanford University, 1985.
11. F. Shakib, 'Finite element analysis of the compressible Euler and Navier-Stokes equations', Ph.D. Thesis, Department of Mechanical Engineering, Stanford University, 1988.
12. A. Soulaimani and M. Fortin, 'Finite element solution of compressible viscous flows using conservative variables', Comput. Methods Appl. Mech. Eng., 118, 319-350 (1994).
13. T. Tezduyar and T. Hughes, 'Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations', AIAA Paper 83-0125, 1983.
14. T. Hughes and T. Tezduyar, 'Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations', Comput. Methods Appl. Mech. Eng., 45, 217-284 (1984).
15. L. Franca and E. Dutra do Carmo, 'The Galerkin-gradient least squares method', Comput. Methods Appl. Mech. Eng., 74, 41-54 (1989).
16. T. Hughes and L. Franca, 'A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity/pressure spaces', Comput. Methods Appl. Mech. Eng., 65, 85-96 (1987).
17. T. Hughes, L. France and G. Hulbert, 'A new finite element formulation for computational fluid dynamics: VIII. 'The Galerkin/least square method for advective-diffusive equations', Comput. Methods Appl. Mech. Eng., 73, 173-189 (1989).
18. Y. Saad, 'A flexible inner-outer preconditioned GMRES algorithm', SIAM J. Sci. Comput., 14, 461-469 (1993).
19. Y. Saad and M. Schultz, 'GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems', SIAM J. Sci. Stat. Comput., 7, 856-869 (1986).
20. M. Storti, C. Baumann and S. Idelsohn. 'A preconditioning mass matrix to accelerate the convergence to the steady Euler solution using explicit schemes', Comput. Methods Appl. Mech. Eng., 34, 519-541 (1992).
21. M. Storti, N. Nigro and S. Idelsohn, 'Steady state incompressible flows using explicit schemes with an optimcal local preconditioning', Comput. Methods Appl. Mech. Eng., 124, 231-252 (1995).
22. Y. Choi and C. Merkle, 'The application of preconditioning in viscous flows', J. Comput. Phys. 105, 207-223 (1993).
23. S. Venkateswaran, J. Weiss, C. Merkle and Y. Choi, 'Propulsion-related flowfields using the preconditioned Navier-Stokes equations', AIAA Paper 92-3437, 1992.
24. N. Nigro, M. Storti and S. Idelsohn, 'Fluid flows around turbomachinery using an explicit pseudo-temporal Euler FEM', Commun. Appl. Numer. Methods, 11, 199-211 (1995).
25. N. Nigro, M. Storti and S. Idelsohn, Two-phase flow in gas-stirred liquid vessels with SUPG-stabilized equal order interpolations', Int. j. numer. methods fluids, 19, 1-22 (1994).
26. M. Storti, N. Nigro and S. Idelsohn, 'Equal-order interpolations: a unified approach to stabilize the incompressible and convective effects', Comput. Methods Appl. Mech. Eng., 143, 3-4, 317, 331 (1997).
27. V. van Leer, W. Lee and P. Roe, 'Characteristic time-stepping or local preconditioning of the Euler equations', AIAA Paper 91-1552-CP, 1991.
28. B. Gustafsson and A. Sundstrom, 'Incompletely parabolic problems in fluid dynamics', SIAM J. Appl. Math., 35, 343-357 (1978).
29. J. Oliger and A. Sundstrom, 'Theoretical and practical aspects of some initial boundary value problems in fluid dynamics'. SIAM J. Appl. Math., 35, 419-446 (1978).
30. D. Rudy and J. Strikwerda, 'A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations', J. Comput. Phys., 36, 55-70 (1980).
31. H. Ashley and M. Landhal, Aerodynamics of Wings and Bodies, General, Toronto, 1965.
32. J. Carter, 'Numerical solution of the Navier-Stokes equations for the supersonic laminar flow over two dimensional compression comer', NASA TR R-385, 1972.
33. C. Hung and R. MacCormack, 'Numerical solutions of supersonic and hypersonic laminar compression comer flows', AIAA J., 14, 475-481 (1976).
34. M. Van Dyke, Perturbation Methods in Fluid Mechanics, Parabolic, Stanford, CA, 1975.
35. G. Batchelor, Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1970.