Massively parallel solution of the biglobal eigenvalue problem using dense linear algebra

AIAA Journal

Volumn 47, Issue 10, 2009, Pages 2449-2459

  Rodriguez, Daniel ^a,b   Theofilis, Vassilis ^a,b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b Plaza Cardenal Cisneros 3 ^*  (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

AMPLITUDE FUNCTIONS; COMPLEX FLOW; DENSE LINEAR ALGEBRA; EIGEN MODES; EIGENSPECTRUM; EIGENVALUE PROBLEM; ENABLING TECHNOLOGIES; FLAT PLATE; GLOBAL INSTABILITY; IN-CORE; LAMINAR SEPARATION BUBBLE; LINEAR INSTABILITIES; LOCAL INSTABILITY; NUMERICAL SOLUTION; PARALLEL SOLUTIONS; SEPARATED FLOWS; SPATIAL DIRECTION; UNSTABLE FLOWS;

AIRFOILS; LAMINAR FLOW; STABILITY; SWITCHING SYSTEMS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 72649093921     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.42714     Document Type: Article

References (26)

1. Drazin, P. G., and Reid, W. H., Hydrodynamic Stability, Cambridge Univ. Press, Cambridge, England, U.K., 1981.
2. Schmid, P., and Henningson, D. S., Stability and Transition in Shear Flows, Springer, New York, 2001.
3. Theofilis, V., "Advances in Global Linear Instability Analysis of Nonparallel and Three-Dimensional Flows," Progress in Aerospace Sciences, Vol.39, No.4, 2003, pp. 249-315. doi:10.1016/S0376-0421(02)00030-1
4. Theofilis, V., and Colonius, T., "Three-Dimensional Instabilities of Compressible Flowover Open Cavities: Direct Solution of the BiGlobal Eigenvalue Problem," AIAA Paper 2004-2544, 2004.
5. Robinet, J.-C., "Bifurcations in Shock-Wave/Laminar-Boundary-Layer Interaction: Global Instability Approach," Journal of Fluid Mechanics, Vol.579, May 2007, pp. 85-112. doi:10.1017/S0022112007005095 (Pubitemid 47304524)
6. Theofilis, V., Hein, S., and Dallmann, U., "On the Origins of Unsteadiness and Three-Dimensionality in a Laminar Separation Bubble," Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol.358, No.1777, 2000, pp. 3229-3324. doi:10.1098/rsta.2000.0706
7. Ehrenstein, U., and Gallaire, F., "On Two-Dimensional Temporal Modes in Spatially Evolving Open Flows: The Flat-Plate Boundary Layer," Journal of Fluid Mechanics,Vol. 536, Aug. 2005, pp. 209-218. doi:10.1017/ S0022112005005112 (Pubitemid 41174790)
8. A˚kervik, E., Ehrenstein, U., Gallaire, F., and Henningson, D., "Global Two-Dimensional Stability Measures of the Flat-Plate Boundary-Layer Flow," European Journal of Mechanics, B: Fluids,Vol. 27, No.5, 2008, pp. 501-513. doi:10.1016/j.euromechflu.2007.09.004
9. Kitsios, V., Rodri´guez, D., Theofilis, V., Ooi, A., and Soria, J., "BiGlobal Instability Analysis of Turbulent Flow over an Airfoil at an Angle of Attack," AIAA Paper 2008-4384, 2008.
10. Edwards,W. S., Tuckerman, L. S., Friesner, R. A., and Sorensen, D. C., "Krylov Methods for the Incompressible Navier-Stokes Equations," Journal of Computational Physics, Vol.110, No.1, 1994, pp. 82-102. doi:10.1006/jcph.1994.1007 (Pubitemid 124013346)
11. Barkley, D., Gomes, M. G. M., and Henderson, R. D., "Three- Dimensional Instability in a Flow over a Backward-Facing Step," Journal of Fluid Mechanics, Vol.473, Dec. 2002, pp. 167-190.
12. Bagheri, S., A˚kervik, E., Brandt, L., and Henningson, D. S., "Matrix- Free Methods for the Stability and Control of Boundary Layers," AIAA Journal, Vol.47, No.5, 2009, pp. 1057-1068. doi:10.2514/1.41365
13. Blackford, L. S., Choi, J., Cleary, A., E. D'Azeuedo, J. Demmel, and I. Dhillon et al., ScaLAPACK User's Guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1997, ISBN 0-89871-397-8. Petitet, A., Whaley, R. C., Demmel, J., Dhillon, I., Stanley, K., Dongarra, J., Hammarling, S., Henry, G., and Walker, D., "ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers: Design Issues and Performance," 1996.
14. Borrill, J., "MADCAP: The Microwave Anositropy Dataset Computational Analysis Package," Proceedings of the 5th European SGI/Cray MPP Workshop, 1999, http://arxiv.org/abs/astro-ph/9911389v1.
15. Bonoli, P., Batchelor, D., Berry, L., Choi, M.,D'Ippolito, D. A., Harvey, R.W., Jaeger, E. F., Myra, J. R., Phillips, C. K., Smithe, D. N., Tang, V., Valeo, E., Wright, J. C., Brambilla, M., Bilato, R., Lancellotti, V., and Maggiora, R., "Evolution of Nonthermal Particle Distributions in Radio Frequency Heating of Fusion Plasmas," Journal of Physics: Conference Series, Vol.78, 2007, p. 012006. doi:10.1088/1742-6596/78/1/012006
16. Macaraeg, M., Streett, C., and Hussaini, M., A Spectral Collocation Solution to the Compressible Stability Eigenvalue Problem, NASA, TR TP-2858, 1988.
17. Malik, M. R., "Numerical Methods for Hypersonic Boundary Layer Stability," Journal of Computational Physics, Vol.86, No.2, 1990, pp. 376-413. doi:10.1016/0021-9991(90)90106-B
18. Theofilis, V., Journal of Engineering Mathematics, Vol.34, Nos. 1-21998, pp. 111-129. doi:10.1023/A:1004366529352
19. Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., Spectral Methods: Fundamentals in Single Domains, Springer, NewYork, 2006.
20. de Vicente, J., Valero, E., and Theofilis, V., "Numerical Considerations in Spectral Multidomain Methods for BiGlobal Instability Analysis of Open Cavity Configurations," Progress in Industrial Mathematics at ECMI 2006, Springer, New York, 2006, ISBN 9783540719922.
21. Golub, G. H., and Van Loan, C. F., Matrix Computations, 2nd ed., John Hopkins Univ. Press, Baltimore, MD, 1989, ISBN 0-8018-3739-1.
22. Saad, Y., "Variations of Arnoldi's Method for Computing Eigenelements of Large Unsymmetric Matrices," Linear Algebra and Its Applications, Vol.34, No.1, 1980, pp. 269-295. doi:10.1016/0024-3795(80)90169-X
23. Theofilis, V., "On Instability Properties of Incompressible Laminar Separation Bubbles on a Flat Plate Prior to Shedding," AIAA Paper 2007-0540, 2007.
24. Tatsumi, T., and Yoshimura, T., "Stability of the Laminar Flow in a Rectangular Duct," Journal of Fluid Mechanics, Vol.212, No.1, 1990, pp. 437-449. doi:10.1017/S002211209000204X
25. Theofilis, V., Duck, P. W., and Owen, J., "Viscous Linear Stability Analysis of Rectangular Duct and Cavity Flows," Journal of Fluid Mechanics, Vol.505, April 2004, pp. 249-286. doi:10.1017/S002211200400850X (Pubitemid 38673041)
26. Rodri´guez, D., and Theofilis, V., "On Instability and Structural Sensitivity of Incompressible Laminar Separation Bubbles in a Flat-Plate Boundary Layer," AIAA Paper 2008-4148, 2008.