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Direct optimal growth analysis for timesteppers

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Barkley, Dwight, Blackburn, H. M. and Sherwin, Spencer J. (2008) Direct optimal growth analysis for timesteppers. In: 14th International Conference on Finite Elements in Flow Problems, Santa Fe, NM, Mar 24-28, 2007. Published in: International Journal for Numerical Methods in Fluids, Volume 57 (Number 9). pp. 1435-1458.

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Abstract

Methods are described for transient growth analysis of flows with arbitrary geometric complexity, where in particular the flow is not required to vary slowly in the streamwise direction. Emphasis is on capturing the global effects arising from localized convective stability in streamwise-varying flows. The methods employ the 'timestepper's approach' in which a nonlinear Navier-Stokes code is modified to provide evolution operators for both the forward and adjoint linearized equations. First, the underlying mathematical treatment in primitive flow variables is presented. Then, details are given for the inner level code modifications and outer level eigenvalue and SVD algorithms in the timestepper's approach. Finally, some examples are shown and guidance provided on practical aspects of this type of large-scale stability analysis. Copyright (C) 2008 John Wiley & Sons, Ltd.

Item Type: Conference Item (UNSPECIFIED)
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
T Technology > TJ Mechanical engineering and machinery
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Large scale systems, System analysis, Stability, Eigenvalues, Navier-Stokes equations
Journal or Publication Title: International Journal for Numerical Methods in Fluids
Publisher: John Wiley & Sons Ltd.
ISSN: 0271-2091
Official Date: 30 July 2008
Volume: Volume 57
Number: Number 9
Number of Pages: 24
Page Range: pp. 1435-1458
Identification Number: 10.1002/fld.1824
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Description:

Special Issue: 14th International Conference on Finite Elements in Flow Problems
Funder: Engineering and Physical Sciences Research Council (EPSRC), Senior Fellowship of the City of Paris
Grant number: EP/E006493/1 (EPSRC)
Title of Event: 14th International Conference on Finite Elements in Flow Problems
Type of Event: Conference
Location of Event: Santa Fe, NM
Date(s) of Event: Mar 24-28, 2007
References:

1. Tuckerman LS, Barkley D. Bifurcation analysis for timesteppers. In Numerical Methods for Bifurcation Problems
and Large-Scale Dynamical Systems, Doedel E, Tuckerman LS (eds). Springer: Berlin, 2000; 453–566.
2. Barkley D, Gomes MGM, Henderson RD. Three-dimensional instability in flow over a backward-facing step.
Journal of Fluid Mechanics 2002; 473:167–190.
3. Barkley D, Henderson RD. Three-dimensional Floquet stability analysis of the wake of a circular cylinder.
Journal of Fluid Mechanics 1996; 322:215–241.
4. Blackburn HM. Three-dimensional instability and state selection in an oscillatory axisymmetric swirling flow.
Physics of Fluids 2002; 14(11):3983–3996.
5. Blackburn HM, Lopez JM. The onset of three-dimensional standing and modulated travelling waves in a
periodically driven cavity flow. Journal of Fluid Mechanics 2003; 497:289–317.
6. Blackburn HM, Sherwin SJ. Instability modes and transition of pulsatile stenotic flow: pulse-period dependence.
Journal of Fluid Mechanics 2007; 573:57–88.
7. Elston JR, Blackburn HM, Sheridan J. The primary and secondary instabilities of flow generated by an oscillating
circular cylinder. Journal of Fluid Mechanics 2006; 550:359–389. 8. Sherwin SJ, Blackburn HM. Three-dimensional instabilities and transition of steady and pulsatile flows in an
axisymmetric stenotic tube. Journal of Fluid Mechanics 2005; 533:297–327.
9. A° kervik E, Hoepffner J, Ehrenstein U, Henningson DS. Optimal growth, model reduction and control in a
separated boundary-layer flow using global eigenmodes. Journal of Fluid Mechanics 2007; 579:305–314.
10. Blackburn HM, Barkley D, Sherwin SJ. Convective instability and transient growth in flow over a backward-facing
step. Journal of Fluid Mechanics 2008; 603:271–304.
11. Ehrenstein U, Gallaire F. On two-dimensional temporal modes in spatially evolving open flows: the flat-plate
boundary layer. Journal of Fluid Mechanics 2005; 536:209–218.
12. Marquet O, Sipp D, Jacquin L. Global optimal perturbations in a separated flow over a backward-rounded-step.
Thirty-sixth AIAA Fluid Dynamics Conference and Exhibit, San Francisco, 2006; Paper No. 2006-2879.
13. Karniadakis GE, Sherwin SJ. Spectral/hp Element Methods for Computational Fluid Dynamics (2nd edn). Oxford
University Press: Oxford, 2005.
14. Cossu C, Chomaz JM. Global measures of local convective instabilities. Physical Review Letters 1997; 78:
4387–4390.
15. Schmid PJ, Henningson DS. Stability and Transition in Shear Flows. Springer: Berlin, 2001.
16. Trefethen LN, Trefethen AE, Reddy SC, Driscoll TA. Hydrodynamic stability without eigenvalues. Science 1993;
261:578–584.
17. Karniadakis GE, Israeli M, Orszag SA. High-order splitting methods for the incompressible Navier–Stokes
equations. Journal of Computational Physics 1991; 97(2):414–443.
18. Guermond JL, Shen J. Velocity-correction projection methods for incompressible flows. SIAM Journal on
Numerical Analysis 2003; 41:112–134.
19. Wilhelm D, Kleiser L. Stability analysis for different formulations of the nonlinear term in PN –PN−2 spectral
element discretizations of the Navier–Stokes equations. Journal of Computational Physics 2001; 174:306–326.
20. Barkley D. Confined three-dimensional stability analysis of the cylinder wake. Physical Review E 2007; 71:017301.
21. Saad Y. Numerical Methods for Large Eigenvalue Problems. Wiley: New York, 1992.
22. Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Hammarling S,
McKenney A, Sorensen D. LAPACK User’s Guide (3rd edn). SIAM: Philadelphia, PA, 1999.
23. Lehoucq RB, Sorenson DC, Yang C. ARPACK Users’ Guide. SIAM: Philadelphia, PA, 1998.
24. Kaiktsis L, Karniadakis GE, Orszag SA. Onset of three-dimensionality, equilibria, and early transition in flow
over a backward-facing step. Journal of Fluid Mechanics 1991; 231:501–528.
25. Blackburn HM, Sherwin SJ, Barkley D. Convective instability and transient growth in steady and pulsatile stenotic
flows. Journal of Fluid Mechanics 2008; 603:271–304.
26. Butler KM, Farrell BF. Three-dimensional optimal perturbations in viscous shear flow. Physics of Fluids A 1992;
4(8):1637–1650.
URI: http://wrap.warwick.ac.uk/id/eprint/29633

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