Stability and accuracy of periodic flow solutions obtained by a POD-penalty method

Physica D: Nonlinear Phenomena

Volumn 202, Issue 3-4, 2005, Pages 218-237

  Sirisup, S ^a   Karniadakis, G E ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Dynamical systems; Galerkin projections; Low dimensional; Penalty methods

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; COMPUTER SIMULATION; GALERKIN METHODS; MATHEMATICAL MODELS; VELOCITY MEASUREMENT; VORTEX FLOW;

DYNAMICAL SYSTEMS; GALERKIN PROJECTIONS; LOW-DIAMENSIONAL; PENALTY METHODS;

FLOW CONTROL;

EID: 16344386614     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.02.006     Document Type: Article

References (31)

1. N. Aubry, W.Y. Lian, and E.S. Titi Preserving symmetries in the proper orthogonal decomposition SIAM J. Sci. Comput. 14 2 1993 483 505
2. W. Cazemier, R.W. Verstappen, and A.E. Veldman Proper orthogonal decomposition and low-dimensional models for driven cavity flows Phys. Fluids 10 7 1998 1685 1699
3. S. Sirisup, and G.E. Karniadakis A spectral viscosity method for correcting the long-term behavior of POD models J. Comp. Phys. 194 1 2004 92 116
4. X. Ma, G.E. Karniadakis, H. Park, and M. Gharib DPIV-driven flow simulation: a new computational paradigm Proc. R. Soc. London A 459 2031 2003 547 565
5. S. Sirisup, G.E. Karniadakis, Y. Yang, and D. Rockwell Wave-structure interaction: simulation driven by quantitative imaging Proc. R. Soc. London A 460 2043 2004 729 755
6. X. Zhou, and L. Sirovich Coherence and chaos in a model of turbulent boundary layer Phys. Fluid A 4 12 1992 2855 2874
7. G. Berkooz, P. Holmes, J.L. Lumley, N. Aubry, E. Stone, Observations regarding 'Coherence and chaos in a model of turbulent boundary layer' by X. Zhou and L. Sirovich [Phys. Fluids A 4 (1992) 2855], Phys. Fluid 6 (4) (1994) 1574-1578.
8. G. Berkooz, P. Holmes, J.L. Lumley, N. Aubry, E. Stone, Observations regarding 'Coherence and chaos in a model of turbulent boundary layer' by X. Zhou and L. Sirovich [Phys. Fluids A 4 (1992) 2855], Phys. Fluid 6 (4) (1994) 1574-1578.
9. G. Berkooz, P. Holmes, J.L. Lumley, N. Aubry, E. Stone, Observations regarding 'Coherence and chaos in a model of turbulent boundary layer' by X. Zhou and L. Sirovich [Phys. Fluids A 4 (1992) 2855], Phys. Fluid 6 (4) (1994) 1574-1578.
10. L. Sirovich, X. Zhou, Reply to 'Observations regarding 'Coherence and chaos in a model of turbulent boundary layer' by X. Zhou and L. Sirovich, [Phys. Fluids A 4 (1992) 2855], Phys. Fluid 6 (4) (1994) 1579-1582.
11. L. Sirovich, X. Zhou, Reply to 'Observations regarding 'Coherence and chaos in a model of turbulent boundary layer' by X. Zhou and L. Sirovich, [Phys. Fluids A 4 (1992) 2855], Phys. Fluid 6 (4) (1994) 1579-1582.
12. L. Sirovich, X. Zhou, Reply to 'Observations regarding 'Coherence and chaos in a model of turbulent boundary layer' by X. Zhou and L. Sirovich, [Phys. Fluids A 4 (1992) 2855], Phys. Fluid 6 (4) (1994) 1579-1582.
13. P. Holmes, J.L. Lumley, and G. Berkooz Turbulence, Coherence Structures, Dynamical Systems and Symmetry 1996 Cambridge University Press
14. J.F. Gibson, Dynamical Systems Models of Wall-Bounded, Shear-Flow Turbulence, PhD thesis, Cornell University, 2002.
15. D. Gottlieb, and S.A. Orszag Numerical Analysis of Spectral Methods: Theory and Applications 1977 SIAM-CMBS Philadelphia
16. Y. Yang, and D. Rockwell Wave interaction with a vertical cylinder: spanwise flow patterns and loading J. Fluid Mech. 460 2002 93 129
17. E.J. Doedel, R.C. Paffenroth, A.R. Champneys, T.F. Fairgrieve, Yu.A. Kuznetsov, B. Sandstede, X. Wang, Auto 2000. Continuation and bifurcation software for ordinary differential equations (with homcont). Technical Report, Caltech, 2001.
18. S. Abarbanel, and A. Ditkowski Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes J. Comp. Phys. 133 2 1996 279 288
19. J.S. Hesthaven, and D. Gottlieb A stable penalty method for the compressible Navier-Stokes equations. I. Open boundary conditions SIAM J. Sci. Comput. 17 3 1996 579 612
20. J. Trujillo, and G.E. Karniadakis A penalty method for the vorticity-velocity formulation J. Comp. Phys. 149 1999 32 58
21. A.E. Deane, I.G. Kevrekidis, G.E. Karniadakis, and S.A. Orszag Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders Phys. Fluids A 3 10 1991 2337 2354
22. X. Ma, and G.E. Karniadakis A low-dimensional model for simulating 3D cylinder flow J. Fluid Mech. 458 2002 181 190
23. G.E. Karniadakis, and S.J. Sherwin Spectral/hp Element Methods for CFD 1999 Oxford University Press
24. S. Sirisup, Issues in low-dimensional modeling of unsteady flows: convergence, asymptotic stability and reconstruction procedures, PhD thesis, Division of Applied Mathematics, Brown University, 2005.
25. T.A. Burton Stability and Periodic Solutions of Ordinary and Functional Differential Equations 1985 Academic Press
26. T. Yoshizawa Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions 1975 Springer-Verlag
27. G. Makay On some possible extensions of Massera's theorem Proceedings of the Sixth Colloquium on the Qualitative Theory of Differential Equations (In EJ Qualitative Theory of Differential Equations), vol. 16, 2000 1 8
28. M. Hannon On the numerical computation of Poincaré maps Physica D 5 1982 412 414
29. W. Tucker Computing accurate Poincaré maps Physica D 171 3 2002 127 137
30. R. Seydel Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos 1994 Springer-Verlag
31. P.J. Diamessis, J.A. Domaradzki, J.S. Hesthaven, A spectral multidomain penalty method model for the simulation of high Reynolds number localized incompressible stratified turbulence, J. Comput. Phys. 202 (1) (2005) 298-322.