Equation-free/Galerkin-free POD-assisted computation of incompressible flows

Journal of Computational Physics

Volumn 207, Issue 2, 2005, Pages 568-587

  Sirisup, Sirod ^a   Karniadakis, George Em ^a   Xiu, Dongbin ^b   Kevrekidis, Ioannis G ^b  

^a BROWN UNIVERSITY   (United States)

^b Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CIRCULAR CYLINDERS; DIRECT NUMERICAL SIMULATION; GALERKIN METHODS; NUMERICAL MODELS; PRINCIPAL COMPONENT ANALYSIS; REYNOLDS NUMBER; VISCOUS FLOW;

BASE FUNCTION; COMPUTATIONAL METHODOLOGY; DIRECT-NUMERICAL-SIMULATION; EQUATION-FREE; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; LONG TERM DYNAMICS; ORTHOGONAL DECOMPOSITION; PROPER ORTHOGONAL;

NAVIER STOKES EQUATIONS;

EID: 18844459925     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.01.024     Document Type: Article

References (41)

1. R.E. Arndt D.F. Long M.N. Glauser The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet J. Fluid Mech. 340 1997 1-33
2. N. Aubry P. Holmes J.L. Stone J.L. Lumley The dynamics of coherent structures in the wall region of a turbulent boundary layer J. Fluid Mech. 192 1988 115
3. N. Aubry W.Y. Lian E.S. Titi Preserving symmetries in the proper orthogonal decomposition SIAM J. Sci. Comput. 14 2 1993 483-505
4. G. Berkooz P. Holmes J.L. Lumley The proper orthogonal decomposition in the analysis of turbulent flows Ann. Rev. Fluid Mech. 25 1993 539-575
5. N.-Z. Cao, N. Aubry, Numerical simulation of wake flow via a reduced system, in: Proc. of the ASME Fluids Engineering Conference, Washington, DC, 1993
6. W. Cazemier R.W. Verstappen A.E. Veldman Proper orthogonal decomposition and low-dimensional models for driven cavity flows Phys. Fluids 10 7 1998 1685-1699
7. J.H. Citriniti W.K. George Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the proper orthogonal decomposition J. Fluid Mech. 418 2000 137-166
8. A.E. Deane I.G. Kevrekidis G.E. Karniadakis 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
9. J. Delville L. Ukeiley L. Cordier J.P. Bonnet M. Glauser Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition J. Fluid Mech. 391 1999 91-122
10. 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
11. C. Foias M.S. Jolly I.G. Kevrekidis E.S. Titi Dissipativity of the numerical schemes Nonlinearity 4 1991 591-613
12. C.W. Gear, T.J. Kaper, I.G. Kevrekidis, A. Zagaris, Projecting on a slow manifold: Singularly perturbed systems and legacy codes, SIAM J. Appl. Dyn. Sys., to appear (original version can be found as Physics/0405074 at arXiv.org)
13. C.W. Gear I.G. Kevrekidis Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum SIAM J. Sci. Comput. 24 2003 1091-1106 (also NEC Technical Report NECI-TR 2001-029, can be obtained as http://www.neci.nj.nec.com/homepages/cwg/ projective.pdf)
14. C.W. Gear I.G. Kevrekidis Telescopic projective methods for parabolic differential equations J. Comput. Phys. 187 1 2003 95-109 (also NEC Technical Report,November 2001, can be obtained as http://www.neci.nj.nec.com/homepages/cwg/itproje.pdf)
15. C.W. Gear I.G. Kevrekidis Computing in the past with forward integration Phys. Lett. A 321 2004 335-343 (original version can be found as nlin.CD/ 0302055 at arXiv.org)
16. C.W. Gear, I.G. Kevrekidis, Constraint-defined manifolds: A legacy-code approach to low-dimensional computations. J. Sci. Comput., in press
17. C.W. Gear J. Li I.G. Kevrekidis The gap-tooth method in particle simulations Phys. Lett. A 316 2003 190-195
18. A. Glezer Z. Kadioglu A.J. Pearlstein Development of an extended proper orthogonal decomposition and its application to a time periodically forced plane mixing layer Phys. Fluids 1 8 1989 1363
19. S.V. Gordeyev F.O. Thomas Coherent structure in the turbulent planar jet. Part 1. Extraction of proper orthogonal decomposistion eigenmodes and their self-similarity J. Fluid Mech. 414 2000 145-194
20. G.E. Karniadakis M. Israeli S.A. Orszag High-order splitting methods for incompressible Navier-Stokes equations J. Comput. Phys. 97 1991 414
21. G.E. Karniadakis S.J. Sherwin Spectral/hp element methods for CFD 1999 Oxford University Press Oxford
22. C.T. Kelley Iterative methods for linear and nonlinear equations 1995 SIAM Philadelphia, PA
23. C.T. Kelley, I.G. Kevrekidis, Q. Liang, Newton-Krylov solvers for time-steppers. SIAM J. Appl. Dyn. Sys., submitted (original version can be found as math.DS/0404374 at arXiv.org)
24. I.G. Kevrekidis C.W. Gear G. Hummer Equation-free: The computer-assisted analysis of complex, multiscale systems AIChE J. 50 7 2004 1346-1354
25. I.G. Kevrekidis C.W. Gear J.M. Hyman P.G. Kevrekidis O. Runborg C. Theodoropoulos Equation-free coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis Commun. Math. Sci. 1 4 2003 715-762 (original version can be found as physics/ 0209043 at arXiv.org)
26. J. Li P.G. Kevrekidis C.W. Gear I.G. Kevrekidis Deciding the nature of the coarse integration through microscopic simulations: The baby-bathwater scheme SIAM J. Multiscale Model. Simulation 1 2003 391-407
27. A. Liakopoulos P.A. Blythe H. Gunes A reduced dynamical model of convective flows in tall laterally heated cavities Proc. Roy. Soc. London Ser. A 453 1997 663
28. X. Ma G.S. Karamanos G.E. Karniadakis Dynamics and low-dimensionality of the turbulent near-wake J. Fluid Mech. 410 2000 29-65
29. A. Makeev D. Maroudas I.G. Kevrekidis Coarse stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples J. Chem. Phys. 116 2002 10083-10091
30. A. Makeev D. Maroudas A. Panagiotopoulos I.G. Kevrekidis Coarse bifurcation analysis of kinetic Monte Carlo simulations: A lattice-gas model with lateral interactions J. Chem. Phys. 117 2002 8229-8240
31. D. Rempfer On low-dimensional Galerkin models for fluid flow Theoret. Comput. Fluid Dyn. 14 2 2000 75-88
32. D. Rempfer H.F. Fasel Evolution of three-dimensional coherent structures in a flat-plate boundary layer J. Fluid Mech. 260 1994 351
33. R. Rico-Martinez C.W. Gear I.G. Kevrekidis Coarse projective kMC integration: Forward/reverse initial and boundary value problems J. Comput. Phys. 196 2004 474-489 (original version can be found as nlin. CG/0308040 at arXiv.org)
34. O. Runborg C. Theodoropoulos I.G. Kevrekidis Effective bifurcation analysis: A time-stepper based approach Nonlinearity 15 2002 491-511
35. S. Setayeshgar, C.W. Gear, H.G. Othmer, I.G. Kevrekidis, Application of coarse integration to bacterial chemotaxis. SIAM J. Multiscale Model. Simulation, in press (also physics/0308040 at arXiv.org)
36. C. Siettos M.D. Graham I.G. Kevrekidis Bifurcation, projective integration and control via stochastic simulation J. Chem. Phys 118 2 2003 10149-10157
37. C.I. Siettos C.C. Pantelides I.G. Kevrekidis Enabling dynamic process simulators to perform alternative tasks: A time-stepper based toolkit for computer-aided analysis Ind. Eng. Chem. Res. 42 26 2003 6795-6801 (original version can be found as math.OC/0302040 at Xiv.org)
38. S.N. Singh H.M. James A.A. Gregory B. Siva K.H. James Optimal feedback control of vortex shedding using proper orthogonal decomposition models Trans. ACME 123 2001 612-618
39. S. Sirisup G.E. Karniadakis A spectral viscosity method for correcting the long-term behavior of POD models J. Comput. Phys. 194 1 2004 92-116
40. L. Sirovich Turbulence and the dynamics of coherent structures, Parts I, II and III Quart. Appl. Math. XLV 1987 561-590
41. C. Theodoropoulos Y. Qian I.G. Kevrekidis Coarse stability and bifurcation analysis using time-steppers: A reaction-diffusion example Proc. Natl. Acad. Sci. 2000 97