Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier-Stokes equation

Journal of Fluid Mechanics

Volumn 729, Issue , 2013, Pages 285-308

  Balajewicz, Maciej J ^a   Dowell, Earl H ^b   Noack, Bernd R ^c  

^a Department of Aeronautics and Astronautics Department of Mechanical Engineering and Industrial for Computational and Mathematical Engineering   (United States)

^b Duke University   (United States)

^c UNIVERSITÉ DE POITIERS   (France)

Author keywords

Computational methods; Low dimensional models; Turbulence modelling

Indexed keywords

COMPUTATIONAL METHODS; DYNAMICAL SYSTEMS; GALERKIN METHODS; KINETIC ENERGY; KINETICS; REYNOLDS NUMBER; SHEAR FLOW; TURBULENCE MODELS; VISCOUS FLOW;

HIGH REYNOLDS NUMBER; HIGH REYNOLDS NUMBER FLOWS; LID-DRIVEN CAVITIES; LOW DIMENSIONAL; LOW-DIMENSIONAL MODELS; POWER BALANCE EQUATIONS; TURBULENT KINETIC ENERGY; TWO-DIMENSIONAL FLOW;

NAVIER STOKES EQUATIONS;

COMPUTATIONAL FLUID DYNAMICS; EDDY; FLOW MODELING; GALERKIN METHOD; KINETIC ENERGY; MIXING; NAVIER-STOKES EQUATIONS; REYNOLDS NUMBER; SHEAR FLOW; TURBULENCE; TWO-DIMENSIONAL FLOW;

EID: 84884595115     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2013.278     Document Type: Article

References (47)

1. AMSALLEM, D. & FARHAT, C. 2011 Stabilization of projection-based reduced-order models. Intl J. Numer. Meth. Engng 91 (4), 358-377.
2. AUBRY, N., HOLMES, P., LUMLEY, J. L. & STONE, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192 (115), 115-173.
3. BAILON-CUBA, J., SHISHKINA, O., WAGNER, C. & SCHUMACHER, J. 2012 Low-dimensional model of turbulent mixed convection in a complex domain. Phys. Fluids 24, 107101.
4. BOGEY, C. 2000 Calcul direct du bruit aérodynamique et validation de modèles acoustiques hybrides. PhD thesis, Ecole Centrale Lyon, France.
5. BOYD, J. P. 2001 Chebyshev and Fourier Spectral Methods, 2nd edn. Dover.
6. BRENT, R. P. 2002 Algorithms for Minimization without Derivatives. Dover.
7. CANUTO, C., HUSSAINI, M. Y., QUARTERONI, A. & ZANG, T. A. 1991 Spectral Methods in Fluid Dynamics. Springer.
8. CANUTO, C., HUSSAINI, M. Y., QUARTERONI, A. & ZANG, T. A. 2006 Spectral Methods: Fundamentals in Single Domains. Springer.
9. CAVALIERI, A., DAVILLER, G., COMTE, P., JORDAN, P., TADMOR, G. & GERVAIS, Y. 2011 Using large eddy simulation to explore sound-source mechanisms in jets. J. Sound Vib. 330, 4098-4113.
10. CAZEMIER, W., VERSTAPPEN, R. W. C. P. & VELDMAN, A. E. P. 1998 Proper orthogonal decomposition and low-dimensional models for driven cavity flows. Phys. Fluids 10 (7), 1685-1699.
11. COLONIUS, T., LELE, S. K. & MOIN, P. 1993 Direct computation of the sound generated by two-dimensional shear layer. In 15th AIAA Aeroacoustics Conference. Long Beach.
12. CORDIER, L., NOACK, B. R., DAVILLER, G., DELVILLE, J., LEHNASCH, G., TISSOT, G., BALAJEWICZ, M. & NIVEN, R. K. 2013 Control-oriented model identification strategy. Exp. Fluids (submitted).
13. DAVILLER, W. 2010 Numerical study of temperature effects in single and coaxial jets. PhD thesis, Ecole Nationale Supérieure de Mécanique et d'Aérotechnique (ENSMA), Poitiers, France.
14. DEMMEL, J. W. 1997 Applied Numerical Linear Algebra. SIAM.
15. DIXON, L. C. W. & SZEGO, G. P. 1975 Towards Global Optimisation: Proceedings of a Workshop at the University of Cagliari, Italy, October 1974. North Holland.
16. FLETCHER, C. A. J. 1984 Computational Galerkin Methods. Springer.
17. GALLETTI, B., BRUNEAU, C. H., ZANNETTI, L. & IOLLO, A. 2004 Low-order modelling of laminar flow regimes past a confined square cylinder. J. Fluid Mech. 503, 161-170.
18. GOTTLIEB, D. & TURKEL, E. 1976 Dissipative two-four method for time dependent problems. Maths Comput. 30 (136), 703-723.
19. HAYDER, M. E. & TURKEL, E. 1993 High-order accurate solutions of viscous problem. In AIAA paper 93-3074.
20. HOLMES, P., LUMLEY, J. L., BERKOOZ, G. & ROWLEY, C. W. 2012 Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 2nd edn. Cambridge University Press.
21. ILIESCU, T. & WANG, Z. 2012 Variational multiscale proper orthogonal decomposition: Navier-Stokes equations. Preprint arXiv: 1210.7389.
22. IOLLO, A., LANTERI, S. & DÉSIDÉ RI, J.-A. 2000 Stability properties of Pod-Galerkin approximations for the compressible Navier-Stokes equations. Theor. Comput. Fluid Dyn. 13 (6), 377-396.
23. JOSEPH, D. D. 1976 Stability of Fluid Motions, I and II. New York, Springer.
24. KRAICHNAN, R. H. & CHEN, S. 1989 Is there a statistical mechanics of turbulence? Physica D: Nonlinear Phenomena 37 (1-3), 160-172.
25. LADYZHENSKAYA, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach.
26. LODATO, G., DOMINGO, P. & VERVISCH, L. 2008 Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows. J. Comput. Phys. 227 (10), 5105-5143.
27. LUMNLEY, J. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Wave Propagation (ed. A. M. Yaglom & V. I. Tatarski), pp. 166-178.
28. Nauka. MOIN, P. & MAHESH, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539-578.
29. NOACK, B. R. & ECKELMANN, H. 1994 A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270, 297-330.
30. NOACK, B. R., MORZYNSKI, M. & TADMOR, G. 2011 Reduced-Order Modelling for Flow Control. Springer.
31. NOACK, B. R., PAPAS, P. & MONKEWITZ, P. A. 2005 The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows. J. Fluid Mech. 523 (1), 339-365.
32. NOACK, B. R., SCHLEGEL, M., AHLBORN, B., MUTSCHKE, G., MORZYNSKI, M., COMTE, P. & TADMOR, G. 2008 A finite-time thermodynamics of unsteady fluid flows. J. Non-Equilib. Thermodyn. 33 (2), 103-148.
33. NOCEDAL, J. & WRIGHT, S. J. 1999 Numerical Optimization. Springer.
34. POPE, S. B. 2000 Turbulent Flows, 6th edn. Cambridge University Press.
35. REMPFER, D. & FASEL, H. F. 1994 Dynamics of three-dimensional coherent structures in a flat-plate boundary layer. J. Fluid Mech. 275, 257-284.
36. ROWLEY, C. W., MEZIC, I., BAGHERI, S., SCHLATTER, P. & HENNINGSON, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115-127.
37. SCHITTKOWSKI, K. 1986 NLPQL: a FORTRAN subroutine solving constrained nonlinear programming problems. Ann. Oper. Res. 5 (1), 485-500.
38. SCHMID, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5-28.
39. SHANKAR, P. N. & DESHPANDE, M. D. 2000 Fluid mechanics in the driven cavity. Annu. Rev. Fluid Mech. 32 (1), 93-136.
40. SIRISUP, S. & KARNIADAKIS, G. E. 2004 A spectral viscosity method for correcting the long-term behavior of POD models. J. Comput. Phys. 194 (1), 92-116.
41. SIROVICH, L. 1987 Turbulence and the dynamics of coherent structures, Part I: coherent structures. Q. Appl. Maths 45, 561-571.
42. TENNEKES, H. & LUMLEY, J. L. 1972 A First Course in Turbulence. The MIT Press.
43. TERRAGNI, F., VALERO, E. & VEGA, J. M. 2011 Local POD plus Galerkin projection in the unsteady lid-driven cavity problem. SIAM J. Sci. Comput. 33 (6), 3538-3561.
44. UKEILEY, L., CORDIER, L., MANCEAU, R., DELVILLE, J., GLAUSER, M. & BONNET, J. P. 2001 Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model. J. Fluid Mech. 441 (1), 67-108.
45. WANG, Z., AKHTAR, I., BORGGAARD, J. & ILIESCU, T. 2011 Two-level discretizations of nonlinear closure models for proper orthogonal decomposition. J. Comput. Phys. 230, 126-146.
46. WANG, Z., AKHTAR, I., BORGGAARD, J. & ILIESCU, T. 2012 Proper orthogonal decomposition closure models for turbulent flows: a numerical comparison. Comput. Meth. Appl. Mech. Engng 237-240, 10-26.
47. WELCH, P. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70-73.