DPIV-driven flow simulation: A new computational paradigm

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 459, Issue 2031, 2003, Pages 547-565

  Ma, X ^a   Karniadakis, G E ^a   Park, H ^b   Gharib, M ^b  

^a BROWN UNIVERSITY   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Galerkin and nonlinear Galerkin projections; Low dimensional flow modelling; Particle image velocimetry

Indexed keywords

ARTICLE; FLUID FLOW; MATHEMATICAL COMPUTING; MOLECULAR MECHANICS; SIMULATION;

EID: 0842332693     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2002.0981     Document Type: Article

References (33)

1. Aubry, N., Holmes, P., Stone, J. L. & Lumley, J. L. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115-173.
2. Ball, K. S., Sirovich, L. & Keefe, L. R. 1991 Dynamical eigenfunction decomposition of turbulent channel flow. Int. J. Numer. Meth. Fluids 12, 585-604.
3. Bangia, A. K., Batcho, P. F., Kevrekidis, I. G. & Karniadakis, G. E. 1997 Unsteady 2-d flows in complex geometries: comparative bifurcation studies with global eigenfunction expansions. SIAM J. Sci. Comput. 18, 775-805.
4. Batcho, P. F. & Karniadakis, G. E. 1994 Generalized Stokes eigenfunctions: a new trial basis for the solution of incompressible Navier-Stokes equations. J. Computat. Phys. 115, 121-146.
5. Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. A. Rev. Fluid Mech. 25, 539-575.
6. Cao, N.-Z. & Aubry, N. 1992 Detection of self-similar structures in turbulence: application to wake flows. In Proc. IUTAM Symposium: Eddy Structure Identification in Free Turbulent Shear Flows. Poitiers, France.
7. Dabiri, D. & Gharib, M. 1991 Digital particle image thermometry: the method and implementation. Expts Fluids 11, 77-86.
8. Deane, A. E., Kevrekidis, I. G., Karniadakis, G. E. & Orszag, S. A. 1991 Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders. Phys. Fluids 3, 2337-2354.
9. Devulder, C. & Marion, M. 1992 A class of numerical algorithms for large-time integration: the nonlinear Galerkin method. SIAM J. Numer. Analysis 29, 462-483.
10. Foias, C., Manley, O. & Temam, R. 1988 Modelling of the interaction of small and large eddies in two-dimensional turbulent flows. Math. Modelling Numer. Analysis 22, 93-118.
11. Foias, C., Jolly, M. S., Kevrekidis, I. G. & Titi, E. S. 1994 On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation. Phys. Lett. A 186, 87-96.
12. Garcia-Archilla, B., Novo, J. & Titi, E. S. 1998 Postprocessing the Galerkin method: a novel approach to approximate inertial manifolds. SIAM J. Numer. Analysis 35, 941-972.
13. Garcia-Archilla, B., Novo, J. & Titi, E. S. 1999 An approximate inertial manifold approach to postprocessing the Galerkin method for the Navier-Stokes equations. Math. Computat. 68, 893-911.
14. Glauser, M. N. & George, W. K. 1987 Orthogonal decomposition of the axisymmetric jet mixing layer including azimuthal dependence. In Advances in turbulence (ed. G. Comte-Bellot & J. Mathieu). Springer.
15. Glezer, A., Kadioglu, Z. & Pearlstein, A. J. 1989 Development of an extended proper orthogonal decomposition and its application to a time periodically forced plane mixing layer. Phys. Fluids 1, 1363-1373.
16. Jolly, M. S., Kevrekidis, I. G. & Titi, E. S. 1990 Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: analysis and computations. Physica D 44, 38-60.
17. Karniadakis, G. E. & Sherwin, S. J. 1999 Spectral/hp element methods for CFD. Oxford University Press.
18. Liakopoulos, A., Blythe, P. A. & Gunes, H. 1997 A reduced dynamical model of convective flows in tall laterally heated cavities. Proc. R. Soc. Lond. A 453, 663-672.
19. Ma, X. 2001 Hierarchical Galerkin and non-linear Galerkin models for laminar and turbulent wakes. PhD thesis, Brown University.
20. Ma, X., Karamanos, G.-S. & Karniadakis, G. E. 2000 Dynamics and low-dimensionality in the turbulent near-wake. J. Fluid Mech. 410, 29-65.
21. Noca, F., Park, H. & Gharib, M. 1998 Vortex formation length of a circular cylinder (300 < Re < 4000) using DPIV. In Proc. on Bluff Body Wakes and Vortex-Induced Vibration, ASME Fluids Engineering Division, Washington, DC, 21-25 June.
22. Norberg, C. 1994 An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. J. Fluid Mech. 258, 287-316.
23. Park, H. G. 1998 A study of heat transport processes in the wake of a stationary and oscillating circular cylinder using digital particle image velocimetry/thermometry. PhD thesis, California Institute of Technology.
24. Park, H. G., Dabiri, D. & Gharib, M. 2001 Digital particle image velocimetry/thermometry and application to wake of a heated circular cylinder. Expts Fluids 30, 327-388.
25. Rempfer, D. & Fasel, H. F. 1994 Evolution of three-dimensional coherent structures in a flat-plate boundary layer. J. Fluid Mech. 260, 351-375.
26. Robinson, J. C. 2001 A rigorous treatment of 'experimental' observations for the two-dimensional Navier-Stokes equations. Proc. R. Soc. Lond. A 457, 1007-1020.
27. Sirovich, L. 1987a Turbulence and the dynamics of coherent structures. 1. Coherent structures. Q. Appl. Math. 45, 561-571.
28. Sirovich, L. 1987b Turbulence and the dynamics of coherent structures. 2. Symmetries and transformations. Q. Appl. Math. 45, 573-582.
29. Sirovich, L. 1987c Turbulence and the dynamics of coherent structures. 3. Dynamics and scalings. Q. Appl. Math. 45, 583-590.
30. Temam, R. 1991 Approximation of attractors, large scale simulations and multiscale methods. Proc. R. Soc. Lond. A 434, 23-39.
31. Titi, E. S. 1990 On approximate inertial manifolds to the Navier-Stokes equations. J. Math. Analysis Applic. 169, 540-577.
32. Vernet, A., Kopp, G. A., Ferre, J. A. & Giralt, F. 1997 Simultaneous velocity and temperature patterns in the far region of a turbulent cylinder wake. J. Fluids Engng 119, 463-466.
33. Willert, C. E. & Gharib, M. 1991 Digital particle-image velocimetry. Expts Fluids 10, 181-193.