Global parametric solutions of scalar transport

Journal of Computational Physics

Volumn 227, Issue 6, 2008, Pages 3032-3057

  Lester, D R ^a   Rudman, M ^a   Metcalfe, G ^a   Blackburn, H M ^b  

^a CSIRO   (Australia)

^b MONASH UNIVERSITY   (Australia)

Author keywords

Chaotic advection diffusion; Numerical methods; Parametric variation; Strange eigenmodes

Indexed keywords

ADVECTION; DIFFUSION; LOCKS (FASTENERS);

ADVECTION - DIFFUSION; ADVECTION-DIFFUSION EQUATION; CHAOTIC ADVECTION; CHAOTIC ADVECTION-DIFFUSION; CHAOTIC FLOWS; EIGEN MODES; PARAMETRIC VARIATION; SCALAR-TRANSPORT; STRANGE EIGENMODE; TRANSPORT RATE;

NUMERICAL METHODS;

EID: 38749154246     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.10.015     Document Type: Article

References (34)

1. Adrover A., Cerbelli S., and Giona M. A spectral approach to reaction/diffusion kinetics in chaotic flows. Computers and Chemical Engineering 26 (2002) 125-139
2. Chella R., and Ottino J.M. Conversion and selectivity modifications due to mixing in unpremixed reactors. Chemical Engineering Science 39 (1984) 551-567
3. Ganesan V., Bryden M.D., and Brenner H. Chaotic heat transfer enhancement in rotating annular flow systems. Physics of Fluids 9 5 (1997) 1296-1306
4. Gilmore R. Baker-Campbell-Hausdorff formulas. Journal of Mathematical Physics 15 (1974) 2090-2092
5. Giona M., Ceribelli S., and Vitacolonna V. Universality and imaginary potentials in advection-diffusion equations in closed flows. Journal of Fluid Mechanics 513 (2004) 221-237
6. Glazier J.A., and Libchaber A. Quasi-periodicity and dynamical systems: an experimentalists view. IEEE Transactions on Circuits and Systems 35 7 (1988) 790-809
7. Golub G.H., and Van Loan C.F. Matrix Computations (1991), Johns Hopkins University Press, Baltimore, MD, USA
8. Golub G.H., and van der Vorst H.A. Eigenvalue computation in the 20th century. Journal of Computational and Applied Mathematics 123 (2000) 35-65
9. Gottlieb D., and Orszag S.A. Numerical Analysis of Spectral Methods: Theory and Applications (1977), Society for Industrial and Applied Mathematics, Philadelphia, PA, USA
10. Haynes P.H., and Vanneste J. What controls the decays of passive scalars in smooth flows?. Physics of Fluids 17 9 (2005) 097103-1-097103-16
11. Hwu T.-Y., Young D.-L., and Chen Y.-Y. Chaotic advections for stokes flow in circular cavity. Journal of Engineering Mechanics 123 8 (1997) 774-782
12. Jana S.C., Metcalfe G., and Ottino J.M. Experimental and computational studies of mixing in complex stokes flows: the vortex mixing flow and multicellular cavity flows. Journal of Fluid Mechanics 269 (1994) 199-246
13. Kirtland J.D., McGraw G.J., and Stroock A.D. Mass transfer to relative boundaries from steady three-dimensional flows in microchannels. Physics of Fluids 18 (2006) 073602-1-073602-13
14. Kusch H.A., and Ottino J.M. Experiments on mixing in continuous flows. Journal of Fluid Mechanics 236 (1992) 319-348
15. Lefèvre A., Mota J.P.B., Rodrigo A.J.S., and Saatjian E. Chaotic advection and heat transfer enhancement in Stokes flow. International Journal of Heat and Fluid Flow 24 (2003) 310-321
16. D.R. Lester, G. Metcalfe, M. Rudman, Low Reynolds number scalar transport enhancement in viscous and non-Newtonian fluids, International Journal of Heat and Mass Transfer, submitted for publication.
17. D.R. Lester, G. Metcalfe, M. Rudman, Complete parametric solutions of scalar transport, Physics Review Letters, submitted for publication.
18. Levin D. Fast integration of rapidly oscillatory functions. Journal of Computational and Applied Mathematics 67 (1996) 95-101
19. Liu W., and Haller G. Strange eigenmodes and decay of variance in the mixing of diffusive tracers. Physica D 188 (2004) 1-39
20. Magnus W. On the exponential solution of differential equations for a linear operator. Communications in Pure and Applied Mathematics 7 (1954) 649-654
21. Metcalfe G., Rudman M., Brydon A., Graham L.J.W., and Hamilton R. Composing chaos: An experimental and numerical study of an open duct mixing flow. AIChE Journal 52 (2006) 9-28
22. Müller S.D., Mezić I., Walther J.H., and Koumoutsakos P. Transverse momentum micromixer optimization with evolution strategies. Computers and Fluids 33 (2004) 521-531
23. Ottino J.M. The Kinematics of Mixing: Stretching, Chaos and Transport (1989), Cambridge University Press, Cambridge
24. J.M. Ottino, G. Metcalfe, S.C. Jana, Experimental studies of chaotic mixing, in: W. Ditto, L. Pecora, M. Shleshinger, M. Spano, S. Vohra, (Eds.), Proceedings of the Second Experimental Chaos Conference, Office of Naval Research, 1995.
25. Pierrehumbert R.T. Tracer microstructure in the large-eddy dominated regime. Chaos, Solitons and Fractals 4 6 (1994) 1091-1110
26. Rodrigo A.J.S., Mota J.P.B., Lefèvre A., and Saatdjin E. On the optimization of mixing protocol in a certain class of three-dimensional Stokes flows. Physics of Fluids 15 6 (2003) 1505-1516
27. Rothstein D., Henry E., and Gollub J.P. Persistent patterns in transient chaotic fluid mixing. Nature 401 (1999) 770-772
28. Saatdjin E., Midoux N., Gastou Chassiang M.I., Leprevost J.C., and André J.C. Chaotic mixing and heat transfer between confocal ellipses: experimental and numerical results. Physics of Fluids 8 3 (1996) 677-691
29. Speetjens M., Metcalfe G., and Rudman M. Topological mixing study of non-Newtonian duct flows. Physics of Fluids (1999)
30. A.D. Stroock, G.J. McGraw, Investigation of the staggered herringbone mixer with a simple analytical model, in: J.M. Ottino, S. Wiggins, (Eds.), Transport and mixing at the microscale, Philosophical Transactions of The Royal Society of London, 2004.
31. Suzuki M. Hybrid Exponential product formulas for unbounded operators with possible applications to Monte Carlo simulations. Physics Letters A 201 5 (1995) 425-428
32. Tel T., de Moura A., Grebogi C., and Károlyi G. Chemical and biological activity in open flows: a dynamical system approach. Physics Reports 413 (2005) 191-196
33. Toussaint V., Carrière P., Scott J., and Gence J.-N. Spectral decay of a passive scalar in chaotic mixing. Physics of Fluids 12 11 (2000) 2834-2844
34. Zhong W.-X. On precise integration method. Journal of Computational and Applied Mathematics 163 (2004) 59-78