Optimizing the source distribution in fluid mixing

Physica D: Nonlinear Phenomena

Volumn 237, Issue 7, 2008, Pages 918-929

  Thiffeault, Jean Luc ^a   Pavliotis, Grigorios A ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Advection diffusion equation; Mixing; Optimization; Stirring

Indexed keywords

ADVECTION; DIFFUSION; LAGRANGE MULTIPLIERS; MIXING; OPTIMIZATION; PARAMETER ESTIMATION; THERMAL EFFECTS;

ADVECTION-DIFFUSION EQUATION; FLUID MIXING; OPTIMAL SOURCE DISTRIBUTIONS; STIRRING;

FLOW VELOCITY;

EID: 42249110376     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.11.013     Document Type: Article

References (18)

1. Franjione J.G., and Ottino J.M. Symmetry concepts for the geometric analysis of mixing flows. Philos. Trans.: Phys. Sci. Eng. 338 1650 (1992) 301-323
2. Grigoriev R.O. Chaotic mixing in thermocapillary-driven microdroplets. Phys. Fluids 17 (2005) 033601
3. Mezić I., and Wiggins S. On the integrability and perturbation of three-dimensional fluid flows with symmetry. J. Nonlinear Sci. 4 2 (1994) 157-194
4. Solomon T.H., and Mezić I. Uniform resonant chaotic mixing in fluid flows. Nature 425 (2003) 365-380
5. D'Alessandro D., Dahleh M., and Mezić I. Control of mixing in fluid flow: A maximum entropy approach. IEEE Trans. Automat. Control 44 10 (1999) 1852-1863
6. Balogh A., Aamo O.M., and Krstic M. Optimal mixing enhancement in 3-d pipe flow. IEEE Trans. Control Sys. Tech. 13 (2005) 27-41
7. Vikhansky A. Enhancement of laminar mixing by optimal control methods. Chem. Eng. Sci. 57 14 (2002) 2719-2725
8. Thiffeault J.-L., and Finn M.D. Topology, braids, and mixing in fluids. Phil. Trans. R. Soc. Lond. A 364 (2006) 3251-3266
9. Sharma A., and Gupte N. Control methods for problems of mixing and coherence in chaotic maps and flows. Pramana-J. Phys. 48 (1997) 231-248
10. Andrievskii B.R., and Fradlov A.L. Control of chaos: Methods and applications. II. Applications, Autom. Remote Control 65 4 (2004) 505-533
11. Mathew G., Mezić I., and Petzold L. A multiscale measure for mixing. Physica D 211 1-2 (2005) 23-46
12. Mathew G., Mezić I., Grivopoulos S., Vaidya U., and Petzold L. Optimal control of mixing in Stokes fluid flows. J. Fluid Mech. 580 (2007) 261-281
13. Doering C.R., and Thiffeault J.-L. Multiscale mixing efficiencies for steady sources. Phys. Rev. E 74 2 (2006) 025301R
14. Shaw T.A., Thiffeault J.-L., and Doering C.R. Stirring up trouble: Multi-scale mixing measures for steady scalar sources. Physica D 231 2 (2007) 143-164
15. Thiffeault J.-L., Doering C.R., and Gibbon J.D. A bound on mixing efficiency for the advection-diffusion equation. J. Fluid Mech. 521 (2004) 105-114
16. Plasting S., and Young W.R. A bound on scalar variance for the advection-diffusion equation. J. Fluid Mech. 552 (2006) 289-298
17. Wigner E.P. Group Theory and its Application to the Theory of Atomic Spectra (1959), Academic Press, New York
18. Hamermesh M. Group Theory and its Application to Physical Problems (1989), Dover, New York