Slow-fast decomposition of an inertialess flow of viscoelastic fluids

Binh K. Lieu, Mihailo R. Jovanovic

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We study frequency responses of an inertialess two-dimensional channel flow of viscoelastic fluids. By rewriting the evolution equations in terms of low-pass filtered versions of the stream function, we show that strongly-elastic flows can be brought into a standard singularly perturbed form that exhibits a slow-fast decomposition. In high-Weissenberg number regime, which is notoriously difficult to study numerically, we demonstrate that the frequency responses are reliably captured by the dynamics of the fast subsystem. We use numerical computations to validate our theoretical findings and to illustrate that our formulation does not suffer from spurious numerical instabilities.

Original languageEnglish (US)
Title of host publication2012 American Control Conference, ACC 2012
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781457710957
StatePublished - 2012
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2012 American Control Conference, ACC 2012
CityMontreal, QC


  • Energy amplification
  • frequency responses
  • singular perturbation analysis
  • viscoelastic fluids

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