Slow-fast decomposition of an inertialess flow of viscoelastic fluids

Binh K. Lieu; Mihailo R. Jovanovic

doi:10.1109/acc.2012.6315679

Slow-fast decomposition of an inertialess flow of viscoelastic fluids

Binh K. Lieu, Mihailo R. Jovanovic

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

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 language	English (US)
Title of host publication	2012 American Control Conference, ACC 2012
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4369-4374
Number of pages	6
ISBN (Print)	9781457710957
DOIs	https://doi.org/10.1109/acc.2012.6315679
State	Published - 2012
Event	2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: Jun 27 2012 → Jun 29 2012

Publication series

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

Other

Other	2012 American Control Conference, ACC 2012
Country/Territory	Canada
City	Montreal, QC
Period	6/27/12 → 6/29/12

Keywords

Energy amplification
frequency responses
singular perturbation analysis
viscoelastic fluids

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10.1109/acc.2012.6315679

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Slow-fast decomposition of an inertialess flow of viscoelastic fluids. / Lieu, Binh K.; Jovanovic, Mihailo R.
2012 American Control Conference, ACC 2012. Institute of Electrical and Electronics Engineers Inc., 2012. p. 4369-4374 6315679 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Lieu, BK & Jovanovic, MR 2012, Slow-fast decomposition of an inertialess flow of viscoelastic fluids. in 2012 American Control Conference, ACC 2012., 6315679, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 4369-4374, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 6/27/12. https://doi.org/10.1109/acc.2012.6315679

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abstract = "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.",

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N2 - 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.

AB - 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.

KW - Energy amplification

KW - frequency responses

KW - singular perturbation analysis

KW - viscoelastic fluids

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PB - Institute of Electrical and Electronics Engineers Inc.

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Y2 - 27 June 2012 through 29 June 2012

ER -

Slow-fast decomposition of an inertialess flow of viscoelastic fluids

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