Reduced order modeling for fluid flows based on nonlinear balanced truncation

Samir Sahyoun; Jin Dong; Seddik M. Djouadi

doi:10.1109/acc.2013.6580013

Reduced order modeling for fluid flows based on nonlinear balanced truncation

Samir Sahyoun, Jin Dong, Seddik M. Djouadi

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

6 Scopus citations

Abstract

For a vast variety of fluid flows the dynamics are governed by the Navier-Stokes equations which are highly nonlinear. In particular, the corresponding Galerkin models involve a quadratic type nonlinearity. The latter incudes the Burgers' equation as well. In this paper, a computational algorithm for nonlinear balanced truncation of the Galerkin models is proposed. The method is based on Taylor series expansion in which the computation of successively higher order terms reduces to solving consecutively higher order systems of linear algebraic equations. This procedure is also used to compute the coordinate transformation that yields the balanced system. Formulas to compute the nonlinear controllability, observability functions and coordinate transformation are derived.

Original language	English
Title of host publication	2013 American Control Conference, ACC 2013
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1284-1289
Number of pages	6
ISBN (Print)	9781479901777
DOIs	https://doi.org/10.1109/acc.2013.6580013
State	Published - 2013
Externally published	Yes
Event	2013 1st American Control Conference, ACC 2013 - Washington, DC, United States Duration: Jun 17 2013 → Jun 19 2013

Publication series

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

Conference

Conference	2013 1st American Control Conference, ACC 2013
Country/Territory	United States
City	Washington, DC
Period	06/17/13 → 06/19/13

Access to Document

10.1109/acc.2013.6580013

Cite this

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title = "Reduced order modeling for fluid flows based on nonlinear balanced truncation",

abstract = "For a vast variety of fluid flows the dynamics are governed by the Navier-Stokes equations which are highly nonlinear. In particular, the corresponding Galerkin models involve a quadratic type nonlinearity. The latter incudes the Burgers' equation as well. In this paper, a computational algorithm for nonlinear balanced truncation of the Galerkin models is proposed. The method is based on Taylor series expansion in which the computation of successively higher order terms reduces to solving consecutively higher order systems of linear algebraic equations. This procedure is also used to compute the coordinate transformation that yields the balanced system. Formulas to compute the nonlinear controllability, observability functions and coordinate transformation are derived.",

author = "Samir Sahyoun and Jin Dong and Djouadi, {Seddik M.}",

year = "2013",

doi = "10.1109/acc.2013.6580013",

language = "English",

isbn = "9781479901777",

series = "Proceedings of the American Control Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "1284--1289",

booktitle = "2013 American Control Conference, ACC 2013",

note = "2013 1st American Control Conference, ACC 2013 ; Conference date: 17-06-2013 Through 19-06-2013",

}

Sahyoun, S, Dong, J & Djouadi, SM 2013, Reduced order modeling for fluid flows based on nonlinear balanced truncation. in 2013 American Control Conference, ACC 2013., 6580013, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1284-1289, 2013 1st American Control Conference, ACC 2013, Washington, DC, United States, 06/17/13. https://doi.org/10.1109/acc.2013.6580013

Reduced order modeling for fluid flows based on nonlinear balanced truncation. / Sahyoun, Samir; Dong, Jin; Djouadi, Seddik M.
2013 American Control Conference, ACC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1284-1289 6580013 (Proceedings of the American Control Conference).

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

TY - GEN

T1 - Reduced order modeling for fluid flows based on nonlinear balanced truncation

AU - Sahyoun, Samir

AU - Dong, Jin

AU - Djouadi, Seddik M.

PY - 2013

Y1 - 2013

N2 - For a vast variety of fluid flows the dynamics are governed by the Navier-Stokes equations which are highly nonlinear. In particular, the corresponding Galerkin models involve a quadratic type nonlinearity. The latter incudes the Burgers' equation as well. In this paper, a computational algorithm for nonlinear balanced truncation of the Galerkin models is proposed. The method is based on Taylor series expansion in which the computation of successively higher order terms reduces to solving consecutively higher order systems of linear algebraic equations. This procedure is also used to compute the coordinate transformation that yields the balanced system. Formulas to compute the nonlinear controllability, observability functions and coordinate transformation are derived.

AB - For a vast variety of fluid flows the dynamics are governed by the Navier-Stokes equations which are highly nonlinear. In particular, the corresponding Galerkin models involve a quadratic type nonlinearity. The latter incudes the Burgers' equation as well. In this paper, a computational algorithm for nonlinear balanced truncation of the Galerkin models is proposed. The method is based on Taylor series expansion in which the computation of successively higher order terms reduces to solving consecutively higher order systems of linear algebraic equations. This procedure is also used to compute the coordinate transformation that yields the balanced system. Formulas to compute the nonlinear controllability, observability functions and coordinate transformation are derived.

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BT - 2013 American Control Conference, ACC 2013

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2013 1st American Control Conference, ACC 2013

Y2 - 17 June 2013 through 19 June 2013

ER -

Reduced order modeling for fluid flows based on nonlinear balanced truncation

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