Stability analysis of fluid flows using sum-of-squares

Author

Goulart, P.J. ; Chernyshenko, S.I.

Author_Institution

Dept. of Aeronaut., Imperial Coll. London, London, UK

fYear

2010

fDate

June 30 2010-July 2 2010

Firstpage

2971

Lastpage

2976

Abstract

In this paper we present a new method for assessing the stability of finite-dimensional approximations to the Navier-Stokes equation for fluid flows. Approximations to the Navier-Stokes equation typically take the form of a set of linear ODEs with an additional bilinear term that conserves the total energy of the system state. We suggest a structured method for generating Lyapunov functions using sum-of-squares optimization that exploits this energy conservation property. We provide a numerical example demonstrating the use of this technique to assess the stability of a model of a shear flow between infinite parallel plates.

Keywords

Lyapunov methods; Navier-Stokes equations; flow instability; flow simulation; linear differential equations; optimisation; shear flow; Lyapunov functions; Navier-Stokes equation; bilinear term; energy conservation property; finite-dimensional approximations; fluid flows; infinite parallel plates; linear ODE; shear flow model; stability analysis; structured method; sum-of-square optimization; system state; total energy; Boundary conditions; Differential equations; Energy conservation; Fluid flow; Fluid flow control; Lyapunov method; Navier-Stokes equations; Optimization methods; Polynomials; Stability analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2010

Conference_Location

Baltimore, MD

ISSN

0743-1619

Print_ISBN

978-1-4244-7426-4

Type

conf

DOI

10.1109/ACC.2010.5531305

Filename

5531305