Computational Hydrodynamic Stability and Flow Control Based on Spectral Analysis of Linear Operators
2012 (English)In: Archives of Computational Methods in Engineering, ISSN 1134-3060, E-ISSN 1886-1784, Vol. 19, no 3, 341-379 p.Article, review/survey (Refereed) Published
This paper considers the analysis and control of fluid flows using tools from dynamical systems and control theory. The employed tools are derived from the spectral analysis of various linear operators associated with the Navier-Stokes equations. Spectral decomposition of the linearized Navier-Stokes operator, the Koopman operator, the spatial correlation operator and the Hankel operator provide a means to gain physical insight into the dynamics of complex flows and enables the construction of low-dimensional models suitable for control design. Since the discretization of the Navier-Stokes equations often leads to very large-scale dynamical systems, matrix-free and in some cases iterative techniques have to be employed to solve the eigenvalue problem. The common theme of the numerical algorithms is the use of direct numerical simulations. The theory and the algorithms are exemplified on flow over a flat plate and a jet in crossflow, as prototypes for the laminar-turbulent transition and three-dimensional vortex shedding.
Place, publisher, year, edition, pages
2012. Vol. 19, no 3, 341-379 p.
Plate Boundary-Layer, Rank Smith Method, Model-Reduction, Cylinder Wake, Lyapunov Equations, Cross-Flow, 3-Dimensional Instability, Elliptic Instability, Balanced-Truncation, Separation-Bubbles
Fluid Mechanics and Acoustics
IdentifiersURN: urn:nbn:se:kth:diva-102613DOI: 10.1007/s11831-012-9074-0ISI: 000307755100001ScopusID: 2-s2.0-84865597795OAI: oai:DiVA.org:kth-102613DiVA: diva2:555662
FunderSwedish Research Council, VR-DNR 2010-3910Swedish e‐Science Research Center
QC 201209212012-09-212012-09-212013-04-08Bibliographically approved