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A method for computing optimal forcing of convectively unstable flows using Laplace preconditioning
KTH, Skolan för teknikvetenskap (SCI), Mekanik, Stabilitet, Transition, Kontroll.ORCID-id: 0000-0001-9446-7477
KTH, Skolan för teknikvetenskap (SCI), Mekanik, Stabilitet, Transition, Kontroll.ORCID-id: 0000-0001-9627-5903
KTH, Skolan för teknikvetenskap (SCI), Mekanik, Stabilitet, Transition, Kontroll.ORCID-id: 0000-0001-7864-3071
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
Abstract [en]

For problems governed by a non-normal operator, the leading eigenvalue of the operator is of limited interest and a more relevant measure of the stability is obtained by considering the harmonic forcing causing the largest system response. Various methods for determining this so-called optimal forcing exist, but they all suffer from great computational expense and are hence not practical for large-scale problems. In the present paper a new method is presented, which is applicable to problems of arbitrary size. The method does not rely on timestepping, but on the solution of linear systems, in which the inverse Laplacian acts as a preconditioner. By formulating the problem of finding the optimal forcing as an eigenvalue problem based on the resolvent operator, repeated system solves amount to power iterations, in which the dominant eigenvalue is seen to correspond to the energy amplification in a system for a given frequency, and the eigenfunction to the optimal forcing function. Implementation of the method requires only minor modifications of an existing time-stepping code, and is applicable to any partial differential equation containing the Laplacian, such as the Navier-Stokes equations. We discuss it in the context of the linear Ginzburg-Landau equation.

HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-175352OAI: oai:DiVA.org:kth-175352DiVA, id: diva2:860468
Merknad

QS 2015

Tilgjengelig fra: 2015-10-12 Laget: 2015-10-12 Sist oppdatert: 2015-10-15bibliografisk kontrollert
Inngår i avhandling
1. Global stability analysis of three-dimensional boundary layer flows
Åpne denne publikasjonen i ny fane eller vindu >>Global stability analysis of three-dimensional boundary layer flows
2015 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis considers the stability and transition of incompressible boundary layers. In particular, the Falkner–Skan–Cooke boundary layer subject to a cylindrical surface roughness, and the Blasius boundary layer with applied localized suction are investigated. These flows are of great importance within the aviation industry, feature complex transition scenarios, and are strongly three-dimensional in nature. Consequently, no assumptions regarding homogeneity in any of the spatial directions are possible, and the stability of the flow is governed by an extensive three-dimensional eigenvalue problem.

The stability of these flows is addressed by high-order direct numerical simulations using the spectral element method, in combination with a Krylov subspace projection method. Such techniques target the long-term behavior of the flow and can provide lower limits beyond which transition is unavoidable. The origin of the instabilities, as well as the mechanisms leading to transition in the aforementioned cases are studied and the findings are reported.

Additionally, a novel method for computing the optimal forcing of a dynamical system is developed. This type of analysis provides valuable information about the frequencies and structures that cause the largest energy amplification in the system. The method is based on the inverse power method, and is discussed in the context of the one-dimensional Ginzburg–Landau equation and a two-dimensional flow case governed by the Navier–Stokes equations.

sted, utgiver, år, opplag, sider
KTH Royal Institute of Technology, 2015. s. x, 30
Serie
TRITA-MEK, ISSN 0348-467X ; 2015:07
Emneord
Hydrodynamic stability, transition to turbulence, global analysis, boundary layers, roughness, laminar flow control, Stokes/Laplace preconditioner, optimal forcing, crossflow vortices, Ginzburg-Landau, Falkner-Skan-Cooke, Blasius, lid-driven cavity
HSV kategori
Identifikatorer
urn:nbn:se:kth:diva-175353 (URN)978-91-7595-725-8 (ISBN)
Presentation
2015-10-30, D3, Lindstedtsvägen 5, KTH, Stockholm, 13:00 (engelsk)
Opponent
Veileder
Merknad

QC 20151015

Tilgjengelig fra: 2015-10-15 Laget: 2015-10-12 Sist oppdatert: 2020-01-08bibliografisk kontrollert

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