Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Computing Optimal Forcing Using Laplace Preconditioning
KTH, Skolan för teknikvetenskap (SCI), Mekanik, Stabilitet, Transition, Kontroll. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW. KTH, Centra, SeRC - Swedish e-Science Research Centre.ORCID-id: 0000-0001-9446-7477
KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW. KTH, Centra, SeRC - Swedish e-Science Research Centre.ORCID-id: 0000-0001-9627-5903
KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW. KTH, Centra, SeRC - Swedish e-Science Research Centre.ORCID-id: 0000-0001-7864-3071
2017 (Engelska)Ingår i: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 22, nr 5, s. 1508-1532Artikel i tidskrift (Refereegranskat) Published
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 search for 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 corresponding forcing function. Implementation of the method requires only minor modifications of an existing timestepping code, and is applicable to any partial differential equation containing the Laplacian, such as the Navier-Stokes equations. We discuss the method, first, in the context of the linear Ginzburg-Landau equation and then, the two-dimensional lid-driven cavity flow governed by the Navier-Stokes equations. Most importantly, we demonstrate that for the lid-driven cavity, the optimal forcing can be computed using a factor of up to 500 times fewer operator evaluations than the standard method based on exponential timestepping.

Ort, förlag, år, upplaga, sidor
Cambridge University Press, 2017. Vol. 22, nr 5, s. 1508-1532
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
URN: urn:nbn:se:kth:diva-214476DOI: 10.4208/cicp.OA-2016-0070ISI: 000408436300012Scopus ID: 2-s2.0-85046660943OAI: oai:DiVA.org:kth-214476DiVA, id: diva2:1148490
Forskningsfinansiär
Swedish e‐Science Research Center
Anmärkning

QC 20171011

Tillgänglig från: 2017-10-11 Skapad: 2017-10-11 Senast uppdaterad: 2018-06-19Bibliografiskt granskad
Ingår i avhandling
1. Studies on instability and optimal forcing of incompressible flows
Öppna denna publikation i ny flik eller fönster >>Studies on instability and optimal forcing of incompressible flows
2017 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis considers the hydrodynamic instability and optimal forcing of a number of incompressible flow cases. In the first part, the instabilities of three problems that are of great interest in energy and aerospace applications are studied, namely a Blasius boundary layer subject to localized wall-suction, a Falkner–Skan–Cooke boundary layer with a localized surface roughness, and a pair of helical vortices. The two boundary layer flows are studied through spectral element simulations and eigenvalue computations, which enable their long-term behavior as well as the mechanisms causing transition to be determined. The emergence of transition in these cases is found to originate from a linear flow instability, but whereas the onset of this instability in the Blasius flow can be associated with a localized region in the vicinity of the suction orifice, the instability in the Falkner–Skan–Cooke flow involves the entire flow field. Due to this difference, the results of the eigenvalue analysis in the former case are found to be robust with respect to numerical parameters and domain size, whereas the results in the latter case exhibit an extreme sensitivity that prevents domain independent critical parameters from being determined. The instability of the two helices is primarily addressed through experiments and analytic theory. It is shown that the well known pairing instability of neighboring vortex filaments is responsible for transition, and careful measurements enable growth rates of the instabilities to be obtained that are in close agreement with theoretical predictions. Using the experimental baseflow data, a successful attempt is subsequently also made to reproduce this experiment numerically.

In the second part of the thesis, a novel method for computing the optimal forcing of a dynamical system is developed. The method is based on an application of the inverse power method preconditioned by the Laplace preconditioner to the direct and adjoint resolvent operators. The method is analyzed for the Ginzburg–Landau equation and afterwards the Navier–Stokes equations, where it is implemented in the spectral element method and validated on the two-dimensional lid-driven cavity flow and the flow around a cylinder.

Ort, förlag, år, upplaga, sidor
Stockholm, Sweden: KTH Royal Institute of Technology, 2017. s. 47
Serie
TRITA-MEK, ISSN 0348-467X ; 2017:19
Nyckelord
hydrodynamic stability, optimal forcing, resolvent operator, Laplace preconditioner, spectral element method, eigenvalue problems, inverse power method, direct numerical simulations, Falkner–Skan–Cooke boundary layer, localized roughness, crossflow vortices, Blasius boundary layer, localized suction, helical vortices, lid-driven cavity, cylinder flow
Nationell ämneskategori
Strömningsmekanik och akustik
Forskningsämne
Teknisk mekanik
Identifikatorer
urn:nbn:se:kth:diva-218172 (URN)978-91-7729-622-5 (ISBN)
Disputation
2017-12-14, D3, Lindstedtsvägen 5, Stockholm, 10:00 (Engelska)
Opponent
Handledare
Anmärkning

QC 20171124

Tillgänglig från: 2017-11-24 Skapad: 2017-11-23 Senast uppdaterad: 2020-01-08Bibliografiskt granskad

Open Access i DiVA

Fulltext saknas i DiVA

Övriga länkar

Förlagets fulltextScopus

Personposter BETA

Brynjell-Rahkola, MattiasSchlatter, PhilippHenningson, Dan S.

Sök vidare i DiVA

Av författaren/redaktören
Brynjell-Rahkola, MattiasSchlatter, PhilippHenningson, Dan S.
Av organisationen
Stabilitet, Transition, KontrollLinné Flow Center, FLOWSeRC - Swedish e-Science Research CentreMekanik
I samma tidskrift
Communications in Computational Physics
Beräkningsmatematik

Sök vidare utanför DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetricpoäng

doi
urn-nbn
Totalt: 271 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf