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Topology optimization of regions of Darcy and Stokes flow
Linköping University, Department of Management and Engineering, Mechanics . Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Mechanics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-8460-0131
Linköping University, Department of Management and Engineering. Linköping University, The Institute of Technology.
2006 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 69, no 7, 1374-1404 p.Article in journal (Refereed) Published
Abstract [en]

This paper treats the topology optimization problem of obtaining an optimal layout of regions of Darcy and Stokes flow, where the objective is the total potential power functional representing average fluid pressure. It extends the work of Borrvall and Petersson, which concerned optimal layout of Stokes flow only. A generalization of Stokes' equations is derived and used as state constraints in the optimization problem. A proof of existence of solutions is provided, and it is seen that although the corresponding proof in Borrvall and Petersson does not need regularization, the present one does. It is also concluded that linear interpolations of state parameters will result in black and white (unfiltered) designs. The method is tested on an area-to-point flow problem of the type discussed by Bejan, where the influence of various parameters and numerical strategies on the design are studied.

Place, publisher, year, edition, pages
2006. Vol. 69, no 7, 1374-1404 p.
Keyword [en]
Topology optimization, fluid mechanics, mixed Darcy-Stokes flow, finite element method
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:liu:diva-14851DOI: 10.1002/nme.1811OAI: oai:DiVA.org:liu-14851DiVA: diva2:25356
Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2017-12-13
In thesis
1. Optimization in Continuum Flow Problems
Open this publication in new window or tab >>Optimization in Continuum Flow Problems
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The work presented in this dissertation was carried out at the Division ofMechanics, Department of Management and Engineering at Link¨oping University,between 2003 and 2008. It was supervised by Prof. Anders Klarbring,head of the division, and financially supported by the National GraduateSchool of Scientific Computing (NGSSC) and the Swedish Research Council(VR).

There are many people to whom I would like to express my gratitude: firstand foremost I would like to thank my supervisor Prof. Anders Klarbring forhis help, support and endless patience during our discussions, and for alwayshaving time to read and comment on the numerous drafts that eventually ledto the research manuscripts presented in this thesis. I would also like to thankmy co–supervisor Dr. Thomas Borrvall for all his help regarding numericalissues, especially with the implementation of the models. Moreover, I wouldlike to thank present and former colleagues for their inspiration and assistanceduring my time as a graduate student at the division.

Last but not least, I am very grateful for having a family that has alwaysbeen there to support me, and for all my friends who enrich my life outsidethe office walls in more ways then I can say.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2008. 37 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1196
Keyword
Fluid mechanics, Continuum flow problem
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:liu:diva-14857 (URN)9789173938518 (ISBN)
Public defence
2008-09-19, C3, C-huset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2017-12-14Bibliographically approved
2. Topology optimization in fluid flow problems
Open this publication in new window or tab >>Topology optimization in fluid flow problems
2006 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, the topic of topology optimization in fluids is studied. With emphasis on modeling aspects, the general framework for formulating such problems is presented through a derivation of a sample problem. A survey of the literature, summarizing the developments in the area, forms the first part of the thesis.

The second part consists of two new contributions to this field. In the first paper, the problem of finding the optimal topology of fluid channels in a permeable material is examined. Theoretical results include proof of existence of solutions, as well as conditions for obtaining completely discrete designs. Numerical examples are provided to demonstrate the method.

Using methodologies from topology opt imization, in paper two, a design method is proposed for creating optimal bottom profiles for shallow water flow systems. Although this is not a topology optimization problem, since a continuous solution is sought, several results carry over due to a close relation to the problem described in the first paper.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2006. 35 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1278
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-41382 (URN)55914 (Local ID)91-85643-69-6 (ISBN)55914 (Archive number)55914 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-12-12

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Wiker, NiclasKlarbring, Anders Borrvall, Thomas

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