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Optimization in Continuum Flow Problems
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
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 [en]
Fluid mechanics, Continuum flow problem
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:liu:diva-14857ISBN: 9789173938518 (print)OAI: oai:DiVA.org:liu-14857DiVA: diva2:25362
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
List of papers
1. Topology optimization of regions of Darcy and Stokes flow
Open this publication in new window or tab >>Topology optimization of regions of Darcy and Stokes flow
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.

Keyword
Topology optimization, fluid mechanics, mixed Darcy-Stokes flow, finite element method
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:liu:diva-14851 (URN)10.1002/nme.1811 (DOI)
Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2017-12-13
2. Simplified shallow water flow equations and their potential use in bottom profile optimization
Open this publication in new window or tab >>Simplified shallow water flow equations and their potential use in bottom profile optimization
2007 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 87, no 11-12, 792-808 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, an optimization method for systems described by linearizedviscous shallow water equations is proposed. It can potentially be used tooptimize bottom profiles and is based on techniques commonly found in thearea of topology optimization of structures, but with the difference that acontinuous, and not discrete, design is sought. The presentation includes aderivation and linearization of the stationary viscous shallow water equations,which are used as state equations in the optimization problem. The finalproblem definition is closely related to the Darcy–Stokes fluid flow topologyoptimization problem, from which many results are derived by analogy.

From the numerical examples it is concluded that natural–like designscan be created for proper choices of parameter values. However, presentlythe model is not physically validated and its exact domain of application isnot yet known.

Keyword
Shallow water flow, bottom profile optimization, topology optimization
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:liu:diva-14852 (URN)10.1002/zamm.200610356 (DOI)
Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2017-12-13Bibliographically approved
3. Applications of Bottom Profile Optimization in Linear Viscous Shallow Water Flow
Open this publication in new window or tab >>Applications of Bottom Profile Optimization in Linear Viscous Shallow Water Flow
2007 (English)In: Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization, Seoul, Korea, May 2007, Guseong-dong, Yuseong-gu, Daejeon, Republic of Korea: ISSMO , 2007, 2283-2292 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, the design method for creating optimal bottom profiles inshallow water flow problems, proposed in Wiker et al., is investigated further.The method was inspired by techniques commonly found in the area oftopology optimization of structures, and uses the linear viscous shallow water

equations as state equations in the optimization problem. In Wiker et al.,an area–to–point flow problem was investigated, seeking the bottom profilewhich most efficiently transports a fluid added inside the domain, towards apoint on the boundary. Specifically, the influence on the solution of some ofthe problem parameters was tested, and it was concluded that natural–likedesigns can be created for proper choices of parameter values.In the present work, bottom profiles of two other problem types are studied— the point–to–line problem and the line–to–line problem. In the firstproblem, in order to mimic a river delta, an inflow is prescribed on a smallpart (point) of the boundary of a domain. To exit the domain on the oppositeside, the fluid is forced to pass a line of limited depth. For the secondproblem, a number of inflows are prescribed on one side (inflow line) of a rectangular domain and the fluid is then allowed to exit anywhere on theopposite side (outflow line). This can be seen as modeling the spillway frome.g. a dam.

Place, publisher, year, edition, pages
Guseong-dong, Yuseong-gu, Daejeon, Republic of Korea: ISSMO, 2007
Keyword
Optimal bottom profile shallow water equations point-to-line flow line-to-flow
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:liu:diva-14853 (URN)
Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2017-05-15
4. Topology Optimization Applied to Crack Patterns in Drying Porous Material
Open this publication in new window or tab >>Topology Optimization Applied to Crack Patterns in Drying Porous Material
2008 (English)Manuscript (preprint) (Other academic)
Abstract [en]

Based on topology optimization techniques, a model for crack formation indrying porous materials is developed. The state problem derived representsthe mulitphysic flow of a mixture of fluid (air) and moister. A topologyoptimization problem is defined, where the layout (topology) of cracks andporous material, as well as the length scale of the crack pattern are used asoptimization variables. The problem is solved using a two–stage continuationmethod, labelled phase I and phase II. In phase I, a relaxed version of theproblem is solved to generate“clever”initial guesses for phase II. In the secondphase, the full problem is solved using a ten–step procedure. Two examplesare provided showing the dependence on different problem parameters, and,given the limitations in the model, the results show nature–like trends.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:liu:diva-14855 (URN)
Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2017-05-15
5. A General Multiphysic Model for Planar (2D) Flow Problems
Open this publication in new window or tab >>A General Multiphysic Model for Planar (2D) Flow Problems
2008 (English)Report (Other academic)
Abstract [en]

A general 2D model for fluid flow mixed with heat/mass transfer is developed.The aim is to derive a framework of planar state equations that includes someboundary effects in the out–of–plane dimension to be used in multiphysicproblems. The use of the framework is demonstrated by deriving a slightextension to an existing model for mixed fluid/heat flow.

Publisher
16 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:liu:diva-14856 (URN)LIU–IEI–R--08/0026--SE (ISRN)
Available from: 2008-09-26 Created: 2008-09-26 Last updated: 2017-05-15

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