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Abstract
This thesis investigates how to apply topology optimization using
the material distribution technique to steadystate viscous
incompressible flow problems. The target design applications are
fluid devices that are optimized with respect to minimizing the
energy loss, characteristic properties of the velocity field or
mixing properties.
To reduce the computational complexity of the topology optimization
problems the primary focus is put on the Stokes equation in 2D and
in 3D. However, the thesis also contains examples with the 2D
NavierStokes equation as well as an example with convection
dominated transport in 2D Stokes flow. Using Stokes flow limits the
range of applications; nonetheless, the thesis gives a
proofofconcept for the application of the method within fluid
dynamic problems and it remains of interest for the design of
microfluidic devices.
Furthermore, the thesis contributes to the development of the
topology optimization method by studying different problem
formulations related to topology optimization of fluid problems. In
addition, the COMSOL software has been used as a post processing
tool. Prior to design manufacturing this allows the engineer to
quantify the performance of the computed topology design using
standard, credible analysis tools with a bodyfitted mesh. Also, the
thesis encompasses work on how to utilize the finite volume method
(FVM) in the topology optimization context. This is motivated by the
momentous position the FVM has in the fluid dynamics community.
Although the study of the FVM is carried out using a simple heat
conduction problem, the work illuminates and discusses the
technicalities of employing the FVM in connection with topology
optimization.
Finally, parallelized solution methods are investigated using the
high performance computing facility at the Technical University of
Denmark. Large topology optimization problems with 2D and 3D Stokes
flow modeling are solved with direct and iterative strategies
employing the parallelized Sun Performance Library and the OpenMP
parallelization technique, respectively.
Original language  English 

Number of pages  202 

ISBN (Print)  8790416236 
Publication status  Published  May 2007 
Series  DCAMM Special Report 

Number  S96 
ISSN  09031685 
Bibliographical note
This thesis work received support from the Research School within the Danish Center for Applied Mathematics and Mechanics ( DCAMM )Keywords
 Finite volume
 Parallel solution
 Multiphysics
 Topology optimization
 Direct solution
 Fluid dynamics
 Iterative solution
 Finite element
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Projects
 1 Finished

Topologioptimering af strømninger under multifysisk belastning
Gersborg, A. R., Bendsøe, M. P., Sigmund, O., Othmer, C., Pironneau, O. & Lund, E.
01/02/2004 → 31/05/2007
Project: PhD