Topology optimization of fluids in Stokes flow

We consider topology optimization of fluids in Stokes flow. The design objective is to minimize a power function, which for the absence of body fluid forces is the dissipated power in the fluid, subject to a fluid volume constraint. A generalized Stokes problem is derived that is used as a base for...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2003-01, Vol.41 (1), p.77-107
Main Authors: Borrvall, Thomas, Petersson, Joakim
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Laminar flows
Low-reynolds-number (creeping) flows
Physics
TECHNOLOGY
TEKNIKVETENSKAP
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Summary:We consider topology optimization of fluids in Stokes flow. The design objective is to minimize a power function, which for the absence of body fluid forces is the dissipated power in the fluid, subject to a fluid volume constraint. A generalized Stokes problem is derived that is used as a base for introducing the design parameterization. Mathematical proofs of existence of optimal solutions and convergence of discretized solutions are given and it is concluded that no regularization of the optimization problem is needed. The discretized state problem is a mixed finite element problem that is solved by a preconditioned conjugate gradient method and the design optimization problem is solved using sequential separable and convex programming. Several numerical examples are presented that illustrate this new methodology and the results are compared to results obtained in the context of shape optimization of fluids. Copyright © 2003 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
1097-0363
DOI:10.1002/fld.426