Structural and Multidisciplinary Optimization

, Volume 30, Issue 3, pp 181–192 | Cite as

Topology optimization of channel flow problems

  • A. Gersborg-HansenEmail author
  • O. Sigmund
  • R.B. Haber
Research Paper


This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low-to-moderate Reynolds numbers. This makes the flow problem nonlinear and hence a nontrivial extension of the work of Borrvall and Petersson (2003).Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity-driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc.


Viscous flow Topology optimization Finite element method Sensitivity analysis FEMLAB  


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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Solid MechanicsTechnical University of DenmarkLyngbyDenmark
  2. 2.Department of MathematicsTechnical University of DenmarkLyngbyDenmark
  3. 3.Department of Theoretical & Applied MechanicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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