Topology optimization of channel flow problems

A. Gersborg-Hansen, O. Sigmund, R. B. Haber

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)181-192
Number of pages12
JournalStructural and Multidisciplinary Optimization
Issue number3
StatePublished - Sep 2005


  • Finite element method
  • Sensitivity analysis
  • Topology optimization
  • Viscous flow

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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