A “poor man’s” approach to topology optimization of natural convection problems

Janus Asmussen, Joe Alexandersen, Ole Sigmund, Casper Schousboe Andreasen*

*Corresponding author for this work

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Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational effort by use of a reduced-order model governed by simplified physics. The proposed method models the fluid flow using a potential flow model, which introduces an additional fluid property. This material property currently requires tuning of the model by comparison to numerical Navier-Stokes-based solutions. Despite the significant simplifications, hereunder neglecting viscous boundary layers, topology optimization based on the reduced-order model is shown to provide qualitatively similar designs, as those obtained using a full Navier-Stokes-based model. The number of DOFs is reduced by 50% in two dimensions and the computational complexity is evaluated to be approximately 12.5% of the full model. We further compare to optimized designs obtained utilizing Newton’s convection law.
Original languageEnglish
JournalStructural and Multidisciplinary Optimization
Issue number4
Pages (from-to)1105-1124
Publication statusPublished - 2019


  • Topology optimization
  • Natural convection
  • Reduced-order model
  • Potential flow
  • Heat sink design


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