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

## Abstract

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.

## Keywords

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

### Acknowledgements

The authors would like to thank the TopOpt group for fruitful discussions.

### Funding information

The work has been partly funded by the TopTEN project granted by Independent Research Fund Denmark.

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