A "poor man's" approach to topology optimization of natural convection problems

TL;DR

This paper introduces a simplified, reduced-order modeling approach for topology optimization of natural convection problems, significantly reducing computational costs while maintaining design quality.

Contribution

A novel reduced-order model using potential flow simplifies natural convection topology optimization, lowering computational effort by 87.5% compared to full Navier-Stokes models.

Findings

Reduced DOFs by 50% in 2D cases

Computational complexity decreased to 12.5% of full model

Qualitative similarity in optimized designs

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. 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.