Topology optimization of convection-dominated, steady-state heat transfer problems

The current push in the topology optimization community is to apply topology optimization to mechanics problems beyond typical structural design to other physical domains. Here, a framework for topology optimization of nonlinear steady-state heat transfer with conduction, convection, and radiation without explicitly accounting for fluid motion is evaluated. Convection-dominated diffusion problems are susceptible to numerical instabilities that, unless they are handled properly in the analysis, can severely affect the optimization. This numerical instability issue is the focus of this work, its origin is discussed in the context of density-design-variable-based topology optimization, and a method for avoiding such instabilities is described. Several design examples demonstrate the approach.