Topology optimization of regions of Darcy and Stokes flow

Abstract

This paper treats the topology optimization problem of obtaining an optimal layout of regions of Darcy and Stokes flow, where the objective is the total potential power functional representing average fluid pressure. It extends the work of Borrvall and Petersson, which concerned optimal layout of Stokes flow only. A generalization of Stokes' equations is derived and used as state constraints in the optimization problem. A proof of existence of solutions is provided, and it is seen that although the corresponding proof in Borrvall and Petersson does not need regularization, the present one does. It is also concluded that linear interpolations of state parameters will result in black and white (unfiltered) designs. The method is tested on an area-to-point flow problem of the type discussed by Bejan, where the influence of various parameters and numerical strategies on the design are studied. Copyright © 2006 John Wiley & Sons, Ltd.