A phase field approach for shape and topology optimization in Stokes flow

Abstract

A new formulation for shape and topology optimization in a Stokes flow is introduced. The investigated problem minimizes the total potential power of the flow. By combining
a porous medium and a phase field approach we obtain a well-posed problem in a diffuse interface setting that can be reformulated into a problem without state equations. We can derive a sharp interface problem with zero permeability outside
the fluid region as a T-limit of this porous medium-phase field problem.