Where must we place obstacles in a flow to minimise its rate ?

Abstract

We propose a numerical method in order to determining how to place fixed obstacles in a Stokes flow, for which the inlet constraint force is imposed, so that the flow rate is minimised. To do this, we study the shape derivative associated to such a Stokes flow, and we propose a descent algorithm. We first consider the case of spherical obstacles, and then general rigid obstacles for which the orientation must be taken into account. Numerical simulations complete the study.