Optimal conduit shape for Stokes flow

HU, WEIWEI; CERETANI, ANDREA N.; RAUTENBERG, CARLOS N.

SYSTEMS AND CONTROL LETTERS

ELSEVIER SCIENCE BV

Año: 2023 vol. 173

0167-6911

We consider the problem of the optimal shape of a two dimensional duct which contains a fluid governed by the Stokes equations with mixed boundary conditions. The conduit domain is assumed to be non-smooth and perturbations are allowed only on the walls, while the objective functional aims at minimizing the head loss and to enforce a uniform velocity profile at the outlet. We show existence of solutions to the shape optimization problem and determine the existence of the shape derivative.