Carlos N. Rautenberg
Humboldt Universität zu Berlin

Abstract: A shape optimization problem of a pipe for the stationary Navier-Stokes equations in an industrial application is considered.
The Navier-Stokes system is provided with mixed boundary conditions: Non-homogeneous Dirichlet-type on one part of the boundary (inlet and walls) and “do nothing” on the remaining part (outlet). The shape design of the duct is focused on two objectives: 1) To obtain an almost-uniform outflow, and 2) To reduce the total pressure drop of the flow. The wellposedness of the optimization problem and existence of solutions to the Navier-Stokes system are studied, and a continuous approach to the derivation of the shape gradient is presented. Details on the derivation of the numerical descent scheme and its implementation are given together with several numerical tests.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.