Project 11

Project 11: Optimal Shape Design of Air Ducts in Combustion Engines


Project Partners:

Weierstraß Institute for Applied Analysis and Stochastics (WIAS), Germany
Math. Tec GmbH, Austria


Project Scientists:

Naomi Auer
Early Stage Researcher (ESR11)


Michael Hintermüller (WIAS, HU Berlin)


Karl Knall (Math. Tec)


Project Description

Many optimal design problems in engineering or biomedical sciences require to determine an optimal shape of a region of interest in order to minimize a number of suitable objectives subject to fluid flow. Often additional geometric constraints impose further restrictions on the possible design.

Mathematically, this problem results in a constrained multi-objective free form shape optimization problem subject to the Navier-Stokes system. The goal of this project is the derivation of adjoint based representations of shape  gradient-related descent directions and the numerical realization of associated minimization schemes. For this purpose and for reasons of efficiency reduced order models (e.g. based on shape-aware adaptive discretization) need to be developed, appropriate primal and dual turbulence models need to be implemented and proper preconditioning of saddle point problems has to be developed. In this context, applications in the automotive industry and quantitative biomedicine will be addressed.