Shape Optimization Algorithms for Fluid Dynamics Applications

Abstract

AbstractIn this work we present a comparison between shape optimization algorithms in different vector spaces. The main goal is to optimize the surface of an object with respect to a physical quantity. The main focus is on applications that require large element deformations as part of the optimization process, as for instance the removal and creation of geometric singularities such as edges and corners. The algorithms take into account the prevention of element degeneracy and overlapping, for instance by enforcing inequality constraints. For this purpose, an approach in the Hilbert space is compared to another in Banach spaces. The former is based on a nonlinear extension equation, whereas the p‐Laplace operator is used in the latter. Computational results are presented in the context of fluid dynamics applications, where the contour of an object is optimized with respect to the energy dissipation.