Combining Sobolev Smoothing with Parameterized Shape Optimization

TL;DR

This paper introduces a novel approach combining Sobolev smoothing with parameterized shape optimization, enhancing aerodynamic design performance and robustness, especially in One Shot optimization with CAD-based shapes.

Contribution

It demonstrates how Sobolev smoothing, as a shape Hessian approximation, benefits shape optimization, particularly in inexact flow conditions and CAD-based engineering applications.

Findings

Improved aerodynamic shape optimization performance.

Enhanced stability in One Shot optimization.

Performance gains over classical Quasi-Newton methods.

Abstract

On the one hand, Sobolev gradient smoothing can considerably improve the performance of aerodynamic shape optimization and prevent issues with regularity. On the other hand, Sobolev smoothing can also be interpreted as an approximation for the shape Hessian. This paper demonstrates, how Sobolev smoothing, interpreted as a shape Hessian approximation, offers considerable benefits, although the parameterization is smooth in itself already. Such an approach is especially beneficial in the context of simultaneous analysis and design, where we deal with inexact flow and adjoint solutions, also called One Shot optimization. Furthermore, the incorporation of the parameterization allows for direct application to engineering test cases, where shapes are always described by a CAD model. The new methodology presented in this paper is used for reference test cases from aerodynamic shape optimization and performance improvements in comparison to a classical Quasi-Newton scheme are shown.