Parameterization adaption for 3D shape optimization in aerodynamics

TL;DR

This paper introduces an adaptive parameterization method for 3D aerodynamic shape optimization using Free-Form Deformation, significantly reducing computational costs while improving optimization efficiency.

Contribution

It presents a novel adaptive parameterization approach based on tensorial Bézier functions for 3D shape optimization in aerodynamics.

Findings

Reduces computational costs in 3D shape optimization

Enhances efficiency of numerical simulations

Provides a flexible parameterization framework

Abstract

When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an explicit geometrical representation, it is natural to seek for an analogous concept of parameterization adaptivity. We propose here an adaptive parameterization for three-dimensional optimum design in aerodynamics by using the so-called "Free-Form Deformation" approach based on 3D tensorial B\'ezier parameterization. The proposed procedure leads to efficient numerical simulations with highly reduced computational costs.