Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Abstract

This work presents a shape parameterisation method based on multi-resolutional subdivision curves and investigates its application to aerodynamic optimisation. Subdivision curves are defined as the limit curve of a recursive application of a subdivision rule, which provides an intrinsically hierarchical set of control polygons that can be used to provide surface control at varying levels of fidelity. This is used to construct a progressive aerofoil parameterisation that allows an optimisation to be initialised with a small number of design variables, and then periodically increased in resolution through the optimisation. This brings the benefits of a low dimensional design space (high convergence rate, increased robustness, low cost finite-difference gradients) while still allowing the final results to be from a high-dimensional design space. In this work the progressive refinement technique is tested on a variety of optimisation problems. For each problem a range of ‘static’ (non-progressive) subdivision schemes (equivalent to cubic B-splines) are also used as a control group. For all the optimisation cases the progressive schemes perform comparably or better than the static methods, often providing a significant computational advantage, and in many cases allowing a solution to be found when the static method would otherwise finish prematurely in a local optimum.