Subdivision Multi-Resolution Systems for Three-dimensional Aerodynamic Optimisation

In this paper, three different approaches to subdivision multi-resolution systems are presented in the context of Catmull-Clark subdivision. One of these involved a modification to the Catmull-Clark method to construct an interpolating subdivision scheme. Subsequently an algorithm to coarsen quadrilateral meshes in such a way as to conform to a subdivision like mesh structure has been developed. This algorithm has been used in conjunction with the presented multi-resolution methods to automatically construct hierarchical parameterisations of the MDO wing and NASA CRM model that allow control over the geometry at varying wavelengths. The behaviour of each multi-resolution method under a simple geometric deformation has then been compared. Subsequently, the performance of each method in an aerodynamic optimisation context has been investigated with a drag minimisation and inverse design case on the MDO wing using a panel method. This showed that the interpolating method performed worse than the other two methods due to geometric artefacts appearing under deformation from the interpolating condition over constraining the surface. It was also found that a hierarchical approach to optimisation, starting at a coarse parameterisation and refining through the optimisation, resulted in improved objective values in both inverse design and drag minimisation cases.