Three-Dimensional Subdivision Parameterisation for Aerodynamic Shape Optimisation

A novel hierarchical wing parameterisation method based on subdivision surfaces is presented and its performance tested on a range of geometric and aerodynamic optimisation test cases. Subdivision surfaces form a limit surface based on the recursive refinement of an initial network of points. This intrinsically creates a hierarchy of control points that can be used to deform the surface at varying degrees of fidelity. This principle is used to create a multi-resolutional surface parameterisation that can make fine and gross surface changes without losing underlying surface detail. This is then extended to allow multi-resolutional control of arbitrary meshes such as computational surface grids. This parameterisation method is then applied to a range of optimisation problems in a ‘multi-level’ procedure that starts with a low fidelity parametrisation and which is then increased sequentially. These cases are compared against a range of ‘single-level’ schemes that use each level in isolation. It was found that by using the multi-level method significant improvements to both convergence rates and robustness were achieved. In some cases this increased robustness lead to improved final results by successfully exploiting high dimensional design spaces that could not be explored using a fixed number of design variables.