Modal analysis of subdivision surfaces for aerodynamic shape parameterisation

Subdivision surfaces offer a compact approach for describing surfaces in a hierarchical manner and permit a recursive refinement scheme that fits a matrix representation. This refinement matrix may be extended to define the limit surface, and from this an eigenanalysis yields wave-form surface shape vectors. This vector basis offers an attractive shape parameterisation where each design variable is a modal amplitude, and because subdivision surfaces are applicable to any surface defined by a quadrilateral or triangular mesh, it may be computed easily for any surface or topology. Optimisation results are presented for geometric inverse design and transonic NACA 0012 and RAE 2822 aerofoil optimisations, showing the parameterisation can recover aerofoil geometries effectively and delivers good optimised results for relatively small numbers of design variables, with 33 counts achieved on the NACA 0012 ADODG case 1 with 24 design variables and 111 with 20 design variables on the RAE 2822 ADODG case 2.