This paper presents an investigation into the influence of shape parameterisation and dimensionality on the optimisation of a benchmark case described by the AIAA Aerodynamic Design Optimisation Discussion Group. This problem concerns the drag minimisation of a NACA0012 under inviscid flowconditions at M = 0.85 and α = 0 subject to a local thickness constraint. The work presented here applies six different shape parameterisation schemes to this optimisation problem with between 4 and 40 design variables. The parameterisation methods used are: Bezier Surface FFD; B-Splines; CSTs; `Hicks-Henne bump functions; a Radial Basis Function domain element method (RBF-DE) and a Singular Value Decomposition (SVD) method. The optimisation framework used consists of a gradient based SQP optimiser coupled with the SU2 adjoint Euler solver which enables the efficient calculation of the design variable gradients. Results for all the parameterisation methods are presented with the best results for each technique converging to two distinct optimised aerofoil shapes with drag counts ranging between 25 and 56 (from an initial value of 469). The optimal result was achieved with the B-Spline method with 16 design variables. Further analysis of results is then presented to investigatethe design spaces, numerical error, flow behaviour and the presence of hysteresis.
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