This paper applies three shape parameterization techniques to few design cases typical in aerospace studies in order to quantify the effect of shape parameterization on automatic aerodynamic shape optimization The three methods in study are mesh points, B-spline surfaces and the Class function / Shape function Transformation (CST). Given the extensive prevalence of CFD in aerodynamic design, it is of interest to study the efnciency of parameterization approaches and compare them in terms of accuracy and performance aspects of the shape optimization process. Initially, the complete formulation of the optimal design problem for the Euler equations is presented. Then, the implementation of these surface representation methods is explored and finally, results are presented for three-dimensional inverse design and drag minimization problems.
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