A Comparison of B-spline Surface and Free-form Deformation Geometry Control Methods for Aerodynamic Shape Optimization

The geometry control method employed in an aerodynamic shape optimization algorithm defines what designs can be considered, directly impacting the aerodynamic performance improvements that are attainable by the algorithm. Two geometry control methods, B-spline surface control and free-form deformation, are applied to a suite of problems of varying complexity and are compared on the basis of the quality of the optimized shape as well as the ease of use for problem setup. B-spline surface optimization is often found to result in slightly lower drag; however in general both methods perform equally well, especially when optimized geometries are evaluated on finer grids. The exception is in the case of a dihedral and sectional optimization, where convergence paths taken by the two geometry control methods are significantly different and the B-spline surface optimization reduces drag more effectively. Free-form deformation provides a more general approach to problem setup.