Multilevel Shape Parameterization for Aerodynamic Optimization – Application to Drag and Noise Reduction of Transonic/supersonic Business Jet

We present the construction and report on the experimentation of a shapeoptimization method applied to the aerodynamic design of a transonic or supersonic business jet. The main numerical ingredients are: a 3D unstructured-grid compressible-flow finite-volume solver, free-form deformation approach for shape and mesh movement based on self-adaptive and multilevel 3D tensorial Bézier polynomial representations by the degree-elevation technique, and a general genetic or simplex optimizer. In our test-cases, we reduce the pressure drag and, for the supersonic case, a criterion of the noise source of supersonic bang. Our experiments demonstrate the versatility of the free-form deformation approach within an unstructured grid volume discretization, and the cost-efficiency of hierarchical optimization strategies (parameterization degree-enhancement or V-cycles).