Volumetric b-splines shape parametrization for aerodynamic shape design

In this paper, volumetric b-splines are employed to deform the aerodynamic surface. The geometry is enclosed in a volumetric parallelepiped, referred to as control box, which in, essence, is similar to Free Form Deformation (FFD). The use of generic volumetric b-splines requires to calculate the parametric coordinates, but offers some important advantages over other parameterization techniques, such as deformation locality. This parameterization can be applied to the design of complex three-dimensional configurations and also offers the possibility to incorporate the geometric description extracted from the Computational Aid Design (CAD) files, which most frequently are in the form of Non-Uniform Rational B-Splines (NURBS), in what we call multilevel deformation; that is, the control box deforms the NURBS, while the NURBS deforms the computational grid, following the chain rule. In this work, a volumetric b-spline parameterization has been applied in an automatic gradient-based optimization strategy in order to optimize the aerodynamic surface of aeronautical configurations. The design variables are the control points, while the gradients are calculated using the continuous adjoint formulation.