Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

Without addressing shape smoothness, gradient-based optimisation methods naturally am-plify high-frequency shape components which can lead to poor convergence of the optimisation problem and a convergence rate exhibiting dependency on the fidelity of shape-control. Recent work by the authors demonstrated that this problem arises due to the discrete shape problem being ill-posed by naturally including geometries that are invalid both in physicality (shape) and discretisation (mesh), and a new shape control methodology has been developed which addresses this explicitly. The new approach uses two-dimensional control to recover shape-relevant displacements and surface gradient constraints to ensure smooth and valid iterates. The shape gradient constraints, approximating a C² continuity condition, are derived for two local shape control methods: discrete grid point control and cubic B-Splines. The local control methods provide high-fidelity control whereas the surface constraints exclude non-physical shapes from the design space making the shape problem well-posed. As a result, high-fidelity shape optimisation is possible at a reasonable computational cost. In this paper, further results are presented for the aerodynamic optimisation of two standard test cases defined by the AIAA aerodynamic design optimisation discussion group. A value of 7 drag counts is achieved on the inviscid case and 66 drag counts on the viscous case; to the authors’ knowledge these are the lowest results published for either case.