Regularisation of High Fidelity Aerodynamic Shape Optimisation Problems Using Gradient Limits

摘要

Recent work highlighting the importance of surface smoothness in shape optimisation has demonstrated that explicit surface gradient constraints can regularise high fidelity shape control methods for significantly improved efficiency and effectiveness. Without addressing shape smoothness, gradient-based optimisation methods naturally amplify 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. Local shape methods such as mesh points or cubic B-Splines, used with two-dimensional control to recover shape-relevant displacements, allow flexible and high fidelity shape control; however on their own such methods permit non-physical geometries and poor quality discretisations into the optimisation design space. Gradient constraints, approximating a C~2 continuity condition, explicitly constrain high-frequency shape components making the optimisation problem well-posed. As a result, high-fidelity shape optimisation is possible at a reasonable computational cost. In this paper, further results are presented using the novel gradient-limiting methodology on test case one of the AIAA aerodynamic design optimisation discussion group. In particular, the effects of shape control fidelity and numerical mesh resolution are investigated. It is shown that the gradient limits regularise the optimisation problem such that convergence rate is independent of both control fidelity and mesh resolution, while still obtaining improved objective results with refinement of each. Optimisation performed with gradient limits on the highest of three mesh resolutions obtained an objective of 1.6 drag counts for the test case.