Sensitivity computation and shape optimisation in aerodynamics using the adjoint methodology and Automatic Differentiation.

Abstract

Adjoint based optimisation has until now demonstrated a great promise for optimisation in aerodynamics due to its independence of the number of design variables. This is essential in large industrial applications, where hundreds of parameters might be needed so as to describe the geometry. Although the computational cost of the methodology is smaller than that of stochastic optimisation methods, the implementation and related program maintenance time and effort could be particularly high. The aim of the present is to contribute to the effort of redusing the cost above by examining whether programs using the adjoint methodology for optimisation can be automatically generated and maintained via Automatic Differentiation, while presenting comparable performance to hand derived adjoints. This could lead to accurate adjoint based optimisation codes, which would inherit any change or addition to the relative original Computational Fluid Dynamics code. Such a methodology is presented and all the different steps involved are detailed. It is found that although a considerable initial effort is required for preparation of the source code for differentiation, hand assembly of the sensitivity algorithms and scripting for the automation of the entire process, the target of this research program is achieved and fully automatically generated adjoint codes with comparable performance can be acquired. After applying the methodology to a number of aerodynamic shape optimisation examples, the logic is also extended to higher derivatives, which could also be included in the optimisation process for robust design.