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The adjoint method is an hot topic in computational fluid dynamics, as it represents the most viable option to apply gradient-based optimization to problems that require the solution of fluid flow equations. The main goal of the present work is the enhancement of available methodologies and the search for new and more performing ones, to achieve high accuracy in a finite-volumes implementation.
Two different approaches to formulate the continuous adjoint problem for aerodynamic optimization are explored. Boundary conditions and surface sensitivity are derived for a number of suitable cost functions, which are then discussed and implemented in an open-source framework. The well known issue of higher-order derivatives in analytic expressions of sensitivity is successfully handled in two of the variants: the first being completely new and the second adapted from the work of Castro et al. [1].
Being accuracy the main weakness of the continuous adjoint method, a validation of sensitivity gradients based on finite differences is performed. The collected results emphasize the importance of having looser discretization requirements on gradients’ evaluation, as the best results are achieved by the two aforementioned formulations. The last one, in particular, succeeded in providing a very accurate evaluation of both drag and lift sensitivities.