Towards Aircraft Design Using an Automatic Discrete Adjoint Solver

Abstract

The ADjoint method is applied to a three-dimensional Computational Fluid Dynamics (CFD) solver to generate the sensitivities required for aerodynamic shape optimization. The ADjoint approach selectively uses Automatic Differentiation (AD) to generate the partial derivative terms in the discrete adjoint equations. By selectively applying AD techniques, the computational cost and memory overhead incurred by using AD are significantly reduced, while still allowing for the the accurate treatment of arbitrarily complex governing equations and boundary conditions. Once formulated, the discrete adjoint equations are solved using the Portable, Extensible Toolkit for Scientific computation (PETSc). With this approach, the computed adjoint vector can be used to calculate the total sensitivities required for aerodynamic shape optimization of a complete aircraft configuration. The resulting sensitivities are compared with complex-step derivatives to establish their accuracy. The tools developed are applied to an infinite wing test case to demonstrate the accuracy and efficiency of the method.

Rapid development and adjoining of transient finite element models

“…This approach has the significant benefit that, given a forward model which can be processed by the AD tool, an adjoint model can (in principle) be generated automatically, without the need to differentiate and adjoin the entire model by hand. AD has seen a diverse range of successful practical applications, including for example in engineering design [38,39] and large-scale ocean state estimation [40,41]. However, the black-box line-by-line application of AD without any consideration of the mathematical structure of the problem can be too inefficient for practical use [42].…”

An Investigation of Induced Drag Minimization Using a Newton-Krylov Algorithm

“…Nielsen and Kleb 29 use the complex-step method 30 with colouring to efficiently and accurately evaluate the entries of the Jacobian matrix. Mader et al 31 construct the residual on a node-by-node basis, and then evaluate each row of the transposed Jacobian by applying the reverse-mode of automatic differentiation.…”