Adjoint Methods

Kurzfassung

Aerospace industry is increasingly relying on advanced numerical flow simulation tools in the early aircraft design phase. Today's flow solvers based on the solution of the Euler and Navier-Stokes equations are able to predict aerodynamic behaviour of aircraft components under different flow conditions quite well. Due to the high computational expense required for flow simulations around realistic 3D configurations, in industry computational fluid dynamics tools are rather used for analysis and assessment of given geometries than for shape design and optimization. However, within the next few years numerical shape optimization will play a strategic role for future aircraft design. It offers the possibility of designing or improving aircraft components with respect to a pre-specified figure of merit subject to gemetrical and physical constraints. Consequently, recently large effort is devoted to develop efficient optimization strategies for industrial aerodynamic aircraft design. There are many ingredients required to establish an efficient and flexible numerical optimization capability. These include suitable techniques for geometry parametrization, meshing and mesh movement methods, efficient and accurate flow solvers as well as a flexible tool-set of containing both deterministic and stochastic based optimizers. Over the last years, numerical shape optimization is one of the major issues of the Institute of Aerodynamics and Flow Technology at DLR. One key activity is the derivation and implementation of a continuous adjoint approach for the DLR flow simulation software MEGAFLOW based on the solution of the Euler and Navier-Stokes equations. Its potential for efficient aerodynamic shape design in compressible flow will be demonstrated. The presentation will have three sections: First the adjoint method will be explained by means of simple linear equations. Then as an exercise the continuous adjoint equations will be derived for the convection-diffusion equations. Finally, the continuous adjoint Euler equations will be discussed and their applications will be presented for 2D airfoil designs as well as 3D wing-body optimizations.