Unsteady Aerodynamic Design on Unstructured Meshes with Sliding Interfaces

A time-accurate, continuous adjoint formulation is developed, verified, and applied. This formulation enables the efficient design of aerodynamic surfaces in unsteady, inviscid flow within a gradient-based optimization framework. A systematic method for the derivation of suitable boundary conditions for the adjoint problem is demonstrated, and a new sliding mesh algorithm for unstructured meshes is also developed and tested. The gradient information provided by the time-accurate adjoint formulation is verified for design variables in two dimensions with and without the use of sliding meshes, and in both situations, gradients compare very favorably with those obtained via finite dierencing. Optimal shape design results for a pitching airfoil demonstrate the eectiveness of the unsteady adjoint approach.

Furthermore, performing shape design with sliding meshes recovers nearly identical results as a non-sliding case, suggesting that their use in conjunction with the unsteady adjoint can provide a stable and accurate design approach. The combination of sliding mesh interfaces and the time-accurate continuous adjoint produces a powerful design tool for unsteady problems with surfaces in relative motion.
Authors: Thomas D. Economon, FranciscoPalacios, Juan J. Alonso
AIAA Paper 2013-0632, 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, Texas, January 7-10, 2013
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