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Adjoint wall functions: A new concept for use in aerodynamic shape optimization
Authors:AS Zymaris  DI Papadimitriou  KC Giannakoglou  C Othmer
Institution:1. National Technical University of Athens, School of Mechanical Engineering, Parallel CFD & Optimization Unit, P.O. Box 64069, 15710 Athens, Greece;2. Volkswagen AG, CAE Methods, Group Research, Letter Box 1777, D-38436 Wolfsburg, Germany
Abstract:The continuous adjoint method for the computation of sensitivity derivatives in aerodynamic optimization problems of steady incompressible flows, modeled through the kε turbulence model with wall functions, is presented. The proposed formulation leads to the adjoint equations along with their boundary conditions by introducing the adjoint to the friction velocity. Based on the latter, an adjoint law of the wall that bridges the gap between the solid wall and the first grid node off the wall is proposed and used during the solution of the system of adjoint (to both the mean flow and turbulence) equations. Any high Reynolds turbulence model, other than the kε one used in this paper, could also profit from the proposed adjoint wall function technique. In the examined duct flow problems, where the total pressure loss due to viscous effects is used as objective function, emphasis is laid on the accuracy of the computed sensitivity derivatives, rather than the optimization itself. The latter might rely on any descent method, once the objective function gradient has accurately been computed.
Keywords:Continuous adjoint method  Sensitivity derivatives  Optimization  Navier&ndash  Stokes equations  Turbulence  Wall functions
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