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An aerodynamic design algorithm for turbulent e ows using unstructured grids is described. The current approachusesadjoint (costate)variablestoobtainderivativesofthecostfunction.Thesolutionoftheadjointequations is obtained by using an implicit formulation in which the turbulence model is fully coupled with the e ow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with e nite difference gradients, and a few sample computations are shown. Recommendations on directions of further research into the Navier ‐Stokes design process are made. Nomenclature A = area of control volume a = speed of sound C ¤ = constant used in Sutherland’ s law for viscosity cb1;cb2;cv1; = constants used in Spalart ‐Allmaras cw1;cw2;cw3 turbulence model cd = drag cl = lift c1
Anderson et al. (Mon,) studied this question.
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