ACCURACY OF GRADIENT COMPUTATIONS FOR AERODYNAMIC SHAPE OPTIMIZATION PROBLEMS

摘要

Applying nonlinear optimization techniques suchrnas quasi-Newton methods to aerodynamic shapernoptimization problems requires the calculationrnof gradients of a given objective function. Anrneffective way of calculating such gradients isrnthrough the use of the so-called adjoint equations.rnTo achieve fast convergence in the optimizationrnalgorithm, accurately computed gradientsrnare needed. In the computation of such gradientsrnthe discretization of the problem and thernchoice of boundary conditions are two importantrnaspects. These issues are studied in the contextrnof shape optimization of a quasi-1D nozzle usingrnphysically relevant boundary conditions. Isentropyrnis enforced at the inlet boundary, and thernstatic pressure is specified at the outlet boundaryrnfor subsonic flows. A cell-centered finitevolumerndiscretization with a standard implementationrnof the boundary conditions is applied, andrnthe corresponding numerical scheme and numericalrnboundary conditions for the adjoint equationsrnare derived in a fully discrete sense.rnNumerical experiments at subsonic and transonicrnspeeds, show that the gradient evaluationsrnare accurate enough to obtain satisfactory convergencernof the quasi-Newton algorithm.