22nd Congress of International Council of the Aeronautical Sciences, Harrogate, UK, 28 August - 1st September, 2000
Paper ICAS 2000-2.4.5

ACCURACY OF GRADIENT COMPUTATIONS FOR AERODYNAMIC SHAPE OPTIMISATION PROBLEMS

M. Chevalier, M. Berggren
The Aeronautical Research Institute of Sweden

Keywords: shape optimization, adjoint equations

Applying nonlinear optimization techniques such as quasi-Newton methods to aerodynamic shape optimization problems requires the calculation of gradients of a given objective function. An effective way of calculating such gradients is through the use of the so-called adjoint equations. To achieve fast convergence in the optimization algorithm, accurately computed gradients are needed. In the computation of such gradients the discretization of the problem and the choice of boundary conditions are two important aspects. These issues are studied in the context of shape optimization of a quasi-1D nozzle using physically relevant boundary conditions. Isentropy is enforced at the inlet boundary, and the static pressure is specified at the outlet boundary for subsonic flows. A cell-centered finitevolume discretization with a standard implementation of the boundary conditions is applied, and the corresponding numerical scheme and numerical boundary conditions for the adjoint equations are derived in a fully discrete sense. Numerical experiments at subsonic and transonic speeds, show that the gradient evaluations are accurate enough to obtain satisfactory convergence of the quasi-Newton algorithm.

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