Adjoint-Based Methods in Aerodynamic Design-Optimization

In this paper we study the use of adjoints in.the calculation of design gradients for cost and constraint functionals in optimization-based aerodynamic design. While there is an extensive literature on numerical implementation of these ideas, the underlying mathematical treatment is usually quite formal. Here we focus on rigorous justification of the approach and on careful characterization of the underlying function spaces. One practical result is the demonstration that just as the flow variables may have internal jumps, so also may the associated adjoints. For a particular flow-matching problem we are able to characterize the jump by a transversality condition.

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