Design sensitivity calculations directly on CAD-based geometry

Multi-disciplinary analysis and optimization (MDAO) has been a long-standing goal in the aerospace community. In order to employ MDAO effectively, one needs to be able to compute the sensitivity of the objective function with respect to the driving parameters in a robust and efficient manner. Over the past decade there have been considerable efforts towards the generation of "adjoint" versions of flow solvers in order to help in this process. Unfortunately, the corresponding efforts have not been expended in the geometry and grid generation processes, especially when the geometries are generated parametrically with a modern computer-aided design (CAD) or CAD-like system. Contained herein is a pair of complementary techniques for computing configuration sensitivities directly on parametric, CAD-based geometries. One technique computes the configuration sensitivity analytically by differentiating the geometry-generating process; the other employs a new finite-difference technique that overcomes the difficulties previously encountered. Modifications to the Engineering Sketch Pad (ESP) (which is built on top of OpenCSM, EGADS, and OpenCASCADE) are described. Then the use of these configuration sensitivities in the computation of the sensitivity of grid-points is discussed. The results of these new techniques are shown on several configurations.