Optimisation of a U-Bend Using a CAD-Based Adjoint Method with Differentiated CAD Kernel

In order to optimise the shape of a three-dimensional CAD-based model using the computationally efficient adjoint methods, the calculation of shape sensitivities, the derivatives of the surface position with respect to the design parameters, is required. This sensitivity is usually not available with CAD systems, but can be obtained by applying the Finite Difference method to CAD-system. Finite-Differences or part-analytic differentiation have been proposed to obtain sensitivities, but have their drawbacks. If source code is available, automatic differentiation can provide accurate derivatives without incurring topology changes or requiring hand-differentiation. This paper proposes the differentiation of the open-source CAD kernel - OpenCascade Technology (OCCT) with AD software tool ADOL-C (Automatic Differentiation by Overloading in C++). As a case study we consider the optimisation of pressure loss in a U-bend pipe. The geometry of the U-bend is parametrised in OCCT with a number of cross-sections lofted along a guiding path line. The corresponding geometric derivatives are used in CFD optimisation loops with the resulting shape outperforming the initial design.