Algorithmic differentiation of the Open CASCADE Technology CAD kernel and its coupling with an adjoint CFD solver

Abstract

Computer Aided Design (CAD) tools are extensively used to design industrial components, however contrary to e.g. Computational Fluid Dynamics (CFD) solvers, shape sensitivities for gradient-based optimisation of CAD-parametrised geometries have only been available with inaccurate and non-robust finite differences. Here Algorithmic Differentiation (AD) is applied to the open-source CAD kernel Open CASCADE Technology using the AD software tool ADOL-C (Automatic Differentiation by OverLoading in C++). The differentiated CAD kernel is coupled with a discrete adjoint CFD solver, thus providing the first example of a complete differentiated design chain built from generic, multipurpose tools. The design chain is demonstrated on the gradient-based optimisation of a squared U-bend turbo-machinery cooling duct to minimise the total pressure loss.

Applications of differentiated CAD kernel in gradient-based aerodynamic shape optimisation

“…The differentiation process was not straightforward and it involved a significant amount of code modification, as we had to deal with a lot of compile-time and run-time issues that are explained in our previous study. 7 Here we are going to give an example how to use the differentiated OCCT sources to compute geometric derivatives with the traceless forward vector mode, as it is easier to use than the trace-based versions.…”

“…We used it to differentiate the OCCT kernel to compute the geometric derivatives. 7 As opposed to finite differences, these geometric derivatives are exact (up to floating point round off). Furthermore, the computational efficiency of the method is superior to the finite difference approach, as demonstrated also in our previous study.…”

“…Furthermore, the computational efficiency of the method is superior to the finite difference approach, as demonstrated also in our previous study. 7 Another requirement for CAD-based shape optimisation workflow is to define the parametrisation of the test-case. Indeed, the parameters that control the CAD model have to be carefully chosen.…”

CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine

“…For example, the gradient of design variable 29, which is the exit width, suggests that both the efficiency and power increase when enlarging the exit area. The CEV assumption indeed affects the accuracy of the adjoint-based gradients, in particular for design parameters of the shroud meridional contour (design variables [21][22][23][24], where this assumption may not be valid due to the tip leakage vortex. However, they are accurate enough for shape optimization as will be shown in Section 4.…”

“…In both cases, the gradient information from the grid to the CAD parameters was calculated by finite-difference approximations. To overcome the limitations that are associated with finite-differences, an open-source CAD system was differentiated by [23] using algorithmic differentiation (AD), which was then applied to optimize a U-Bend shape found in high-pressure turbine blades as cooling devices. A trivariate B-spline parameterization was used by [24] for the same test case that allows a rapid meshing of the domain suitable for a one-shot optimization method while the geometry maintains the link to a CAD representation.…”