Topological Design Based on Highly Efficient Adjoints Generated by Automatic Differentiation

We report on a proof-of-concept study for the application of an automatically generated adjoint Navier-Stokes code in the automotive design process. The design application consists in the optimisation of the topology of a duct for the cabin ventilation. The numerical model is a three-dimensional Navier-Stokes solver based on Griebel’s NaSt2D. The design approach is based on a descent algorithm, which relies on the gradient of dissipated energy with respect to the duct topology. This gradient is provided by the adjoint of the solver, which is generated from the solver’s source code by the automatic differentiation tool TAF. To render the solver TAF-compliant, a few initial modifications were necessary. Subsequent modifications of the TAF compliant solver such as a change of the objective function have been transferred to an updated adjoint in an automated process chain. The computational cost of a combined nominal and adjoint solve, i.e. of a function and gradient evaluation, is less than twice the cost of a nominal solve.