Aerodynamic Shape Optimization Using the Adjoint-based Truncated Newton Method

This paper presents the development and application of the Truncated Newton (TN) method for shape optimization problems based on continuous adjoint. The method is presented for laminar, incompressible flows. OpenFOAM R  is chosen as the CFD toolbox in which the method is developed. The Newton equations are solved using the restarted linear GMRES algorithm which requires only the product of the Hessian matrix of the objective function (with respect to the design variables) with a vector. This overcomes the cost for computing the Hessian matrix itself, which unfortunately scales with the number of design variables. The computation
of Hessian-vector products is conducted via the combination of continuous adjoint and direct differentiation that gives the minimum cost. The developed method is used for the shape optimization of two 3D ducts and the speed-up gained compared to rival methods is showcased.