Non-intrusive aerodynamic shape optimisation with a discrete empirical interpolation method

This work presents a strategy to build reduced order models suitable for aerodynamic shape optimization, resulting in a multi-fidelity optimisation framework. A reduced-order model (ROM) based on a Discrete Empirical Interpolation (DEIM) method is employed in lieu of computational fluid dynamics solvers, for fast, nonlinear, aerodynamic modeling. The DEIM builds a set of interpolation points that allows it to reconstruct the flow fields from set of basis obtained by Proper Orthogonal Decomposition of a matrix of snapshots. The aerodynamic reduced order model is completed by introducing a nonlinear mapping function between surface deformation and the DEIM interpolation points. The optimisation problem is managed by a trust-region algorithm linking the multiple fidelity solvers, with each subproblem solved using a gradient-based algorithm. The design space is initially restricted; as the optimisation trajectory evolves, new samples enrich the ROM. The proposed methodology is evaluated using a transonic viscous test case based on the Onera M6 wing. Results show that for cases with a moderate number of design variables, the approach proposed is competitive with state-of-the-art gradient based methods; in addition, the use of the trust-region methodology mitigates the likelihood of the optimiser converging to, shallower, local minima.