Nonintrusive Aerodynamic Shape Optimisation with a POD-DEIM Based Trust Region Method

Marques, Simão
Kob, Lucas
Robinson, Trevor T.
Yao, Weigang
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This work presents a strategy to build reduced-order models suitable for aerodynamic shape optimisation, resulting in a multifidelity optimisation framework. A reduced-order model (ROM) based on a discrete empirical interpolation (DEIM) method is employed in lieu of computational fluid dynamics (CFD) solvers for fast, nonlinear, aerodynamic modelling. The DEIM builds a set of interpolation points that allows it to reconstruct the flow fields from sets 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 series of transonic viscous test cases based on wing configurations. 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 trust region methodology mitigates the likelihood of the optimiser converging to, shallower, local minima.
open access article
Marques, S., Kob, L., Robinson, T.T., Yao, W. (2023) Nonintrusive Aerodynamic Shape Optimisation with a POD-DEIM Based Trust Region Method. Aerospace. 10 (5), 470
Research Institute