Assessment of hyper-reduction techniques in the context of CFD-based intrusive reduced order modeling

Abstract

The aircraft design and optimization process relies on an extensive numbers of computations for a wide range of parameters defining flight conditions, mass cases or shape variations. As the deployment of high-fidelity methods like computational fluid dynamics (CFD) is still too expensive for such multi-query scenarios, reduced order models (ROMs) are a popular approach to reduce the computational costs while retaining sufficient accuracy levels. ROMs are usually based on a low-dimensional representation of the full order model (FOM), that is utilized to map a set of input parameters to an approximative solution of the FOM. This thesis investigates a physics-based ROM that seeks an optimized representation of the FOM in a proper orthogonal decomposition (POD) reduced space by minimizing the steady residual obtained from a CFD solver. The so called least squares ROM (LSQ-ROM) is extended by a consistent hyperreduction, which aims for a reduction of the entries of the residual vector that is minimized during the prediction. In particular, hyperreduction has been proposed by former studies on LSQ-ROM in order to decouple the algorithm computational complexity from the problem size. However, limitations within the DLR’s CFD solver TAU prevent the consistent application of the hyperreduction. The CFD solver "CFD for ONERA, DLR and AIRBUS" (CODA), which is currently under development, allows the implementation and investigation of a consistent hyperreduction that effectively removes the dependency on the original problem size. The main goal of this thesis is the implementation and the performance assessment of a consistent hyperreduction for the LSQ-ROM that is coupled with the solver CODA and based on a reduced CFD mesh. The reduced mesh is identified by a set of hyperreduction indices selected by the discrete empirical interpolation method (DEIM) and missing point estimation (MPE) and allows a direct reduction of the effort for the residual evaluation in the CFD solver CODA. For an assessment of the performance of the hyperreduction with respect to accuracy and prediction time, the consistent hyperreduction implementation is applied to the steady flow prediction of two 2D test cases in the subsonic and transonic regime and one 3D test case in the transonic regime. It can be shown that the implemented hyperreduction effectively reduces the time for the predictions while causing only minor accuracy deterioration. The results highlight that the new hyperreduction is superior to the former implementation of the hyperreduction. In particular, for high reduction levels, the consistent hyperreduction becomes significantly faster than the former one with speed-up factors of around 5 for the 2D test cases and up to 25 for the 3D test case.