Modern aircraft design requires efficient prediction of complex, time-dependent flow phenomena. While high-fidelity datasets offer accuracy, they come with high computational costs. To address this, NATO’s research group AVT-351 is investigating reduced-order models (ROMs). Proper Orthogonal Decomposition (POD) is widely used in ROMs, but truncated POD bases struggle with sharp gradients and shocks. The enriched POD-LSTM neural network ROM
(ePOD-LSTM-ROM) has demonstrated improved accuracy for airfoil pressure distributions
and was extended to full wing surfaces. This approach was effective for sharp discontinuities
moving significantly in time. For realistic cases, such as the ONERA M6 wing with multiple shocks, domain decomposition allowed for multiple enrichments in separate subdomains,
but at the cost of rapidly increasing degrees of freedom. To improve LSTM-NN accuracy,
enrichments were optimized using mutual information, filtering, and error trade-offs, reducing the total ePOD-LSTM-ROM error by 23.8%. Finally, a goal-oriented reduced-order model
(GOROM) was developed to alter POD modes optimized for a specific goal function, improving
shock accuracy by 5.0% with minor losses elsewhere.

Maneuvering or Stability and Control (S&C) characteristics of an aircraft constitute the most challenging and expensive phase of its design process. The S&C design phase extends into the development process, sometimes leading to unexpected aerodynamic issues. Thus, identifying aerodynamic issues and their consequences, e.g. transonic buffet, in the early stages of development, is crucial. Recent advancements in Computational Fluid Dynamics (CFD) have expanded its utilization. However, despite improvements in CFD, the comprehensive representation of dynamic effects for all possible maneuvers is still unfeasible due to the high computational expense.

Reduced Order Models (ROMs) have been combined with CFD data to predict an aircraft's dynamics in all possible maneuvers. ROMs enable the efficient utilization of high-fidelity CFD data, providing valuable insights into flight dynamic effects. This thesis project took place at the Netherlands Aerospace Center (NLR). The NLR in cooperation with TUDelft, has developed a ROM method for predicting unsteady aerodynamic loads of air vehicles. The current ROM approach combines the Proper Orthogonal Decomposition (POD) of pressure distribution with a Long Short-Term Memory (LSTM) type Neural Network (NN). So far, the POD-LSTM ROM method predicts the pressure distribution well in the incompressible flow regime. However, the increased number of spatial POD modes required to accurately represent the shock discontinuities in a pressure distribution poses challenges to POD-LSTM ROM. This leads to high computational costs, rendering the application of the POD-LSTM ROM in transonic flows impractical. Therefore, this thesis aims to set the foundation for expanding the POD-LSTM ROM for predicting the pressure distribution over sections of the DLR-F22 model in transonic conditions.

This research introduced a novel approach to address the increased number of spatial POD modes needed to approximate shock discontinuities in transonic flows. The enriched Proper Orthogonal Decomposition (ePOD) method introduces an enrichment basis into the standard truncated POD basis. The enrichment basis explicitly accounts for pressure discontinuities caused by shock waves, allowing the standard basis to focus on representing the remaining pressure distribution. The results confirm that the ePOD reduces the DoF required to approximate pressure distribution in transonic flows.

An LSTM neural network was utilized to forecast the time-dependent coefficients and parameters of the enriched reduced-order basis in unseen flow conditions. The results also showed that the ePOD reduced the complexity of the time-variant parameters of the reduced-order basis compared to the standard POD with the same number of degrees of freedom (DoF), facilitating more efficient training of the neural network.