Advancements in aircraft performance require increasingly complex design processes and tools. Simulating the unsteady non-linear aerodynamic interaction between a maneuvering aircraft and the surrounding flowfield poses serious challenges. High-Fidelity Computational Fluid Dynamics (CFD) methods, based on the numerical solution of the Navier-Stokes equations, can in general provide accurate solutions but at a computational cost that is often unfeasible for many applications that require real-time evaluation of the aerodynamic responses over a large range of conditions.
Reduced Order Models (ROMs) are methods that can alleviate the computational burden of performing High-Fidelity simulations while providing accurate solutions over a wide extent of parametric variations.
In the context of unsteady aerodynamics simulations, most traditional Reduced Order Models are limited to the prediction of integral loads and do not scale well for the treatment of high-dimensional systems.
Recently, within the Science and Technology Organization work-group of NATO, a data-driven ROM based on the Proper Orthogonal Decomposition and Neural Networks (POD-LSTM) has been proposed for the prediction of the unsteady pressure fields on the UCAV MULDICON aircraft configuration, showing good potential in terms of computational efficiency and interpretability compared to the previously developed ROM based on end-to-end Convolutional Neural Networks.
The POD-LSTM model is limited by the linear modal decomposition method that shows a slow convergence rate, in terms of latent space dimension, to the full-order solution. The high-projection error, localized in specific regions of the parameter space, translates into a consistent inaccuracy in the prediction of integral loads.
In order to overcome these limitations, two main methodologies are proposed to replace the Global POD basis with modal bases localized in i) the computational space or ii) in the parameter space, yielding the development of Local ROMs.
The first methodology is based on a Domain Decomposition strategy and aims to reduce the projection error in specific regions of the wing surface.
The second methodology, the Cluster-POD, focuses on partitioning the parameter space in relevant flow regimes and constructs Local Reduced Order models on each cluster.
The choice of surrogate models, for latent dynamics modeling, is also discussed and Machine Learning methods based on the Long Short Term Memory Neural Network, Multi-layer-Perceptron, and Gaussian Process Regression are tested and compared.
Results show that Local ROMs can improve the efficiency of the global latent representation, by generating sets of modes with more localized information content. The proposed Cluster-POD-based ROM, in particular, can be developed using a systematic procedure that automatically detects the parameter space partitions based on an a-posteriori error indicator. It is also briefly shown, as a proposal for future research, how Gaussian Mixture Models can be used to generate overlapping clusters, that solve some of the limitations of traditional Cluster-based ROMs based on the K-means clustering.
Furthermore, improvements in the prediction of integral loads are demonstrated by including the loads coefficients directly in the Machine Learning surrogate models targets, in order to remove the projection error emerging from the use of a reduced order basis.