Machine learning based model order reduction of inviscid transonic flow past an airfoil

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Abstract
Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve due to high degrees of freedom as well as the coupled nature of the conservation laws. While this poses a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced order models. However, such models are known to incur huge off-line costs which can sometimes outweigh their potential benefits. Furthermore, their prediction accuracy is known to be poor under transonic flow conditions. In this work, we propose a machine learning method to construct reduced order models via deep neural networks. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack show that the proposed approach adapts to parameter variation very well. Notably, the proposed framework precludes knowledge of numerical operators utilized in the data generation phase. Furthermore, the proposed approach incurs significantly lower offline costs compared to existing approaches while still producing comparable accuracy.

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