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This paper presents a parametric reduced-order model (ROM) based on manifold learning (ML) for use in steady transonic aerodynamic applications. The main objective of this work is to derive an efficient ROM that exploits the low-dimensional nonlinear solution manifold to ensure an improved treatment of the nonlinearities involved in varying the inflow conditions to obtain an accurate prediction of shocks. The reduced-order representation of the data is derived using the Isomap ML method, which is applied to a set of sampled computational fluid dynamics (CFD) data. In order to develop a ROM that has the ability to predict approximate CFD solutions at untried parameter combinations, Isomap is coupled with an interpolation method to capture the variations in parameters like the angle of attack or the Mach number. Furthermore, an approximate local inverse mapping from the reduced-order representation to the full CFD solution space is introduced. The proposed ROM, called Isomap+I, is applied to the two-dimensional NACA 64A010 airfoil and to the 3D LANN wing. The results are compared to those obtained by proper orthogonal decomposition plus interpolation (POD+I) and to the full-order CFD model.

Numerical simulation is already an important cornerstone for aircraft design, although the application of highly accurate methods is mainly limited to the design point. To meet future technical, economic and social challenges in aviation, it is essential to simulate a real aircraft at an early stage, including all multidisciplinary interactions covering the entire flight envelope, and to have the ability to provide data with guaranteed accuracy required for development and certification. However, despite the considerable progress made there are still significant obstacles to be overcome in the development of numerical methods, physical modeling, and the integration of different aircraft disciplines for multidisciplinary analysis and optimization of realistic aircraft configurations. At DLR, these challenges are being addressed in the framework of the multidisciplinary project Digital-X (4/ 2012-12/2015). This paper provides an overview of the project objectives and presents first results on enhanced disciplinary methods in aerodynamics and structural analysis, the development of efficient reduced order methods for load analysis, the development of a multidisciplinary optimization process based on a multi-level/variable-fidelity approach, as well as the development and application of multidisciplinary methods for the analysis of maneuver loads.

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