Reduced order modelling for aerodynamic applications is known to be challenging because of the inherent nonlinearities in the flow problem. The objective of this thesis is to construct a non-intrusive parametric ROM capable of solving fluid problems with strong nonlinearities, in particular, for steady transonic flow problems to resolve the shock gradients better. The proposed ROM does not require any knowledge of the governing equations. Manifold learning methods are applied to extract low dimensional information from the flow solu- tion manifold. Three manifold learning methods are applied, including a global property preserv- ing method Isomap and two local property preserving methods Laplacian eigenmaps and Hessian eigenmaps. To utilise the low-dimensional information, manifold learning methods are combined with an interpolation scheme and a proper back-mapping method to predict flow solutions under new parameter configuration, which is not included in the pre-computed solution database. Three reverse mapping methods are introduced. The first is a pure data-based method based on the inverse mapping of local linear embedding, called Manifold+I. The second is based on least-square flux residual minimization, referred to as Manifold+LSQ. In order to give priority to residual minimisation in the shock region, the third method is enhanced with the k-means algorithm, called Manifold+LSQ+KM. The proposed ROMs are illustrated with two test cases of two-dimensional transonic flows. The first test case considers the steady transonic flow past an airfoil under varying angles of attack and Mach number. The second test case considers, in addition to the parameters in the first test case, a shape parameter. Flow solutions are obtained from the commercial software StarCCM+. Flow solutions of the second test case are of different length and are thus first mapped to a constant Lagrange grid before further dimension reduction is conducted. Good correlations with results obtained from high-fidelity simulations and the manifold learning based ROMs are reported. Compared to the state-of-the-art method POD+I, an improvement of the result     «

Reduced order modelling for aerodynamic applications is known to be challenging because of the inherent nonlinearities in the flow problem. The objective of this thesis is to construct a non-intrusive parametric ROM capable of solving fluid problems with strong nonlinearities, in particular, for steady transonic flow problems to resolve the shock gradients better. The proposed ROM does not require any knowledge of the governing equations. Manifold learning methods are applied to extract low...     »