Manifold learning-based reduced-order model for full speed flow field

Reduced-order models (ROMs) can effectively balance the accuracy and efficiency of computational fluid dynamics (CFD). The nonlinear flow field characteristics cannot be captured accurately by traditional ROMs, such as proper orthogonal decomposition (POD). Combining isometric mapping (ISOMAP) and local linear embedding (LLE), a novel manifold learning method (ISOMAP-Local LLE) is proposed, performing global and accurate reconstruction of the nonlinear flow field. First, the nonlinear dimensionality reduction is derived by considering the global isometric characteristic and the local reconstruction relationship simultaneously. Then, the local interpolation model is constructed to improve the interpolation accuracy introduced by the global interpolation model. Finally, the flow field reconstruction is accomplished based on the inverse mapping. Furthermore, the criteria of hyperparameters have been established to achieve high-precision prediction. Several examples covering full speed flow field are carried out to demonstrate the accuracy and efficiency of ISOMAP-Local LLE. The proposed manifold learning-based ROM achieves prediction accuracy that surpasses that of other ROMs (such as POD, ISOMAP, LLE, etc.), resulting in significant time cost savings for CFD simulations.