Adaptive reduced basis method for the reconstruction of unsteady vortex-dominated flows

A local adaptive Reduced Basis approach is presented with a focus on the accuracy in reconstructing unsteady vortex-dominated flow fields generated by impulsively started lifting surfaces and bodies. The adaptive approach is built on the combination of methods based on Proper Orthogonal Decomposition, Spectral Orthogonal Decomposition, Dynamic Mode Decomposition and Recursive Dynamic Mode Decomposition and aims at making possible to explicitly take into account the temporal correlation between available snapshots of the problem. The latter has proven to be a critical element when building a Reduced Model for complex non-periodic and nonlinear unsteady flows. For a given instant of time in which the reconstruction is needed, the most accurate Reduced Model is automatically selected on the basis of an estimation of the error of the various methods in reconstructing the entire flow field. The impulsive start of a 2D symmetric airfoil, which evolves towards a periodic limit cycle, and the impulsive start of a three element airfoil and a 3D wing in high-lift configurations will be considered as demonstration cases.