Spatio-Temporal Identification And Collocation Of Vortex Breakdown Using Reduced Basis Methods - MF5

Abstract Reduced order modelling techniques have been applied to a set of given Computational Fluid Dynamics (CFD) flow solutions over a high angle of attack delta wing to investigate their ability to reconstruct vortex breakdown. Where possible, a criteria for breakdown has been applied to the flow reconstructions and a bisection method implemented to allow the known interval in which the occurrence of breakdown lies to be reduced. Two and four snapshots have been used for each method to see how the methods perform given a small amount of ‘training‘ data. Different breakdown criteria found within literature have been presented and discussed, with the stagnation point criteria being selected due to its simplicity and ease of implementation. Dynamic Mode Decomposition (DMD) produced the most accurate reconstructions in comparison to the CFD solutions with both two and four snapshots, whereas Proper Orthogonal Decomposition (POD) could not produce feasible results when using two snapshots, but was able to reconstruct the flow using four snapshots to a similar a degree of accuracy as DMD. Spectral-POD (SPOD) and Recursive-DMD (RDMD) did not perform as expected in the reconstructions due to the limited number of available snapshots, meaning their algorithms to better extract the modes when compared to POD and DMD could not be used effectively. DMD with both two and four snapshots along with POD with four snapshots all produced feasible flow reconstructions thus were all able to be iterated to narrow the interval in which breakdown occurs. A high fidelity simulation of flow over a delta wing was attempted however due to the assumptions made (laminar and inviscid) along with improper mesh refinement no solutions were gained.