A multilevel proper orthogonal decomposition (mPOD) is introduced for obtaining the proper orthogonal decomposition (POD) of data sets with a large number of snapshots without requiring the solution of an equally large eigenvalue problem. mPOD works by producing the PODs for subsets of data first and then applying the POD again to the modes obtained from these subsets. A proof is given that mPOD reproduces identically the modes that would be obtained with the standard POD. mPOD also provides a systematic way to combine POD modes obtained from different simulations and to update POD modes using new data. A numerical algorithm based on mPOD is developed that shows a factor of 10 reduction in computation time compared to snapshot POD. The method is applied to data for fluid flow over a NACA 0015 at R e = 1000 with an actuator jet on the top surface of the airfoil, and results are compared to methods such as subsampling, double proper orthogonal decomposition, sequential mode generation methods, recursive singular value decomposition (R-SVD), and partitioned R-SVD. The examples demonstrate that mPOD provides more accurate eigenvalues, requires fewer disk accesses, and generates modes that create more reliable reduced-order models and have better orthogonality properties than any of the other methods.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Multilevel Algorithm for Obtaining the Proper Orthogonal Decomposition


    Contributors:

    Published in:

    AIAA Journal ; 56 , 11 ; 4423-4436


    Publication date :

    2018-11-01




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Guide to Spectral Proper Orthogonal Decomposition

    Schmidt, Oliver T. / Colonius, Tim | AIAA | 2020

    Free access

    Proper orthogonal decomposition analysis for engine research

    Sick,V. / Chen,H. / Abraham,P. et al. | Automotive engineering | 2012




    Proper Orthogonal Decomposition of Turbine RotorStator Interaction

    Paul G. A. Cizmas / Antonio Palacios | AIAA | 2003