Derivation and analysis of the analytical velocity and vortex stretching expressions for an O (N log N)-FMM

T. Berdowski, Jens Honore Walther, Célia Maria Dias Ferreira, F. Meng

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    In the current paper, a method for deriving the analytical expressions for the velocity and vortex stretching terms as a function of the spherical multipole expansion approximation of the vector potential is presented. These terms are essential in the context of 3D Lagrangian vortex particle methods combined with fast summation techniques. The convergence and computational efficiency of this approach is assessed in the framework of an O (N log N)-type Fast Multipole Method (FMM), by using vorticity particles to simulate a system of coaxial vortex rings for which also the exact results are known. It is found that the current implementation converges rapidly to the exact solution with increasing expansion order and acceptance factor. An investigation into the computational efficiency demonstrated that the O(N log N)-type FMM is already viable for a particle size of only several thousands and that this speedup increases significantly with the number of particles. Finally, it is shown that the implementation of the FMM with the current analytical expressions is at least twice as fast as when opting for using even the simplest implementation of finite differences instead.
    Original languageEnglish
    Article number082023
    Book seriesJournal of Physics: Conference Series (Online)
    Number of pages11
    Publication statusPublished - 2016
    EventThe Science of Making Torque from Wind 2016 - Technische Universität München (TUM), Munich, Germany
    Duration: 5 Oct 20167 Oct 2016
    Conference number: 6


    ConferenceThe Science of Making Torque from Wind 2016
    LocationTechnische Universität München (TUM)
    Internet address

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