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    More efficient time integration for Fourier pseudo-spectral DNS of incompressible turbulence

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    Name:
    Ketcheson_et_al-2019-International_Journal_for_Numerical_Methods_in_Fluids.pdf
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    3.408Mb
    Format:
    PDF
    Description:
    Accepted manuscript
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    Type
    Article
    Authors
    Ketcheson, David I. cc
    Mortensen, Mikael cc
    Parsani, Matteo cc
    Schilling, Nathanael
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Extreme Computing Research Center
    Date
    2019-10-30
    Online Publication Date
    2019-10-30
    Print Publication Date
    2020-02
    Embargo End Date
    2020-10-15
    Permanent link to this record
    http://hdl.handle.net/10754/658659
    
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    Abstract
    Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge–Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order Runge–Kutta pairs and automatic step size control based on local error estimation. We find that the fifth-order accurate Runge–Kutta pair of Bogacki & Shampine gives much greater accuracy at a significantly reduced computational cost. Specifically, we demonstrate speedups of 2x-10x for the same accuracy. Numerical tests (including the Taylor–Green vortex, Rayleigh–Taylor instability, and homogeneous isotropic turbulence) confirm the reliability and efficiency of the method. We also show that adaptive time stepping provides a significant computational advantage for some problems (like the development of a Rayleigh–Taylor instability) without compromising accuracy.
    Citation
    Ketcheson, D. I., Mortensen, M., Parsani, M., & Schilling, N. (2019). More efficient time integration for Fourier pseudo-spectral DNS of incompressible turbulence. International Journal for Numerical Methods in Fluids. doi:10.1002/fld.4773
    Sponsors
    This research used the resources of the Supercomputing Laboratory and Extreme Computing Research Center at the King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia. N.S. was supported by the KAUST Visiting Student Research Program. N.S. alsoacknowledges support from the Priority Programme SPP1881 Turbulent Superstructures of theDeutsche Forschungsgemeinschaft. M. M. acknowledges support from the 4DSpace StrategicResearch Initiative at the University of Oslo.
    Publisher
    Wiley
    Journal
    International Journal for Numerical Methods in Fluids
    DOI
    10.1002/fld.4773
    Additional Links
    http://doi.wiley.com/10.1002/fld.4773
    ae974a485f413a2113503eed53cd6c53
    10.1002/fld.4773
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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