More efficient time integration for Fourier pseudo-spectral DNS of incompressible turbulence
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Ketcheson_et_al-2019-International_Journal_for_Numerical_Methods_in_Fluids.pdf
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Accepted manuscript
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center
Date
2019-10-30Online Publication Date
2019-10-30Print Publication Date
2020-02Embargo End Date
2020-10-15Permanent link to this record
http://hdl.handle.net/10754/658659
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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.4773Sponsors
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
WileyDOI
10.1002/fld.4773Additional Links
http://doi.wiley.com/10.1002/fld.4773ae974a485f413a2113503eed53cd6c53
10.1002/fld.4773