More efficient time integration for Fourier pseudospectral DNS of incompressible turbulence |
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Authors: | David I Ketcheson Mikael Mortensen Matteo Parsani Nathanael Schilling |
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Institution: | 1. King Abdullah University of Science and Technology (KAUST), Extreme Computing Research Center (ECRC), Computer Electrical and Mathematical Science and Engineering Division (CEMSE), Thuwal, Saudi Arabia;2. Department of Mathematics, University of Oslo Mathematics and Natural Sciences, Oslo, Norway;3. Center for Mathematics, Technical University of Munich, Garching, Germany |
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Abstract: | Time integration of Fourier pseudospectral DNS is usually performed using the classical fourth-order accurate Runge-Kutta method or other second- or third-order methods, 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 and Shampine gives much greater accuracy at a significantly reduced computational cost. Specifically, we demonstrate speedups of 2× to 10× 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. |
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Keywords: | adaptivity error estimation incompressible flow spectral time integration turbulent flow |
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