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arXiv · 1810.10197

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

David I. Ketcheson·Mikael Mortensen·Matteo Parsani·Nathanael Schilling
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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.

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David I. Ketcheson, Mikael Mortensen, Matteo Parsani, Nathanael Schilling. 2019-11-07. More efficient time integration for Fourier pseudo-spectral DNS of incompressible turbulence. https://doi.org/10.1002/fld.4773

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