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Fast Multipole Method vs. Spectral Method for the Simulation of Isotropic Turbulence on GPUs

Rio Yokota, L. A. Barba
Department of Mechanical Engineering, Boston University, Boston, MA, 02215, USA
arXiv:1110.2921v1 [cs.NA] (13 Oct 2011)

@article{2011arXiv1110.2921Y,

   author={Yokota, Rio and Barba, LA},

   title={"{Fast Multipole Method vs. Spectral Method for the Simulation of Isotropic Turbulence on GPUs}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1110.2921},

   primaryClass={"cs.NA"},

   keywords={Computer Science, Numerical Analysis, Computational Physics, Fluid Dynamics},

   year={2011},

   month={oct}

}

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This paper presents calculations of homogeneous isotropic turbulence at Re_{lambda} = 100 using both a pseudo-spectral method and a fast multipole vortex method on a 256^3 grid. For the vortex method, both algorithmic and hardware acceleration are applied using a highly parallel fast multipole method (FMM) on GPUs. The spectral methods uses the FFTW library for the computation of Fourier transforms. Comparison of the results obtained with the two methods, under the same calculation conditions and on the same machine, show quantitative agreement. The quantitative agreement between the pseudo-spectral method and the vortex method for high-order turbulence statistics exemplifies the high accuracy of the present vortex method simulation. Furthermore, with the help of GPUs, the vortex method can simulate isotropic turbulence at similar speed to pseudo-spectral methods.
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