The vortex method is applied to the calculation of a decaying homogeneous isotropic turbulence of Re k = 25, 50 and the results are compared with a spectral method calculation. Vortex method calculations were accelerated by the use of a fast multipole method for periodic boundary conditions. The core spreading method and particle strength exchange were selected as the viscous diffusion scheme. The effect of spatial resolution was examined along with Reynolds number dependence and the effect of spatial adaption of elements.

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Abstract-The present study discusses some numerical techniques on the simultaneous use of the Fast Multipole Method (FMM) and special-purpose computer (MDGRAPE-3) to make the impractically expensive calculation feasible without the loss of numerical accuracy. In the present calculations, the impingement of two identical inclined vortex rings has been studied, and the computation time has been reduced by a factor of 1000 at N = 1.18×10 6 where N is the number of vortex elements. The direct and MDGRAPE-3 calculations both have a scaling of O(N 2 ), and the use of the FMM brings them both down to O(N ). The global kinetic energy, enstrophy and energy spectra have been investigated to address the numerical accuracy and have good agreement with other similar works.