  The Lagrangian vortex method offers an alternative numerical approach for
direct numerical simulation of turbulence. The fact that it uses the fast
multipole method (FMM)--a hierarchical algorithm for N-body problems with
highly scalable parallel implementations--as numerical engine makes it a
potentially good candidate for exascale systems. However, there have been few
validation studies of Lagrangian vortex simulations and the insufficient
comparisons against standard DNS codes has left ample room for skepticism. This
paper presents a comparison between a Lagrangian vortex method and a
pseudo-spectral method for the simulation of decaying homogeneous isotropic
turbulence. This flow field is chosen despite the fact that it is not the most
favorable flow problem for particle methods (which shine in wake flows or where
vorticity is compact), due to the fact that it is ideal for the quantitative
validation of DNS codes. We use a 256^3 grid with Re_lambda=50 and 100 and look
at the turbulence statistics, including high-order moments. The focus is on the
effect of the various parameters in the vortex method, e.g., order of FMM
series expansion, frequency of reinitialization, overlap ratio and time step.
The vortex method uses an FMM code (exaFMM) that runs on GPU hardware using
CUDA, while the spectral code (hit3d) runs on CPU only. Results indicate that,
for this application (and with the current code implementations), the spectral
method is an order of magnitude faster than the vortex method when using a
single GPU for the FMM and six CPU cores for the FFT.
