Application of the nonuniform fast Fourier transform to the direct numerical simulation of two-way coupled particle laden flows

We present the application of the Nonuniform Fast Fourier Transform (NUFFT) to the pseudo-spectral Eulerian–Lagrangian direct numerical simulation of particle-laden flows. In the two-way coupling regime, when the particle feedback on the flow is taken into account, a spectral method requires not only the interpolation of the flow fields at particle positions, but also the Fourier representation of the particle back-reaction on the flow fields on a regular grid. Even though the direct B-spline interpolation is a well-established tool, to the best of our knowledge the reverse projection scheme has never been used, replaced by less accurate linear reverse interpolation or Gaussian regularization. We propose to compute the particle momentum and temperature feedback on the flow by means of the forward NUFFT, while the backward NUFFT is used to perform the B-spline interpolation. Since the backward and forward transformations are symmetric and the (non local) convolution computed in physical space is removed in Fourier space, this procedure satisfies all constraints for a consistent interpolation scheme, and allows an efficient implementation of high-order interpolations. The resulting method is applied to the direct numerical simulation of a forced and isotropic turbulent flow with different particle Stokes numbers in the two-way coupling regime. A marked multifractal scaling is observed in the particle statistics, which implies that the feedback from the particles on the fields is far from being analytic and therefore only high-order methods, like the one here proposed, can provide an accurate representation.