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

The ability of the non-uniform Fast Fourier Transform (NUFFT) to predict the particle feedback on the flow in particle-laden flows in the two-way coupling regime is examined. In this regime, the particle back-reaction on the fluid phase can substantially modify the flow statistics across all the scales, when particle loading is significant. While many works in the literature focus on the direct B-spline interpolation, which is now a well-established method for the one-way coupling, only a few methods are available for the computation of particle back-reaction, which are often lower order and reduce the overall accuracy of the simulation. In our implementation, particle momentum and temperature back-reactions on the fluid flow are computed by means of the forward NUFFT with B-spline basis, while the B-spline interpolation is performed as a backward NUFFT. An application of the NUFFT to the simulation of a statistically steady and isotropic turbulent flow, laden with inertial particles is presented. The effect of particle feedback on velocity and temperature structure functions and on particle clustering is discussed as a function of the Stokes number, together with the spectral characterization of the particle phase.