  We propose a novel model to obtain the subgrid-scale velocity in the context
of large-eddy simulation (LES) of particle-laden turbulent flows, to recover
accurate particle statistics. In the new wavelet enrichment model, the
subgrid-scale velocity is discretized with a divergence-free wavelet vector
basis, and the coefficients of the expansion are obtained by minimizing the
squared error of the linearized subfilter Navier-Stokes equations (SFNSE). The
compact support of the wavelet basis is exploited to achieve continuously
varying subgrid-scale velocity statistics across the domain. The performance of
the new wavelet enrichment model is evaluated in single-phase and
particle-laden flow simulations, comparing the results with the results of
direct numerical simulations (DNS). The simulations show that the model can
generate inhomogeneous and anisotropic velocity statistics, accurate
strain-rotation relations, and a good approximation of the kinetic energy
spectrum of the corresponding DNS. Furthermore, the model significantly
improves the prediction of the particle-pair dispersion, the clustering of the
particles, and the turbulence modulation by particles in two-way coupled
simulations. The proposed model recovers the most important interactions
between fluid turbulence and the behavior of the particles, while maintaining
the computational cost on the order of a LES.
