Turbulence models are expected to satisfy the conflicting requirements of accuracy and computational efficiency. Here we discuss a new model that was recently developed in order to accurately and efficiently describe the dynamic of a clouds of tracers particles in Large Eddy Simulations of homogeneous and isotropic turbulent flows. The models incorporates the multi-scale nature of time and space turbulent velocity correlations that are essential in order to correctly reproduce the relative dispersion of multi-particle clouds. The model can be seen as an off-grid solver for the Eulerian velocity field at the positions of a given number of Lagrangian tracers that self-consistently move with it. Extensions to non homogeneous and isotropic turbulence as well as to the dynamics of particles will be discussed.