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In the present work, the Eulerian Large Eddy Simulation of dilute dispersephase flows is investigated. By highlighting the main advantages and drawbacksof the available approaches in the literature, a choice is made in terms ofmodelling: a Fokker-Planck-like filtered kinetic equation proposed by Zaichiket al. 2009 and a Kinetic-Based Moment Method (KBMM) based on a Gaussianclosure for the NDF proposed by Vie et al. 2014. The resulting Euler-likesystem of equations is able to reproduce the dynamics of particles for small tomoderate Stokes number flows, given a LES model for the gaseous phase, and isrepresentative of the generic difficulties of such models. Indeed, itencounters strong constraints in terms of numerics in the small Stokes numberlimit, which can lead to a degeneracy of the accuracy of standard numericalmethods. These constraints are: 1/as the resulting sound speed is inverselyproportional to the Stokes number, it is highly CFL-constraining, and 2/thesystem tends to an advection-diffusion limit equation on the number densitythat has to be properly approximated by the designed scheme used for the wholerange of Stokes numbers. Then, the present work proposes a numerical schemethat is able to handle both. Relying on the ideas introduced in a differentcontext by Chalons et al. 2013: a Lagrange-Projection, a relaxation formulationand a HLLC scheme with source terms, we extend the approach to a singular fluxas well as properly handle the energy equation. The final scheme is proven tobe Asymptotic-Preserving on 1D cases comparing to either converged oranalytical solutions and can easily be extended to multidimensionalconfigurations, thus setting the path for realistic applications.

On the Eulerian Large Eddy Simulation of disperse phase flows: an asymptotic preserving scheme for small Stokes number flows