Comparison between Lagrangian and Eulerian mesoscopic modelling approaches for inertial particles suspended in decaying isotropic turbulence

The purpose of this paper is to evaluate an unsteady Eulerian approach from a direct comparison with a Lagrangian approach for the simulation of an ensemble of non-colliding particles interacting with a decaying homogeneous isotropic turbulence given by DNS. Comparison between both approaches is is carried out for two different particle inertia from global instantaneous quantities such as particle kinetic energy, local instantaneous Eulerian quantities such as particle number density and spectral quantities such as spectral particle kinetic energy. The proposed Eulerian approach yields instantaneous three dimensional velocity and number density fields which are in very good agreement, at large scales, with the discrete particle simulation results. However, appreciable discrepancies between the two approaches are measured at small scales for the particles with larger inertia. Indeed, for Stokes number value close to unity, segregation effects are very important and due to the stiff gradients in number density the Eulerian method is limited by spatial grid resPreprint submitted to J. Comp. Physics 15 May 2006 olution. To overcome this numerical difficulty, a simulation approach using a bulk viscosity is proposed.