Coarse-grid simulations of gas-solids flows are common practice with continuum-based models, which is necessary to obtain numerical results quickly enough to be useful. Such coarse-grid simulations are able to qualitatively resolve large-scale behaviors, such as bubbles and large clusters of solids that have been observed experimentally. It is well known that the continuum approach fails to capture the small-scale heterogeneous flow structures unless very high grid resolutions are employed. Such grid refinement studies have also led to the development of sub-grid models that can be used with coarse-grid continuum simulations and result in faster simulations of gas-solids flows [1, 2].
Discrete particle models that track the trajectory and collisions of every particle are more accurate than continuum models but are not economical for many practical gas-solids flow systems due to the large amount of particles involved. A more affordable discrete technique, called multiphase particle-in-cell (or MP-PIC) is based on lumping many particles together in a parcel in order to track fewer particles and replaces the collisional interactions with a continuum pressure gradient . The MP-PIC technique still requires coarse computational grids so that fewer parcels can be used and the computational cost remains affordable. In this study we examine if the MP-PIC approach, when applied over coarse grids, requires similar sub-grid corrections as continuum models.
To address this issue, we have conducted continuum and MP-PIC simulations of gas-particle flows in a 2D periodic domain at several grid resolutions. The simulations assumed that the particles were all of the same size. The constitutive models for the continuum approach was chosen to match those employed in the MP-PIC approach; specifically, both of these modeling approaches used the same solids pressure model and the Wen & Yu  drag law. Both continuum and MP-PIC simulations using coarse grids manifested nearly homogeneous flows where the domain-average slip velocity was essentially the same as that for homogeneous flow. When the grid was refined, the numerical results for both approaches manifested heterogeneous flow structures that increased the domain-average gas-particles slip velocity to 2.5-3 times that for homogeneous flow; importantly, both approaches manifested very similar flow structures and yielded essentially the same domain-average slip velocity. These results confirm the inherent equivalence between the two approaches. From a practical point of view, our study indicates that the sub-grid models that are being developed for the continuum approach can (and should) be imported to the MP-PIC approach.
References:  Andrews, A. T.; Loezos, P. N.; Sundaresan, S. Coarse-grid simulation of gas-particle flows in vertical risers. Ind. Eng. Chem. Res. 2005, 44, 6022.  Igci, Y.; Andrews, A. T.; Sundaresan, S.; Pannala, S.; O'Brien, T. Filtered two-fluid models for fluidized gas-particle suspensions. AIChE J. 2008, 54, 1431.  Snider, D.M. An incompressible three-dimensional multiphase particle-in-cell model for dense particle flows. J. Comput. Phys. 2001, 170, 523549.  Wen, C. Y.; Yu, Y. H. Mechanics of Fluidization. Chem. Eng. Prog. Symp. Ser. 1966, 62, 100-111.