The nuclear source term is greatly affected by the formation and presence of aerosols in the reactor primary vessel and the containment. In simulations, the aerosol distribution is often assumed spatially homogeneous (well mixed), and there have been relatively few studies of the effects of spatial inhomogeneity on aerosol evolution in nuclear accidents. We have explored here an extension of some of our recent work on the Direct Simulation Monte Carlo (DSMC) method to spatially inhomogeneous aerosol. In doing so, we have also departed from the traditional applications of the DSMC method where the computational domain is divided into fixed cells. We have explored here an alternative, mesh-free method by utilizing a clustering technique. This technique associates particles according to a distance parameter and is commonly used in group theory and machine learning. To benchmark this mesh-free modeling, we have verified the DSMC results against those obtained from the use of the cell balanced sectional technique for a spherical geometry where both coagulation and diffusion take place.