**6. Algorithm of interaction between particles and particle-free materials**

The algorithm for volume flux calculations has a modification to deal with mixed cells containing materials with and without particles.

Consider the case of a cell filled with heterogeneous materials, one described only by grid quantities, and the other, by particles (1 and 2, respectively, in **Figure 4**). Suppose we need to divide the flux moving from left to right (shown with a darker color) between the materials. The volume flux leaving the cell is first filled with the volume of migrating particles. If the migrating particles' total volume exceeds this volume flux, then the above particle splitting algorithm is engaged (see Section 4, case δV < 0).

Otherwise, the missing part of the outflowing volume flux is filled with the particle-free material. If there are several particle-free materials, the volume is distributed among them based on the VOF algorithm [1]. If the particle-free materials are still not enough, the remaining volume flux is filled with particles using the splitting algorithm for the case of δV > 0 from Section 4.
