### Test Cases  
The assessment of the computational approaches and their experimental validations are based on four different test cases that seek to represent a wide range of regimes. For each case, a 3D cylindrical domain is considered using the geometry described in Section 2. Table 1 shows the bed depth, rotational velocity, and the regime observed experimentally, and Figure 4 shows the four regimes studied on a Bed Behavior Diagram (BBD). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Bed Depth [m]** & **Rotational Speed [rpm]** & **Observed Regime** \\ \hline A & 0.125 & 0.25 & Slumping \\ B & 0.075 & 25 & Transitional (Rolling/Cascading) \\ C & 0.075 & 2.5 & Rolling \\ D & 0.125 & 25 & Cascading \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test cases. Figure 4: Bed Behavior Diagram for DAP. For both computational methods, uniformly distributed spherical particles that have a 4-mm diameter are considered. The particles density for DAP is 1600 Kg/m\({}^{3}\) and the static friction coefficient is \(\mu_{1}=0.53\). Case B and D require around 3 s to reach a steady state while Case C needed less than 10 seconds. The regime observed experimentally for Case A is slumpling, so a steady state is never reached, but a statistically steady state (where particles bed move back and forth at a fixed time period) is reached after the first 5 s from the beginning of the experiment. Table 2 shows the numerical and physical parameters adopted for the CM. For the CM simulations, an O-grid FVM mesh of 168.000 cells, with 5 cells in the depth, is adopted (as shown in Figure 5). Finer and coarser grids where tested beforehand and the current refinement was selected based on preserving a well-balanced relation between the computational cost involved in the simulations and the accuracy of the solution. It was observed that the solution fields do not change significantly for finer grids. A rotating wall boundary condition is imposed for all the surrounding walls of the drum. No turbulence model is used for the CM simulations and the air is treated as an incompressible fluid with properties at  
DEM simulations were performed using LIGGGHTS which is an open-source software for modeling granular materials [49]. The stability of DEM simulations can be ensured by setting the time step equal to 20% of the Raleigh time step sizes (see LIGGGHTS documentation and also [61]). Spherical particles (urea and DAP) with the same radii (2 mm) were used in all DEM simulations. Most of the constants were chosen on a purely empirical basis or were obtained by the calibration procedure (see below) and are summarized in Table 3.  
The calibration procedure was the following. To determine the values of the coefficients of friction (sliding and rolling friction) for one type of material (DAP), two experiments were chosen: Static and dynamic angles of repose. The angle of repose is defined as the angle of inclination of the free surface to the horizontal of a conical bulk solid stack. It strongly depends on material properties such as sliding and rolling friction, but is not sensitive to the density of particles, Poisson's ratio, or Young's modulus [62; 63; 64]. Pile formation experiments in hoppers were performed to measure the static angle of repose, and the dynamic angle of repose was measured in the rotating drum tests. For the mixture of DAP and urea, the same parameter values were used except for the density and number of particles. Particles were generated in a parallelepipedic region of the domain (400 \(\times\) 47 \(\times\) 100 mm) located 200 mm from the bottom of the drum. A uniform distribution in size but random in position was followed, with a rate of 200,000 particles/s, by generating new particles every 5000 timesteps. This is so because particles must leave the domain before new ones can be generated. As they are generated, particles fall by gravity and settle to the bottom of the drum by forming a pile.