## 4 Results
### Particles Distribution  
Figure 6 shows side-by-side the distribution of particles for the four proposed cases in the experiments and by computational simulations. In particular, for Case A, DEM is able to predict the slumping regime as in the experiment, where the free surface of the bed of particles oscillates between two different angles and does not reach a steady position in time. Conversely, the continuum model does not capture this transient effect, showing a steady distribution with the plane of the free surface at an angle within the limits observed experimentally. This can be attributed to the absence of a yield criterion in the model above in which the pack of grains behave as a rigid body. Without this physical characteristic, the stick-and-slide effect of the slumping regime cannot occur. For Case B, DEM predicts more splashing of particles in the right upper part of the bed compared to the experiment, while the continuum model does not. The same behavior is observed in Case C, where isolated particles move following the cylindrical wall of the drum and leave the dense core of particles before falling for their own weight. At the left-most part of the particles bed, in each of the CM simulations, an unphysical \"noise\" in the solids fraction field might also be observed. This is due to the fact that particles are modeled as a continuum and the use of a refined grid with cells smaller than the particles size. In these conditions, it is possible to obtain intermediate volume fractions (between 0 and 1) at certain places where there should be only particles or air. In any case, the amount of solids fraction here represents less than 0.1% of the granular bed which does not affect the general results. Although in general the results of the CM are in good agreement with the experiments, the regimes with higher velocities (Case B and D) exhibit a lack of accuracy to predict the length of the \"tail\" of the bed surface (bottom-left part region of the bed). This could be observed in more detail in Figure 7, where the interfaces between the bed of particles and air are plotted simultaneously for the three methods of observation/prediction. The reason behind the differences is that the CM is preserving the initial volume while the volume of mixture in DEM and experiment expands. This is due to the presence of air that percolates through the core of the bed as the drum is rotating. This effect is emphasized at higher velocities (Case B and D) and cannot be captured by the CM. For the continuum model, the bed surface is defined as an isosurface with 0.5 of concentration. Overall, the distribution of particles is accurately predicted by the CM and DEM, with the exception of Case A where the slumping effect cannot be captured by CM. In addition, for Case D, the bed surface predicted by CM does not match perfectly with the results of the experiment and DEM. Regarding the computational costs, the simulations of Case C are taken as a reference. To achieve a steady distribution of particles for this problem, 12 s of physical time is required. Both methods of simulation use a set of numerical parameters that optimize the costs for a similar level of accuracy of the solution. This is achieved in practice by repeating the simulations, each time modifying certain numerical parameters with the purpose of increasing the time step as long as the numerical stability is not lost. For DEM, the simulation required 10.530 s, where a maximum time step of \(\Delta t=2\times 10^{-5}\) s was used. For CM, the simulation required 8.340 s, where a fixed time step of \(\Delta t=2\times 10^{-3}\) s was needed. For these conditions, and given the FVM mesh adopted, CM saves around 20% of computational costs compared to DEM. While this saving could be considered marginal given the accuracy requirements for this problem and the overall time consumed (no more  
Figure 6: Particles distribution for the four test cases: (_a_) Experiment, (_b_) DEM, and (_c_) CM.