Application of the Continuum Particle Method to bubbling-fluidized and spout-fluidized beds

We develop a new implementation of the Continuum Particle Method (CPM) introduced by Verma and Padding (2020), a novel approach to multiphase particle-in-cell (MP-PIC) simulations, based on a face interpolation method that aims to improve robustness and accuracy. We present a comprehensive comparison of CPM, MP-PIC, and computational fluid dynamics coupled with the discrete element method (CFD-DEM) against experimental data from the literature for fluidized and spout-fluidized systems. We evaluate the methods using two drag models and show that CPM agrees better with both experiments and CFD-DEM. We demonstrate that the unsatisfactory performance of MP-PIC does not primarily arise from the selected drag model. Instead, it results from the simplified particle stress model, which depends only on the local particle volume fraction. This model accounts only for isotropic particle pressure and neglects viscous and frictional particle stresses, thereby missing key resistance mechanisms associated with shear and elongational deformation in dense particle regions. We also examine the role of smoothing in CPM by varying the characteristic smoothing length applied to particle fields. We show that smoothing strongly affects the predicted flow behavior and that the optimal level of smoothing depends on the operating flow regime. Finally, we assess particle mixing and find that CPM predicts faster mixing than CFD-DEM under the investigated conditions. Overall, we show that CPM offers a promising and computationally efficient alternative for simulating dense gas-solid flows while retaining improved agreement with benchmark numerical and experimental results.