Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications

In recent years, the fast growth of computational power has allowed the application of computational fluid dynamics (CFD) in a wide range of areas of interest, such as gas–solid unit operations. In this context, the multiphase particle-in-cell (MP-PIC) method appears as an option to represent fluid–particle and particle–particle interactions, avoiding the complexity of tracking each particle and the high computational cost derived from this. The MP-PIC method can represent the particles as a group with the same characteristics, allowing the simulation of gas–solid systems at different scales. To achieve this, the particle–particle interactions are simplified using the solid stress tensor to represent them; this does not require explicit expressions. This approach has a low computational cost, allowing the simulation of industrial cases using just workstations. This paper provides a review of the literature on the solid stress tensor and its commercial and non-commercial applications, including its historical and mathematical development in the description of particle–particle interactions. In addition, to consolidate the knowledge and advancing understanding in this crucial aspect of multiphase flow simulations, this review identifies the current challenges and opportunities for future research in multiphase systems based on the solid stress tensor. In addition, this review identifies the current challenges and opportunities for future research in multiphase systems based on the solid stress tensor.