Within engineering applications, particles and particulate systems are of great interest. Advances in the understanding of particulate systems can bring great economic benefits to the industry; however the knowledge available is still limited enormously due to the lack of measurement techniques. The establishment of a theoretical system for particulate matters is in its infancy. Numerical modeling based on mathematical equations, regarded as an important branch of applied mathematics, provides an alternative and powerful tool to understand the fundamental science governing the particulate flows in order to optimize various processes in engineering.

This special issue welcomes both original research and review articles summarizing the state-of-the-art of the numerical modeling work concerning particulate systems across the fields of applied mathematics, chemical engineering, and energy engineering. No limitation is imposed on either the size of the particles, which may range from nanometer scale to that of mined or quarried materials, or on the complexity of the system in which multiphase interaction phenomenon may exist. Particle-based methods on continuous materials are also welcome. As a result, the expected studies can be either an establishment or improvement of the mathematical solver (accuracy or efficiency) or the direct use of the mathematical model for applications involving particulate materials.

Potential topics include but are not limited to the following:

• Analytical and numerical predictions of particulate systems
• Interaction laws for dry or wet particle-particle collisions
• Numerical modeling of particle/droplet/bubble flows and applications
• Numerical modeling of fluid-solid interaction problems
• Numerical modeling of multiscale and multiphase particulate flows
• High performance computation using particle-based methods