Review on numerical algorithms for solving general dynamic equations of the acoustic agglomeration

Owing to the rapid growth of advanced manufacturing, particulate pollutants generated during machining processes pose significant risks to human health, equipment safety, atmosphere quality and climate. Current industrial control technologies struggle to effectively remove these particles. Acoustic agglomeration technology is an effective particle pretreatment that uses acoustic waves to facilitate the growth and subsequent removal of particles.

Particle dynamics simulation is adept at depicting particle acoustic agglomeration. It utilises numerical algorithms to address the general dynamic equation (GDE), which quantifies the evolution of particle dynamics. Using conventional numerical techniques to solve the GDE is challenging because of its typical partial integro-differential nature and the intricate agglomeration mechanisms it encompasses. Therefore, drawing on acoustic agglomeration GDE, the research provide a comprehensive review of the characteristics and recent research progress of various algorithms used to solve the GDE of acoustic agglomeration, including method of moments, partition method, the Monte Carlo (MC) algorithm and discrete element method (DEM). MC algorithm, DEM and the coupling of DEM and other method are reviewed in detail. Finally, limitations and future opportunities are discussed about algorithm's applications. This review offers valuable insights into visualising particle acoustic agglomeration, elucidating its microscopic mechanisms and predicting its macroscopic effects on particle agglomeration. Meanwhile, it provides a comprehensive perspective for the optimization, integration and innovation of subsequent numerical algorithms. Thereby, the healthy industrial environment is established, and the achievement of the Sustainable Development Goals is advanced.