An Overview of Numerical Methods for Incompressible Viscous Flow with Moving Particles

The importance of the fluid–particle interaction problem is considerable. Tremendous attention has been paid by researchers in the past two decades. This paper presents an overview of the representative methods for the simulation of incompressible viscous flow with moving boundaries based on conforming or nonconforming meshes. These methods include the distributed Lagrange multiplier/fictitious domain method, the immersed boundary method, the lattice Boltzmann method, and the arbitrary Lagrange–Eulerian method. The classification of the selected methodology is made to create a firm foundation for the future. The latest developments in the field during past few years are also reviewed. The opportunities and limits of all the methods are discussed to improve the research of particulate flow. Finally, the paper points out several directions of future researches.