## 1 Introduction  
Particle flow exists in various fields, such as submarine granular flows, particle settlement, fluid beds combustion, motion of blood cells, and so on. However, capturing the micro-interaction of particles by experiment is difficult. Simulation is a remarkable technique that can well-represent a phenomenon or system. To acknowledge the hydrodynamic motion and collective behavior at grain scale, particle flow simulation is suggested. Particle flow simulation with conventional finite element method (FEM) results in mesh distortion as the boundary of particles move. Arbitrary Lagrangian-Eulerian (ALE) and adaptive mesh refinement (AMR) techniques were proposed to reorganize the boundary grid [1]; however, FEM still suffers additional error in force coupling between fluid and particle. Since 1986, the Los Alamos lab has proposed the concept of discrete simulation of fluid dynamic [2]. A number of mesh-free methods such as smoothed particle hydrodynamics (SPH), material point method (MPM), and lattice Boltzmann method (LBM) were rapidly developed in recent years, which bypass the usual necessary grid, thereby avoiding mesh tangling and distortion. LBM is widely used in hydrodynamic simulation, which replaces fluid macroscopic properties with distribution function, and progresses stream and collision on a background regular grid. Because moving boundary has an influence on background grid flag change, it is easy to simulate the fluid-structure interaction problem such as particle flow with a suitable coupling technique. There are two kinds of fluid-structure interaction boundariesfor LBM: (a) stationary boundary, and (b) moving boundary. [PERSON] [3] proposed a simple bounce back scheme of stationary boundary which turns the incident distribution function to the opposite direction. [PERSON] [4] first applied the lattice Boltzmann method to gas-particle flow, which allowed the flow to pass through fixed deposition of particles with irregular surface shape. For the moving boundary, three popular coupling methods exist: (a) modified bounce back method (MBB) [5], (b) immersed boundary method (IB) [6], and (c) immersed moving boundary method (IMB). In this paper, particle motion is governed by discrete element method (DEM), which is coupled with lattice Boltzmann method (LBM) to simulate particle flow. [PERSON] [5] proposed MBB-LBM, introducing an additional term to the collision operator, causing momentum change of particle's neighbor fluid lattice, which then causes a reaction force on particle (hydrodynamic force) as a result of momentum change of fluid. When the boundary interface chain is not in the lattice center, the streaming point is not on the lattice. As a result, [PERSON] et al. [7] proposed a method of calculating the streaming point distribution function by spatial interpolation. [PERSON] et al. [8] stated that momentum exchange only happens between solid interface and fluid lattice, and that force calculation only depends on neighbor fluid lattice. [PERSON] [9] combined DEM with MBB-LBM for landslide simulation. In addition, [PERSON] et al. [10] studied the rheology of bijel nano particle in confined flow. The drawback of MBB-LBM is the discontinuance of flag change of lattice, which causes complex interpolation, and fluctuation in population updating and hydrodynamic force on particle, which increases programming difficulty. [PERSON] [11] suggested the immersed boundary method to simulate flow membranes interaction by using a spring between different interface chain node, and by interpolating chain node velocity from neighbor fluid lattice. Calculation of the restoring force depended on the chain node's relative displacement by [PERSON]'s law, and the reaction boundary body force on fluid is obtained by interpolation of restoring force of boundary. [PERSON] and [PERSON] [12] combined IB and LBM to simulate the fluid-structure interaction (FSI) problem.