Unified gas-kinetic particle method for dilute granular flow and its application in a solid jet

Abstract

Because of its complexity, the problem of multiscale structure in granular flow has been receiving increasing attention. In this work, in order to conduct an in-depth exploration of the multiscale structure, a unified gas-kinetic particle (UGKP) method suitable for granular flow is constructed, in which the collision damping term and return-to-isotropy term are added to characterize the collision between particles. For the above two collision terms, the former characterizes the inelastic collision of particles, while the latter emphasizes the importance of the isotropic distribution of particles, which makes the results more reliable and reasonable. The construction of unified gas-kinetic schemes (UGKS) for granular flow has been reported in previous research. However, because of the need for discrete velocity space, the calculation size is quite large, making it impossible to use UGKS directly to investigate the multiscale problem. However, for UGKP, the flux contributed by particle free transport is calculated by free-streaming particles instead of discrete velocity space so that the corresponding calculation is much smaller than UGKS. The validity of the method is verified by numerical simulation of the solid jet compared with the particle-in-cell (PIC) method. In addition, since the sampled particles are used to obtain the flux contributed by the free transport, UGKP is more efficient than UGKS for solving multiscale problems.