Lagrangian modelling of dilute granular flow—modified stochastic DSMC versus deterministic DPM

Abstract

In this paper, a modified Direct Simulation Monte Carlo (DSMC) algorithm is introduced which is tailored towards achieving quantitative agreement with deterministic Discrete Particle Model (DPM) simulations for the collision frequency between particles in dilute granular flows. To avoid lattice artifacts, we use a spherical searching scope in which a particle searches for a collision partner during each particle time step. The particle collision frequency is calculated on the basis of particle concentration, particle sizes and relative velocities of neighbouring particles within the searching scope, similar to existing DSMC methods found in the literature. However, when the particle time step is limited by an external time step, such as the time step for the solver of the gas equations, without additional measures, the resulting searching scope often contains a single or even no neighbours, with detrimental effects on estimates of the average collision frequency. We modified the method to automatically and self-consistently increase the searching scope until it contains a minimum number of neighbouring particles to ensure that a statistically accurate and unbiased estimate of the average collision frequency is made. The developed stochastic-DSMC model is verified qualitatively and quantitatively with DPM simulations of two colliding streams of elastic as well as inelastic monodisperse spheres. The major advantage of the stochastic-DSMC model is its capability to handle many millions of particles for simulation in a reasonable computation time. This number increases even more when each simulated particle represents a large group of real particles, called a parcel. We investigate how far the parcel size can be increased before the DSMC approach breaks down.