Numerical Simulation of the Formation of Granular Shock Wave Over Cylindrical Obstacle

A two dimensional (2-D) stream of granular flow with zero initial granular temperature passing over a cylindrical obstacle is simulated by means of both molecular dynamics (MD) simulation and finite volume method (FVM). In experiments, a bow-shaped shock wave with higher area fraction forms in front of the obstacle that was reproduced in our simulations. Due to the different circumstances to which particles are subjected, the granular flow is divided in two zones. One is undisturbed where quantities, such as space fraction (volume fraction for 3-D and area fraction for 2-D geometries), velocity and granular temperature are uniformly distributed and the other is called the shock wave zone. In this region, the values of the space fraction increases and the velocity of particles changes. From the MD simulation, it is found that the area fraction of the shock wave depends on surface roughness, coefficient of restitution (COR) of particles, the obstacle diameter as well as velocity of the granular stream, and a triangular region forms with almost zero velocity, and granular temperature forms in front of the cylindrical obstacle. The bigger is the size of the obstacle, the more stable this region is. In FVM simulations solid phase velocity and area fraction distributions similar to the MD simulation results are obtained for proper parameters.