This paper studies some interesting features of two-dimensional granular shearing flow by using molecular dynamic approach for a specific granular system. The obtained results show that the probability distribution function of velocities of particles is Gaussian at the central part, but diverts from Gaussian distribution nearby the wall. The macroscopic stress along the vertical direction has large fluctuation around a constant value, the non-zero average velocity occurs mainly near the moving wall, which forms a shearing zone.. In the shearing movement, the volume of the granular material behaves in a random manner. The equivalent fl＇iction coefficient between moving slab and granular material correlates with the moving speed at low velocity, and approaches constant as the velocity is large enough.
Performance of the LSFD method is compared with conventional FD schemes. Generally, 9-point stencils for 2D cases and 27-point stencils for 3D cases are used for the approximation of the first and second order derivatives obtained with conventional central difference schemes. When the same stencils are used, explicit LSFD formulations for approximation of the first and second order derivatives are presented. The LSFD formulations are actually a combination of conventional central difference schemes along relevant mesh lines. It has been found that LSFD formulations need much less iteration steps than the conventional FD schemes to converge, and the ratio of mesh spacing in the x and y directions is an important parameter in the LSFD application, with a great impact on stability of LSFD computation.
