Numerical simulation of two-dimensional granular shearing flows and the friction force of a moving slab on the granular media

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.

Explicit formulations and performance of LSFD method on Cartesian mesh

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.

Three-Dimensional Waves in Tilt Thermal Boundary Layers

We numerically and theoretically study the stabilities of tilt thermal boundary layers immersed in stratified air. An interesting phenomenon is revealed： the stationary longitudinal-roll mode becomes unstable to some oscillating state even when the Grashof number is smaller than its corresponding critical value. By stability analysis, this phenomenon is explained in terms of a new three-dimensional wave mode. The effect of the tilt angle on the stability of the boundary flows is investigated. Since the new three-dimensional wave is found to be the most unstable mode when the title angle is between 30° and 64°, it is expected to play an important role in the transition to turbulence.

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

The Ellipsoidal Statistical model(ES-model)and the Shakhov model(S-model)were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heatflux.With the introduction of a new pa-rameter to combine the ES-model and S-model,a generalized kinetic model can be developed.This new model can give the correct Navier-Stokes equations in the con-tinuumflow regime.Through the adjustment of the new parameter,it provides abun-dant dynamic effect beyond the ES-model and S-model.Changing the free parameter,the physical performance of the new model has been tested numerically.The unified gas kinetic scheme(UGKS)is employed for the study of the new model.In transitionflow regime,many physical problems,i.e.,the shock structure and micro-flows,have been studied using the generalized model.With a careful choice of the free parameter,good results can be achieved for most test cases.Due to the property of the Boltz-mann collision integral,the new parameter in the generalized kinetic model cannot be fully determined.It depends on the specific problem.Generally speaking,the S-model predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model,while ES-model performs better in the cases where theflow is mostly driven by temperature gradient,such as a channelflow with large boundary temperature variation at high Knudsen number.

A Memory-Saving Algorithm for Spectral Method of Three-Dimensional Homogeneous Isotropic Turbulence

Homogeneous isotropic turbulence has been playing a key role in the research of turbulence theory.And the pseudo-spectral method is the most popular numerical method to simulate this type of flow fields in a periodic box,where fast Fourier transform(FFT)is mostly effective.However,the bottle-neck in this method is the memory of computer,which motivates us to construct a memory-saving algorithm for spectral method in present paper.Inevitably,more times of FFT are needed as compensation.In the most memory-saving situation,only 6 three-dimension arrays are employed in the code.The cost of computation is increased by a factor of 4,and that 38 FFTs are needed per time step instead of the previous 9 FFTs.A simulation of isotropic turbulence on 20483 grid can be implemented on a 256G distributed memory clusters through this method.