This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.
A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow. An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow, saltating grains, and a kind of electrostatic force exerted on the grains are considered in this theoretical model. The numerical results show that the effect of the thermal diffusion on the evolution process of wind-blown groan flow is quite obvious and very similar to the effect of the electrostatic force on the evolution. Not only the time for the entire system to reach a steady state （called the duration time）, the transport rate of grains, the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.
