The standard Lattice BGK (LBGK) scheme often encounters numerical instability in simulation of fluid flow with small kinematic viscosity or as the nondimensional relaxation timey is close to 0.5. In this paper, based on a timesplitting scheme for the Boltzmann equation with discrete velocities, a new LBGK scheme with general propagation step is proposed to address this problem. In this model, two free parameters are introduced into the propagation step, which can be adjusted to obtain a small kinematic viscosity and improved numerical stability as well. Numerical simulations of the two-dimensional Taylor vortex and the unsteady Womersley flow are carried out to test the kinematic viscosity, numerical diffusion, and numerical stability of the proposed scheme.

本文对具有不同温度竖壁的封闭容器中二维自然对流问题进行了直接数值模拟。控制方程在非均匀网格上使用空间二阶精度和时间一阶精度进行离散，程序是在国家高性能计算中心（武汉）的并行计算机曙光1000A上实现的。使用4个结点，获得的加速比和效率分别约为2.89和0.72。

Two type of structures-Turing patterns and spiral waves-are obtained in chloride-iodide-malonic acid (CIMA) reaction-diusion model by using lattice Bhatnagar-Gross-Krook (LBGK) method.

A second-order moment (SOM) gas-phase turbulence model, combined with a Monte-Carlo (MC) simulation of stochastic particle motion using Langevin equation to simulate the gas velocity seen by particles, is called an SOM-MC two-phase turbulence model. The SOM-MC model was applied to simulate swirling gas-particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement data and those predicted using the Langevin-closed unified second-order moment (LUSM) model. The comparison shows that both models give the predicted time-averaged flow field of particle phase in general agreement with those measured, and there is only slight difference between the prediction results using these two models. In the near-inlet region, the SOM-MC model gives a more reasonable distribution of particle axial velocity with reverse flows due to free of particle numerical diffusion, but it needs much longer computation time. Both models underpredict the gas and particle fluctuation velocities, compared with those measured. This is possibly caused by the particle-wall and particle-particle interaction in the near-wall region, and the effect of particles on dissipation of gas turbulence, which is not taken into account in both models.

For tangential fired furnace, the false diffusion will occur when the flow is oblique to the grid lines. It is a major factor to cause serious errors to the prediction of tangential fired furnace. In order to decrease this false diffusion, this study has considered several alternative to the widely used upwind-differencing scheme with the aim of identifying which could be regarded as the most suitable in a general-purpose solving procedure for tangential furnace. The representations adopted are 'hybrid', 'quick' and '27-point' treatments. Here, '27-point' is a new discrete arithmetic scheme developed by the authors. All these schemes are used to simulate a constrained jet and a lab-scale tangential furnace and to compare solutions with the datum. Overall, the '27-point' approximation emerged as the most satisfactory for simulating tangential furnace.