We show discrcte lattice offects must be considered in the introduotion of a foree into the lattice Boltzmann equation, A representation of the forcing temp is then proposed. With the representation, the Navier-Stokes equation is derived from the lattice. Boltzmann equation through the Chapman-Enskng expansion. Several other exisling force treatments are also examined.

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 lattice Bhatnagar-Gross-Krook (LBGK) model for reaction-diffusion systems is presented. This model provides a mesoscopic approach to the dynamics of spatially-distributed reacting systems. Pure diffusion phenomena are computed and the results are agreement with the theoretical predictions. This method is also applied to formation of Turing patterns in chloride-iodide-malonic acid (CIMA) reactive model. We get hexagonal structures and stripes which are agreement with other numerical results and experimental results.

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。