Simple lattice Boltzmann model for traffic flows

A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed. Using the Chapman-Enskog expansion and multi-scale technique, we obtain the higher-order moments of equilibrium distribution function. A simple traffic light problem is simulated by using the present lattice Boltzmann model, and the result agrees well with analytical solution.

用格子Boltzmann方法研究Burgers方程

提出了用于Burgers方程的格子Boltzmann模型。应用Chapman-Enskog展开和多重尺度技术，通过选择平衡态分布函数的高阶矩，得到了几种精度的Burgers方程，模型中的参数通过分析耗散性质和色散性质给出。

Rossby Vortex Simulation on a Paraboloidal Coordinate System Using the Lattice Boltzmann Method

In this paper, we apply our compressible lattice Boltzmann model to a rotating parabolic coordinate system to simulate Rossby vortices emerging in a layer of shallow water flowing zonally in a rotating paraboloidal vessel. By introducing a scaling factor, nonuniform curvilinear mesh can be mapped to a flat uniform mesh and then normal lattice Boltzmann method works. Since the mass per unit area on the two-dimensional (2D) surface varies with the thickness of the water layer, the 2D flow seems to be "compressible" and our compressible model is applied. Simulation solutions meet with the experimental observations qualitatively. Based on this research, quantitative solutions and many natural phenomena simulations in planetary atmospheres, oceans, and magnetized plasma, such as the famous Jovian Giant Red Spot, the Galactic Spiral-vortex, the Gulf Stream, and the Kuroshio Current, etc,, can be expected.

Lattice Boltzmann方法模拟多孔介质Klinkenberg效应

格子Boltzmann数值模拟方法是研究复杂的多孔介质结构特别是Klinkenberg效应的有效方法之一，对处理复杂边值问题尤其有效。用格子Boltzmann方法研究了气流穿越多孔介质问题，并将数值计算结果与实验结果进行了比较，结果表明格子Boltzmann方法是数值模拟气流穿越多孔介质问题的有效方法之一。

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation.

Lattice Boltzmann method for compressible flows with high Mach numbers

In this paper we present a lattice Boltzmann model to simulate compressible flows by introducing an attractive force. This scheme has two main advantages: one is to soften sound speed effectively, which greatly raises the Mach number (up to 5); another is its relative simple procedure. Simulations of the March cone and the comparison between theoretical expectations and simulations demonstrate that the scheme is effective in the simulation of compressible flows with high Mach numbers, which would create many new applications.

A lattice Boltzmann equation for waves

We propose a lattice Boltzmann model for the wave equation. Using a lattice Boltzmann equation and the Chapman-Enskog expansion, we get 1D and 2D wave equations with truncation error of order two. The numerical tests show the method can be used to simulate the wave motions.

高Mach数格子Boltzmann模型的改进

对文献「７」所提出的高Ｍａｃｈ数格子Ｂｏｌｔｚｍａｎｎ模型作了改进，克服了原模型拟结果与理论偏差较大、存在色散效应的缺陷，并进一步把Ｍａｃｈ数提高到５以上，据我们所知，这是目前同类研究的最好结果。

A Lagrangian lattice Boltzmann method for Euler equations

A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution function consists of macroscopic Lagrangian variables at time steps n and n + 1. It is different from the standard lattice Boltzmann method. In this method the element, instead of each particle, is required to satisfy the basic law. The element is considered as one large particle, which results in simpler version than the corresponding Eulerian one, because the advection term disappears here. Our numerical examples successfully reproduce the classical results.

Recovery of the solitons using a lattice Boltzmann model

We formulate a lattice Boltzmann model which simulates Korteweg-de Vries equation by using a method of higher moments of lattice Boltzmann equation. Using a series of lattice Boltzmann equations in different time scales and the conservation law in time scale to, we obtain equilibrium distribution function. The numerical examples show that the method can be used to simulate soliton.

Euler方程的双分布函数格子Boltzmann Godunov方法

应用双分布函数系统，通过Ｇｏｄｕｎｏｖ分解，构造了一维Ｅｕｌｅｒ方程的格子Ｂｏｌｔｚｍａｎｎ算法。解决了传统格子气固有的ＧＣ问题与能量方程之间的矛盾，实现了分布函数与宏观物理量之间的一一对应。

基于Lattice Boltzmann模型的液-液混合流模拟

引入了一种二元Lattice Boltzmann Model(LBM),实现了两种液体组成的混合流的模拟.不同于其它的类似模型,它区分考虑了流体的粘性和扩散特性,可以很容易地模拟各种互溶或者不互溶的混合流现象.此外,由于LBM的运算大都是线性的局部运算,这使得它很容易在可编程图形处理器(Graphics Process Unit,GPU)上进行加速,从而进行实时模拟.给出了若干二元混合流的模拟结果.