利用格子Boltzmann方法数值模拟Rayleigh-Benard对流

采用格子Boltzmann方法对较大Rayleigh数范围下的二维Rayleigh-Benard对流进行了模拟研究.引入能量分布函数,利用该能量分布函数与粒子速度分布函数耦合来求解一个热流场,能量分布函数与粒子速度分布函数和Boltzmann方程构成了一个新的双分布格子Boltzmann模型.在考虑密度随温度变化的情况下,进行数值模拟,得到了Rayleigh-Benard对流速度、温度随时间的变化规律、系统的流线和等温线分布及平均Nusselt数与Rayleigh数的之间的关系,与相关文献数据进行了对比,模拟结果非常吻合,证明了改进的双分布格子Boltzmann模型的有效性.     

用格子Boltzmann模型模拟Lotka-Volterra系统

用格子Boltzmann方法模拟了Lotka-Voltcrra系统的动力学行为．通过使用多尺度技术,我们得到了扩散反应系统。以及零扩散的反应系统。从而得到常微分方程系统，这个理论结果表明该格子Boltzmann模型包含了Lotka-Volterra系统的非线性行为，数值结果表明附加的人为扰动可以改变某些初始分布。     

Ginzburg—Landau方程的格子Boltzmann解

本文给出了用于求解Ginzburg-Landau方程的格子Boltzmann模型。通过构造平衡态分布函数的矩函数，我们给出了宏观物理量与平衡态分布函数之间的变换。作为一种特殊情况，得到了各向同性的平衡态分布函数，这后，我们证明了该算法收敛到Ginzburg-Landau方程。     

基于格子 Bhatnagar-Gross-Krook模型的地震压力波模拟

给出一种新的用于模拟地震压力波的格子Boltzmann模型. 通过使 用Chapman-Enskog展开和多重尺度技术，得到了一系列的格子Boltzmann方程和时间 尺度$t_0$上守恒律，给出了满足地震压力波方程所要求的高阶矩以及简单的平衡态分布 函数表达式. 数值结果表明这种方法可以用来模拟地震压力波.     

基于格子Boltzmann方法的挤出胀大的数值模拟

将单相格子Boltzmann方法(lattice Boltzmann method,LBM)引入到粘弹流体的瞬态挤出胀大的数值模拟中,建立了基于双分布函数的自由面粘弹性流动格子Boltzmann模型.分析得到的流道中流动速度分布和构型张量结果与理论解十分吻合.对粘弹流体瞬态挤出胀大过程进行了模拟,并分析了运动粘度比和剪切速率对挤出胀大率的影响,得到的胀大率结果与理论分析和其它模拟结果基本一致.表明给出的LBM可以捕捉挤出胀大的瞬态效应.     

基于格子Boltzmann两相模型的粘弹流体挤出胀大分析

挤出胀大的数值模拟是非牛顿流体研究中具有挑战性的问题．本文运用格子Boltzmann方法(LBM)分析Oldroyd-B和多阶松弛谱PTT粘弹流体的挤出胀大现象，采用颜色模型模拟出口处粘弹流体和空气的两相流动，通过重新标色获得两种流体的界面，并最终获得胀大的形状．Navier-Stokes方程和本构方程的求解采用双分布函数模型．将胀大的结果与解析解、实验解和单相自由面LBM结果进行了比较，发现格子Boltzmann两相模型结果与解析解和实验结果相吻合，相比于单相模型，收敛速度更快，解的稳定性更高．研究了流道尺寸对胀大率的影响，并对挤出胀大的内在机理进行了分析．     

基于格子玻尔兹曼方法的局部网格加密算法——粗细网格间的数据转换

格子Boltzmann方法作为一种高效的介观计算流体力学方法在过去20多年里得到快速发展,其相对较高的计算效率和灵活性使其可以适用于各种复杂流动的模拟.然而标准的格子Boltzmann方法只能使用均匀的直角网格,这种网格排布方式并不利于复杂流动的计算.为此,基于格子Boltzmann方法的局部网格加密算法在文献中被提出.该算法需要在局部加密的界面处将粗细网格间的分布函数转换后交换.目前分布函数的转换方式大多是在没有源项的情况下推导的,而且现存考虑源项时转换公式的推导也都是基于Chapman-Enskog展开;其推导过程相对复杂,且需要对分布函数的非平衡态部分做一阶Chapman-Enskog近似,这有可能会限制局部网格加密算法在高阶格子Boltzmann方法中的应用.文章在忽略时空离散误差的前提下,以保证连续分布函数变量以及物理松弛系数一致为基础,构建了一套规范且简洁的粗细网格间在考虑任意源项时,分布函数转换关系的推导过程,该方法不依赖于Chapman-Enskog展开以及Chapman-Enskog近似,且该方法既可以适用于单松弛碰撞模型也可以适用于多松弛碰撞模型.此外,还从理论上证...     

格子Boltzmann方法中基于内插值的曲线边界处理新方法

对格子Boltzmann方法提出了一种新的曲面边界条件处理方法。在笛卡尔坐标系中,这种处理方法是现有的格子Boltzmann方法有关边界条件处理与浸入式边界条件的混合,它采用内插值方法计算靠近物理边界的网格点速度,使其保证最低精度为二阶,然后利用格子Boltzmann方法中的边界条件技术得到相应的分布函数。由理论推导和数值计算表明,本文提出的方法比其他方法更稳定且具有二阶精度。     

基于热格子Boltzmann方法的自然对流数值模拟

对Eggels和 Somers提出的热格子Boltzmann格式进行了改进. 在不可压缩流动的假设下，提出了一种新 的温度平衡分布函数，可以克服压缩性对温度统计的影响，并且相应地修正了统计宏观温度 的方法. Eggels和Somers的方法对速度和温度均采用半步长反弹格式边界条件，适合无滑移的速度边界条件. 但是对温度采用该边界条件在物理本质上显得不够准确，所以在边界上对二者统一采取 算法既简单又容易实现的非平衡态外推格式，同时可以与Boltzmann格式的整体二阶精度保 持一致. 最后，利用改进的热格子Boltzmann方法(TLBM)模拟了Ra=10^6 和Pr=0.71(空气)的方腔中的自然对流，模拟得到的流动参数与其它数值方法的结果吻合得很好，表 明改进的热格子Boltzmann方法可以有效准确地模拟非等温流动.     

浸没边界-简化热格子Boltzmann方法研究及其应用

针对流固耦合传热问题,本文提出了一种基于浸没边界-简化热格子玻尔兹曼方法(immersed boundary method-simplified thermal lattice Boltzmann method,IB-STLBM)的耦合模型.不同于传统的格子玻尔兹曼方法使用分布函数演化流场和温度场,简化热格子玻尔兹曼方法(simplified thermal lattice Boltzmann method,STLBM)的演化过程不需要依赖分布函数,只涉及平衡态分布函数和非平衡态分布函数,能够直接演化宏观量,极大减小了计算过程中所占用的虚拟内存,简化了边界条件的实现方式,同时具有较高的稳定性.传统的浸没边界法对流场的计算采用欧拉网格,对固体边界采用拉格朗日网格,认为固体边界是对流场产生某种体积力.在应用浸没边界法时,汲取介观的思想,把固体的介入看作是对流场的干扰,打破了固体附近流体介观微团颗粒原始的平衡状态,这种干扰可以看作是在耦合边界上产生的一个非平衡项,可用非平衡态分布函数来表示.基于此,在模型中浸没边界法与简化热格子玻尔兹曼方法更紧密联系在一起,更大程度发挥二者的优点,整个计算过程更加简单直观,符合物理特性.通过对热圆柱绕流和内含热颗粒的封闭方腔自然对流问题的模拟以及对其结果的分析,验证了该算法在求解流固耦合传热问题的有效性和可行性.      

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 lattie Boltzmann model, and the result agrees well with analytical solution.     

模拟MKDV方程的格子BGK模型

目前,格子Boltzmann方法已被广泛应用于模拟各种非线性方程.文中用D1Q4模型给出MKDV方程的带修正项的BGK型格子Boltzmann法.数值模拟与理论结果吻合很好.     

Pressure-driven and electroosmotic non-Newtonian flows through microporous media via lattice Boltzmann method

The lattice Boltzmann method is developed to simulate the pressure-driven flow and electroosmotic flow of non-Newtonian fluids in porous media based on the representative elementary volume scale. The flow through porous media was simulated by including the porosity into the equilibrium distribution function and adding a non-Newtonian force term to the evolution equation. The non-Newtonian behavior is considered based on the Herschel–Bulkley model. The velocity results for pressure-driven non-Newtonian flow agree well with the analytical solutions. For the electroosmotic flow, the influences of porosity, solid particle diameter, power law exponent, yield stress and electric parameters are investigated. The results demonstrate that the present lattice Boltzmann model is capable of modeling non-Newtonian flow through porous media.     

A lattice Boltzmann model for the compressible Euler equations with second‐order accuracy

In this paper, we propose a new lattice Boltzmann model for the compressible Euler equations. The model is based on a three‐energy‐level and three‐speed lattice Boltzmann equation by using a method of higher moments of the equilibrium distribution functions. In order to obtain second‐order accuracy, we employ the ghost field distribution functions to remove the non‐physical viscous parts. We also use the conditions of the higher moment of the ghost field equilibrium distribution functions to obtain the equilibrium distribution functions. In the numerical examples, we compare the numerical results of this scheme with those obtained by other lattice Boltzmann models for the compressible Euler equations. Copyright © 2008 John Wiley & Sons, Ltd.     

A lattice Boltzmann model for simulation of compressible flows

This paper presents a new model of lattice Boltzmann method for full compressible flows. On the basis of multi‐speed model, an extra potential energy distribution function is introduced to recover the full compressible Navier–Stokes equations with a flexible specific‐heat ratio and Prandtl number. The Chapman–Enskog expansion of the kinetic equations is performed, and the two‐dimension‐seventeen‐velocity density equilibrium distribution functions are obtained. The governing equations are discretized using the third order monotone upwind scheme for scalar conservation laws finite volume scheme. The van Albada limiter is used to avoid spurious oscillations. In order to verify the accuracy of this double‐distribution‐function model, the Riemann problems, Couette flows, and flows around a NACA0012 airfoil are simulated. It is found that the proposed lattice Boltzmann model is suitable for compressible flows, even for strong shock wave problem, which has an extremely large pressure ratio, 100,000. Copyright © 2014 John Wiley & Sons, Ltd.     

Convection-dominated melting of phase change material in partially heated cavity: lattice Boltzmann study

Heat transfer and fluid flow processes of natural convection melting of a phase change material are simulated numerically inside a partially heated square cavity. The momentum and energy equations are solved by using enthalpy-based lattice Boltzmann method combined with multi distribution function model. In this communication, the dependence of liquid fraction, temperatures of vertical nodes and average Nusselt number on the positions of heated plates is investigated quantitatively.     

A multi-entropy-level lattice Boltzmann model for the one-dimensional compressible Euler equations

In this paper, we propose a new lattice Boltzmann model for the one-dimensional compressible Euler equations. The new model is based on a three-entropy-level and three-speed lattice Boltzmann equation by using a method of higher-order moments of the equilibrium distribution functions. In order to obtain the second-order accuracy model, we employ the ghost field distribution functions to remove the non-physical dissipation terms in the Euler equations. We also use the conditions of the higher-order moments of the ghost field equilibrium distribution functions to obtain the equilibrium distribution functions. The numerical examples show that the numerical results can be compared with those classical methods.     

徐州矿区采空塌陷区公路工程地质灾害与防治对策分析

采用格子Boltzmann方法模拟可变形膜与周围流体的相互作用. 分析了格子Boltzmann 方法中的边界处理方法和边界受力的计算方法，并且用此方法计算流场中可变形膜的受力. 可将离散化后的膜看作一系列的质点，从而得到膜的动力学方程. 将可变形膜在流场中受到 的力引入方程中，可以计算膜的变形. 求解了几种不同情况下，膜的形状随时间的变化. 发现，如果可变形膜非常软或者非常硬，经过足够长的时间后，膜的形状会接近一 条直线，即回到初始状态. 模拟过程是二阶精度的.     

Impulse and mass transport in a cartilage bioreactor using the lattice Boltzmann method

Mass and Impulse transport of oxygen enriched water in cartilage cell breeding reactor are simulated using the lattice Boltzmann method (LBM). The solver is attached with a shear stress and pressure calculator to quantify the load distribution on the cells. The solver was validated using the backward-facing step flow, which is a classical benchmark of similar discrete geometry for the bioreactor. This is achieved by comparing the qualitative and quantitative results obtained by LBM with the traditional solution and experimental approach for such a problem. The D2Q9 lattice model is used to carry out the calculations for the flow field, with a first order bounce-back boundary condition. Oxygen consumption efficiency levels in the bioreactor were reported.