广义Ginzburg-Landau方程的格子Boltzmann模型

本文为了求解广义Ginzburg-Landau方程,提出了带有附加项的五点单弛豫格子Boltzmann模型.首先通过使用Chapman-Enskog展开和Taylor展开,得到了一系列不同时间尺度的偏微分方程和平衡态分布函数的高阶矩.然后我们利用平衡态分布函数的矩方程构造了具有截断误差的格子Boltzmann模型,得到了数值耗散项,并应用Hirt启示性稳定化方法得到模型的稳定条件.最后,我们给出了广义Ginzburg-Landau方程的数值例子.数值结果表明这种方法可以用来模拟广义Ginzburg-Landau方程.     

泥石流的增强碰撞算子格子Boltzmann模型

利用增强碰撞算子格子的Boltzmann方法,分析泥石流作为非Newton体的特点,根据泥石流的Bingham体模型,构造了一个特殊的增强碰撞算子的格子Boltzmann模型,并由此成功地模拟了泥石流入汇主河的运动过程,为预测和防治泥石流入汇主河所造成的灾害提供了一些理论依据。     

考虑温度时变效应氯离子侵蚀混凝土的格子Boltzmann数值模型

对于长期暴露在氯盐环境下的混凝土结构,在外界温度影响下氯离子的侵蚀作用非常复杂,会影响钢筋锈蚀进程及其耐久性.为此,基于格子Boltzmann方法,采用双分布函数分别描述混凝土温度场和氯离子浓度场的演化过程,考虑外界温度的时变效应,建立氯离子侵蚀混凝土的数值模型.在此基础上,讨论水灰比、饱和度和昼夜温差等因素对氯离子侵蚀机制以及混凝土服役寿命的影响.研究表明:随着水灰比的增大,氯离子扩散系数逐渐增大,从而加剧了氯离子的侵蚀作用.混凝土饱和度越大,氯离子的扩散速率越快,从而导致混凝土的服役寿命缩短,当饱和度超过75%时,混凝土的服役寿命变化趋势逐渐趋于稳定.此外,昼夜温差越大,其对扩散系数的影响越显著,但总体而言,昼夜温差的变化对混凝土服役寿命的影响并不突出.     

桥梁气动导数的格子Boltzmann大涡模拟仿真

为将格子Boltzmann方法(Lattice Boltzmann Method, LBM)用于桥梁气动导数的识别,该文将壁面自适应局部(Wall-Adapting Local Eddy, WALE)涡黏性模型引入到多松弛时间格式(Multiple Relaxation Time,MRT)的LBM中,构造了一种能够有效模拟桥梁结构高雷诺数绕流的LBM大涡模拟方法—MRT-LBM-WALE。采用MRT-LBM-WALE和动边界技术驱动主梁断面在流场中做正弦竖向或扭转振动,在虚拟风洞中实现了强迫振动法识别气动导数的LBM仿真。利用方柱非定常绕流问题验证MRT-LBM-WALE的可靠性后,对理想平板和Great Belt东桥的气动导数进行了计算。研究证明MRT-LBM-WALE能够得到近壁面上真实的亚格子涡黏性,可以准确地预测湍流流动的发展。同时,研究表明气动导数的MRT-LBM-WALE仿真值与理论解或试验值吻合较好。     

基于格子Boltzmann方法非饱和土体水热耦合模型研究

考虑热源作用下非饱和土体水热耦合作用机制,基于格子Boltzmann方法,采用双分布函数分别描述温度场及水分场的演化过程,建立了相应的水热耦合模型。同时,编制了计算程序,并结合半无限空间的水热耦合算例,验证了该计算模型的正确性。最后考虑水热耦合作用模式、热源温度以及土体孔隙率等因素的影响,讨论了非饱和土体温度场及水分场的演化规律。研究结果表明：传统的单向耦合模式无法表征水分迁移对土体导热特性的影响,从而导致温度场的演化规律有所偏差,而所提出的双向耦合模式更具合理性。在恒温热源作用下,不同热源温度对土体温度场及水分场的演化均会产生较大影响,且在非饱和土体温度升高速率较快的位置,体积含水率也相应的变化较快。在相同热源作用下,当初始体积含水率一定时,孔隙率较小的土体,温度升高速度较快,但总体差别不大,从而使得体积含水率分布也较为接近。     

基于格子Boltzmann方法的微气体流动速度滑移边界条件的检验

为研究微气体流动的速度滑移边界条件,建立适用于滑移区和过渡区的微气体流动的格子Boltzmann模型,从气体动理学理论及Knudsen层效应出发推导了Knudsen数与无量纲松弛时间的关系,基于Succi的边界处理方法和广义二阶速度滑移边界条件推导出壁面滑移速度和反弹比例系数的计算公式,并以微尺度Poiseuille流动为例,对七类速度滑移边界条件进行研究.计算结果表明,在各个速度滑移模型下,中心线上的无量纲速度的偏差小于边界上的无量纲滑移速度的偏差.Guo模型、Hisa模型、Zhang模型表现较好,其次是Hadjiconstantinou模型,而Cercignani模型、Schamberg模型、Deissler模型的表现较差.     

基于格子Boltzmann方法的疏水表面润湿性数值模拟

润湿性对固体表面上液体的各种动力学行为具有重要影响,疏水表面的特殊润湿性是其在减阻、降噪、防污等领域有着广泛应用前景的根本原因。基于Shan-Chen模型的格子Boltzmann方法对疏水表面润湿性进行数值模拟,获得了材料属性和微形貌对疏水表面润湿性的影响规律。研究表明,要使疏水表面处于Cassie-Baxter润湿状态,微形貌高度必须大于某一临界值,而当疏水表面一旦处于Cassie-Baxter润湿状态后,继续增加微形貌高度也不会提高其疏水性能;疏水表面的表观接触角随气液界面分数先增大后减小,且存在一个最佳的气液界面分数使表观接触角达到最大。     

异形纤维捕集颗粒过程的格子Boltzmann法数值模拟

为了探究异形纤维的截面形状和放置角度对捕集效率、系统压降及除尘器综合性能的影响,对布袋除尘器中三角形、十字形及三叶形3种异形纤维捕集颗粒的过程进行研究;采用格子Boltzmann-元胞自动机气-固两相流模型定量描述颗粒的运动过程,计算扩散、拦截及惯性碰撞3种捕集机制下纤维的捕集效率,并且与相同体积分数的圆柱纤维进行比较。结果表明:对于十字形和三叶形纤维,当长短轴比越大时,捕集效率也越大;对于拦截机制占主导时较难捕集的中等大小颗粒,三角形和三叶形纤维放置角度为60°时更有利于捕集。     

格子玻尔兹曼模型的图像去噪方法

为了实现快速去噪以及更好地保护图像的边缘信息,从各向同性扩散模型出发,提出了一种基于索贝尔(Sobel)梯度算子的格子玻尔兹曼去噪模型,通过该模型求解非线性扩散方程实现图像去噪.模型引入了Sobel算子作为检测边缘的工具,同时满足前向扩散的要求,保证了方程的稳定性.实验分析表明,应用该方法进行图像去噪,能够在保护图像边缘的情况下进行快速去噪.     

惯量松弛因子在格子Boltzmann方法中的应用

格子Boltzmann方法作为一种较成熟的数值模拟方法被广泛应用到了各个领域,尤其在解决多孔介质问题时有其独特的优越性,但当流动问题过于复杂时计算效率较低.因此本文将惯量松弛因子引入到格子Boltzmann方法中,对二维、三维顶盖驱动方腔流动进行了数值模拟.模拟分别从计算效率、计算精度、以及计算稳定性等方面将使用不同惯量松弛因子所得的结果与基准解进行比较,并进行讨论和分析.结果显示当惯量松弛因子取0.03到0.05之间时能使模拟结果在保持较高精度的同时提高计算效率,而且随着惯量松弛因子的增大计算效率提高得也越快,在工程材料与能源环境领域将有着重要应用.     

Hybrid Lattice Boltzmann Equation Method in Problems of Coupled Heat Transfer

Journal of Engineering Physics and Thermophysics - A hybrid (LB–FD) mathematical model has been constructed to investigate thermogravitational convection in closed rectangular cavities...     

Lattice Boltzmann method for adiabatic acoustics

The lattice Boltzmann method (LBM) has been proved to be a useful tool in many areas of computational fluid dynamics, including computational aero-acoustics (CAA). However, for historical reasons, its applications in CAA have been largely restricted to simulations of isothermal (Newtonian) sound waves. As the recent kinetic theory-based reformulation establishes a theoretical framework in which LBM can be extended to recover the full Navier-Stokes-Fourier (NS) equations and beyond, in this paper, we show that, at least at the low-frequency limit (sound frequency much less than molecular collision frequency), adiabatic sound waves can be accurately simulated by the LBM provided that the lattice and the distribution function ensure adequate recovery of the full NS equations.     

Simulation on Thermocapillary-Driven Drop Coalescence by Hybrid Lattice Boltzmann Method

A hybrid two-phase model, incorporating lattice Boltzmann method (LBM) and finite difference method (FDM), was developed to investigate the coalescence of two drops during their thermocapillary migration. The lattice Boltzmann method with a multi-relaxation-time (MRT) collision model was applied to solve the flow field for incompressible binary fluids, and the method was implemented in an axisymmetric form. The deformation of the drop interface was captured with the phase-field theory, and the continuum surface force model (CSF) was adopted to introduce the surface tension, which depends on the temperature. Both phase-field equation and the energy equation were solved with the finite difference method. The effects of Marangoni number and Capillary numbers on the drop’s motion and coalescence were investigated.     

Lattice Boltzmann equation for relativistic quantum mechanics

Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.     

Lattice Boltzmann algorithm for three-dimensional liquid-crystal hydrodynamics

We describe a lattice Boltzmann algorithm to simulate liquid-crystal hydrodynamics in three dimensions. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic effects such as shear-thinning and shear-banding. We describe the implementation of velocity boundary conditions and show that the algorithm can be used to describe optical bounce in twisted nematic devices and secondary flow in sheared nematics with an imposed twist.     

Lattice Boltzmann schemes without coordinates

We discuss recent developments extending the scope of the lattice Boltzmann method to unstructured (coordinateless) grids with arbitrary connectivity. Besides their intrinsic interest as examples of discrete kinetic systems living in irregular phase-space, the above extensions bear a direct relevance as computational tools for multi-scale applications.     

Particulate flow simulation using Lattice Boltzmann Method: A rheological study

This work deals with calculating rheological properties of a suspension of particles in a fluid. A suspension of mono- and poly-disperse circular particles in shear flow is studied using two different methods for application of shear force: (a) by placing parallel walls at the top and bottom of the domain which are moving in opposite directions with the same velocity, and (b) using the Lees–Edwards boundary condition. The system which starts moving from rest, is allowed to reach a statistically steady state. Rheological properties namely, bulks shear stress, effective viscosity and normal stress difference of the suspension at different particle-based Reynolds numbers and different mean particle area fractions are calculated. Furthermore, the effect of size distribution on the relative effective viscosity of the suspension is investigated. Comparison of the present results with empirical formulations found in the literature shows reasonable agreement.     

Parallel Implementation of the Hybrid Lattice Boltzmann Method on Graphics Accelerators

Journal of Engineering Physics and Thermophysics - An analysis has been conducted for the computational performance of a hybrid mathematical model for investigating the laws of thermogravitational...     

Dual Grid Lattice Boltzmann method for multiphase flows

We present a new methodology for implementing multiphase flow solvers using the Lattice Boltzmann method. Two grids of different size are used to discretize the momentum and the order parameter so that derivatives of the latter (responsible for the forcing terms at the interfaces) are calculated with high accuracy while maintaining a moderate computational cost. We apply the technique to two recently proposed formulations of the multiphase Lattice Boltzmann method, and show that this technique produces significant improvements over a homogeneous mesh refinement in both cases. Copyright © 2010 John Wiley & Sons, Ltd.