基于Shan-Chen模型的格子Boltzmann方法在微流动模拟研究中的应用

对格子Boltzmann方法的本质及Shan-Chen模型的核心机制进行了全面阐述, 并从应用实例角度对基于Shan-Chen模型的格子Boltzmann方法在微流动模拟方面的有效性、适应性进行了详细分析. 结果表明, Shan-Chen模型易于耦合微观条件下占主导作用的微观力, 拓宽了格子Boltzmann方法在微流动模拟方面的应用. 同时, Shan-Chen模型在润湿性边界条件表征方面的优势, 使得这种方法在微结构表面的滑移效应模拟方面具有很好的应用前景.     

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.     

颗粒流体系统的格子Boltzmann数值方法研究进展

介绍Euler-Lagrange框架下基于格子Boltzmann方法LBM (Lattice Boltzmann Method)发展的两种不同层次(即不同时-空尺度和精度)的颗粒流体系统离散模拟方法,即格子Boltzmann颗粒解析直接数值模拟(LB-based PR-DNS)方法和格子Boltzmann离散颗粒模拟(LB-based DPS)方法,总结了Euler-Euler框架下基于格子Boltzmann双流体模型(LB-based TFM)方面的探索研究。LB-based PR-DNS方法中颗粒尺寸远大于格子步长,能够直接解析出流体在颗粒表面的流动以及颗粒所受完整的动力学信息;LB-based DPS方法中格子步长远大于颗粒直径,其在计算精度、时间耗费和计算效率之间能达到很好的平衡,可获得流体的宏观平均流动及颗粒的运动轨迹信息。LB-based DNS和DPS是探索颗粒流体系统的有力手段,但LB-based TFM应用于模拟颗粒流体系统仍需进一步探索。     

利用格子Boltzmann方法模拟单个气泡在复杂流道内的运动特性

利用格子Boltzmann方法模拟了单个气泡在具有三个半圆形喉部的复杂流道内的上升过程.通过分析气泡运动过程中的形态、运动轨迹及运动速度的变化,研究复杂流道对气泡运动特性的影响.研究结果表明,在上升过程中,由于壁面的影响,气泡的形状发生严重的变形,运动轨迹也发生相应的偏转.通过实验结果的对比,验证了模拟结果的正确性.结果表明格子Boltzmann方法可以用于模拟具有复杂边界的两相流问题.     

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.      

用格子Boltzmann方法模拟Belousov-Zhabotinsky反应中的靶型波

构造了用于Belosov-Zhabotinsky反应的格子Boltzmann模型。通过对使用多组分的分布函数满足的格子Boltzmann方程，进行多重尺度Knudsen数展开，得到了模型的平衡态分布函数的各向同性解。作为算例，给出随机初始条件下反应区域内的靶型波的模拟结果，再现了Belousov-Zhabotinsky反应的经典结果。     

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．     

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。     

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.     

格子Boltzmann模型的改进与流体力学方程

流体的流动可以看成是分子以上水平的粒子基本运动组合而成,任何一个粒子系统的Hamiltonian都是由动能和势能这两部分所组成.借助于Hamiltonian建立了微观粒子和宏观流体之间的能量守恒准则,发展了一个适合于热流场数值模拟的格子Boltzmann模型.从该模型可以还原出宏观的流体力学方程,所得动量方程的黏性输运项除了具有Navier-Stokes黏性力的特征外还与非定常的、非线性的动量通量和非定常的内能相关.用该模型对Benard热对流进行了数值模拟,很好地再现了Benard cell,并且克服了热格子Boltzmann模型数值稳定性差的不足.     

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This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third-order accurate Adams-Moulton method and the second-order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.     

格子Boltzmann方法处理复杂边界新进展

格子玻尔兹曼方法是相对较新的计算流体力学方法,具有其独特的优点,如自然并行计算以及复杂边界的处理．在日益重要的高性能计算上,将发挥越来越大的作用．在已经较为成熟的计算模型基础上,为计算复杂几何边界对流场的作用,大量学者提出了各类针对格子玻尔兹曼方法的边界处理格式．边界处理方式对计算的影响主要有三个方面：计算精度,算法稳定性以及并行性．本文简单介绍格子玻尔兹曼方法在边界处理上的一些最新进展．并通过对实际算例的计算比较各类边界处理方式的优劣．     

Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

A method combining the immersed boundary technique and a multirelaxation-time(MRT) lattice Boltzmann flux solver(LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations(LBEs). The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution.The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.     

柔性微粒介电泳分离过程的多尺度模拟

介电泳分离是一种高效的微细颗粒分离技术,利用非均匀电场极化并操纵分离微流道中的颗粒. 柔性微粒在介电泳分离过程中同时受多种物理场、多相流和微粒变形等复杂因素的影响,仅用单一的计算方法对其进行模拟存在一定的难度,本文采用有限单元——格子玻尔兹曼耦合计算的方法处理这一难题.介观尺度的格子玻尔兹曼方法将流体看成由大量微小粒子组成,在离散格子上求解玻尔兹曼输运方程,易于处理多相流及大变形问题,特别适合模拟柔性颗粒在介电泳分离过程中的变形情况.另一方面,介电泳分离过程的模拟需求解流体、电场和微粒运动方程,计算量相当庞大,通过有限单元法求解介电泳力,提高计算效率.利用这种多尺度耦合计算方法,对一款现有的介电泳芯片分离过程进行了模拟.分析了微粒在电场作用下产生的介电泳力,揭示了介电泳力与电场变化率等因素之间的关系.对微粒运动轨迹及其变形的情况进行了研究,发现微粒的变形主要与流体剪切作用有关.这种多尺度耦合计算方法,为复杂微流体的计算提供了一种有效的解决方案.      

Simplified lattice Boltzmann method for non-Newtonian power-law fluid flows

In this paper, we present a simplified lattice Boltzmann method for non-Newtonian power-law fluid flows. The new method adopts the predictor-corrector scheme and reconstructs solutions to the macroscopic equations recovered from the lattice Boltzmann equation through Chapman-Enskog expansion analysis. The truncated power-law model is incorporated into this method to locally adjust the physical viscosity and the associated relaxation parameter, which recovers the non-Newtonian behaviors. Compared with existing non-Newtonian lattice Boltzmann models, the proposed method directly evolves the macroscopic variables instead of the distribution functions, which eliminates the intrinsic drawbacks like high cost in virtual memory and inconvenient implementation of physical boundary conditions. The validity of the method is demonstrated by benchmark tests and comparisons with analytical solution or numerical results in the literature. Benchmark solutions to the three-dimensional lid-driven cavity flow of non-Newtonian power-law fluid are also provided for future reference.     

A lattice Boltzmann method for solute transport

A lattice Boltzmann method is developed for solute transport. Proper expressions for the local equilibrium distribution functions enable the method to be formulated on rectangular lattice with the same simple procedure as that on a square lattice. This provides an additional advantage over a lattice Boltzmann method on a square lattice for problems characterized by dominant phenomenon in one direction and relatively weak in another such as solute transport in shear flow over a narrow channel, where the problems can efficiently be approached with fine and coarse meshes, respectively, resulting in more efficient algorithm. The stability conditions are also described. The proposed method on a square lattice is naturally recovered when a square lattice is used. It is verified by solving four tests and compared with the analytical/exact solutions. They are in good agreement, demonstrating that the method is simple, accurate and robust for solute transport. Copyright © 2008 John Wiley & Sons, Ltd.     

Development of LBGK and incompressible LBGK‐based lattice Boltzmann flux solvers for simulation of incompressible flows

This paper presents lattice Boltzmann Bhatnagar–Gross–Krook (LBGK) model and incompressible LBGK model‐based lattice Boltzmann flux solvers (LBFS) for simulation of incompressible flows. LBFS applies the finite volume method to directly discretize the governing differential equations recovered by lattice Boltzmann equations. The fluxes of LBFS at each cell interface are evaluated by local reconstruction of lattice Boltzmann solution. Because LBFS is applied locally at each cell interface independently, it removes the major drawbacks of conventional lattice Boltzmann method such as lattice uniformity, coupling between mesh spacing, and time interval. With LBGK and incompressible LBGK models, LBFS are examined by simulating decaying vortex flow, polar cavity flow, plane Poiseuille flow, Womersley flow, and double shear flows. The obtained numerical results show that both the LBGK and incompressible LBGK‐based LBFS have the second order of accuracy and high computational efficiency on nonuniform grids. Furthermore, LBFS with both LBGK models are also stable for the double shear flows at a high Reynolds number of 10⁵. However, for the pressure‐driven plane Poiseuille flow, when the pressure gradient is increased, the relative error associated with LBGK model grows faster than that associated with incompressible LBGK model. It seems that the incompressible LBGK‐based LBFS is more suitable for simulating incompressible flows with large pressure gradients. Copyright © 2014 John Wiley & Sons, Ltd.     

A modified lattice boltzmann method for herschel-bulkley fluids

As one kind of the most important non-Newtonian fluids, Herschel-Bulkley fluids have been applied in practical engineering widely. In order to improve the stability and accuracy in the simulation of Herschel-Bulkley fluids with lattice Boltzmann method (LBM), a modified lattice Boltzmann method was proposed. With Poiseuille flow as the example, the shear-thinning fluids and the shear-thickening fluids were used, respectively, to introduce the method in detail. The comparison between the velocity distributions and the analytical solutions demonstrated the feasibility of the modified method. Also the effect of the power law index, lattice nodes, and the region of the shear rate on the relative error was discussed. Then, the method was applied into the simulation of the cement paste flow in the 3D printing extruder. The streamline figure was obtained and then conducted the flow simulation by the modified method and multiple-relaxation-time lattice Boltzmann method (MRT-LBM), respectively; the comparison further proved the modified method was feasible for Herschel-Bulkley fluids.