THE NUMERICAL STUDY OF LATTICE BOLTZMANN METHOD BASED ON DIFFERENT GRID STRUCTURE

传统的格子波尔兹曼方法(lattice-Boltzmann method, LBM)通常基于标准均匀网格, 这主要取决于速度的空 间离散格式.均匀网格结构的特点, 使LBM在处理具有复杂边界的问题时遇到较大的困难, 从而限制了它的应用.另外, 对于较为复杂的流动, 其流场存在流动变化剧烈和平缓的区域, 在流动变化剧烈的区域, 往往需要足够的网格点才能更好地捕捉到流场信息, 而均匀网格会使得网格数量过多, 这会增加计算量, 但网格数量过少又无法获得必要的流场信息, 使LBM的计算效率降低.为了解决上述问题, 用不同的网格结构, 以顶盖驱动的腔体内流、柱体绕流和翼型绕流为例, 探讨了提高LBM算法的计算效率和适用性问题.     

不同壁面绕流特性的格子Boltzmann模拟研究

为了探讨不同壁面的绕流特性,针对粘性流场中,不同壁面诱导的涡脱落现象以及升阻力系数等流场特性进行了格子Boltzmann数值研究。利用基于分子动理论的格子Boltzmann方法(LBM)求解Navier-Stokes方程,实现对流体运动的描述,针对不同的壁面条件,分别采用不同的格子Boltzmann流-固壁面处理方法。采用Half-way反弹边界条件来处理平直壁面,而曲壁面则采用LBM与有限差分法相结合的形式进行处理,计入了壁面与标准网格不重合对结果造成的影响。开发相应的计算程序,计算结果与已发表文献结果吻合良好,验证了数值模型的正确性。同时,探讨了进出口边界与钝体中心的距离对结果的影响。对比分析了不同壁面的绕流模型中升阻力系数、斯托罗哈数和涡量云图等,并进一步研究了雷诺数条件的影响。结果表明,不同壁面的绕流特性具有明显差异,且同时受雷诺数的显著影响;一般地,平直壁面对于来流作出的响应更迅速。     

FVM与LBM分区耦合模拟圆柱绕流

构造了用于模拟远场边界下圆柱绕流的有限容积法(FVM)与格子Boltzmann方法(LBM)的分区耦合模型.模型中,靠近圆柱处采用多块网格的LBM,远离圆柱处采用FVM,并将计算结果同适体网格LBM以及多块网格LBM进行了比较.结果表明,耦合模型能在保证计算精度的前提下,显著提高计算效率.     

方腔双壁反向驱动流涡结构演化的数值模拟

采用微分求积法计算分析了不同雷诺数的二维方腔驱动流涡结构特性.数值模拟着重研究了雷诺数从0.01到1000变化对方腔双壁反向驱动流涡结构演化的影响,给出了涡演化过程的流型图和分叉图.结果表明,当雷诺数接近0时,腔内流动呈现对称的涡结构流型;随着雷诺数增加,子涡的大小和中心位置发生变化,鞍点始终位于方腔的中心,腔内流动形成非对称的斜扭流型;当雷诺数增大到某一临界值后,单一大涡占住整个方腔,大涡的形状变得更圆;如果雷诺数继续增加,方腔左上角和右下角同时出现二级涡,大涡中心始终位于方腔中心不变.     

黏弹性流体扩展及收缩流动的格子Boltzmann模拟分析

本文应用格子Boltzmann 方法(LBM)并结合Oldroyd-B 模型,讨论了不可压缩的 Navier-Stokes 方程和平流扩散本构方程的解耦及各自求解方法,以及两类问题的边界处理格式,实现了黏弹性流体在二维1:3 扩展流道以及3:1 收缩流道中的流动的数值模拟．获得了不同雷诺数Re 和维森伯格数Wi 以及黏度vs 下流动的流线分布,计算给出了漩涡的涡心位置和大小,并分析了参数Re、Wi 和vs 对流动特点的影响．模拟结果表明本文所采用模型和边界处理方法具有良好的精度和稳定性．     

格子玻尔兹曼法多块网格的交界结构优化研究

基于格子玻尔兹曼方法LBM(Lattice Boltzmann Method)对多块网格方法(Multi-Block)的粗细网格交界结构进行了研究,提出了一种新的优化处理方案。解决了原有网格交界结构存在的三个问题,即两套插值运算造成的程序结构复杂的问题,存储前几个时间步的节点流场数据以备插值运算造成内存浪费的问题和基于时间插值结果进行空间插值计算造成插值误差积累的问题。用一次多点二维空间插值的方式,将原方法的空间和时间双插值,简并成一次空间插值。通过对经典的非定常的圆柱绕流算例和定常的标准顶盖方腔驱动流算例的仿真模拟,验证了交界面处质量、动量及应力的连续性以及网格交界面数据过渡的流畅度,最终验证了改进方法的正确性。数值模拟结果表明,改进后多块算法可实现局部网格细化,进一步推动LBM方法在实际工程问题中的应用。     

谱元法和高阶时间分裂法求解方腔顶盖驱动流

详细推导了谱元方法的具体计算公式和时间分裂法的具体计算过程 ;对一般的时间分裂法进行了改进 ,即对非线性步分别用 3阶 Adams-Bashforth方法和 4阶显式 Runge-Kutta法 ,粘性步采用 3阶隐式 Adams-Moulton形式 ,提高了时间方向的离散精度 ,同时还改进了压力边界条件 ,采用 3阶的压力边界条件 ;利用改进的时间分裂方法分解不可压缩 Navier-Stokes方程 ,并结合谱元法计算了移动顶盖方腔驱动流 ,提高了方法可以计算的 Re数 ,缩短了达到收敛的时间 ,并将结果与基准解进行比较 ;分析了移动顶盖方腔驱动流中 Re数对流场分布的影响。     

格子Boltzmann方法模拟多孔介质惯性流的边界条件改进

格子Boltzmann方法可以有效地模拟水动力学问题,边界处理方法的选择对于可靠的模拟计算至关重要.本文基于多松弛时间格子Boltzmann模型开展了不同边界条件下,周期对称性结构和不规则结构中流体流动模拟,阐述了不同边界条件的精度和适用范围. 此外,引入一种混合式边界处理方法来模拟多孔介质惯性流, 结果表明:对于周期性对称结构流动模拟,体力格式边界条件和压力边界处理方法是等效的,两者都能精确地捕捉流体流动特点; 而对于非周期性不规则结构,两种边界处理方法并不等价,体力格式边界条件只适用于周期性结构;由于广义化周期性边界条件忽略了垂直主流方向上流体与固体格点的碰撞作用,同样不适合处理不规则模型;体力-压力混合式边界格式能够用来模拟周期性或非周期性结构流体流动,在模拟多孔介质流体惯性流时,比压力边界条件有更大的应用优势,可以获得更大的雷诺数且能保证计算的准确性.      

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．     

通道中并列旋转圆柱的LB-DF/FD模拟

通过结合格子Boltzmann方法(LBM)和DF(Direct Forcing)/FD(Fictitious Domain)思想,建立了一种新的LB-DF/FD方法。采用两套网格系统,欧拉网格用于流体,拉格朗日网格用于固体,有效地避免了计算中重新生成网格的步骤,同时在处理流固问题方面优于LBM方法。通过模拟通道中单圆柱旋转的流场,验证了该方法的正确性;并利用该方法模拟了低雷诺数下通道中并列旋转圆柱周围的流场,分析了圆柱距离壁面间距gw和雷诺数Re对流场结构的影响。研究结果表明:gw显著影响了流场的结构及圆柱的受力;而Re对圆柱升力及Stokes单元数目的影响较大。     

A thermal LBM-LES model in body-fitted coordinates: Flow and heat transfer around a circular cylinder in a wide Reynolds number range

In order to apply the lattice Boltzmann method (LBM) for modeling passive heat transfer at high Reynolds numbers, a number of models were proposed by introducing the large eddy simulation (LES) into the LBM framework to improve numerical stability. Our study finds that the generalized form of interpolation-supplemented LBM (GILBM), likewise, can locally modify the dimensionless relaxation time, thus enhancing the numerical stability at high Reynolds numbers. Given additional advantages of the GILBM in dealing with complicated geometries and improving computing accuracy, a thermal LBM-LES model in body-fitted coordinates is established in this paper. Numerical validation is performed by investigating the flow and heat transfer around a circular cylinder over a wide range of Reynolds numbers. The obtained results agree well with both experimental and numerical data in the previous work. Meanwhile, the effects of Reynolds number and Prandtl number on thermodynamic features of flow past a circular cylinder are revealed. It is found out that when the Reynolds number exceeds the critical value, the local Nusselt number fluctuates rapidly in a specific region of the rear cylinder surface affected by the Prandtl number. In the near-wake region, the temperature field exhibits significant dependence on the Prandtl number at moderate Reynolds numbers, while such effects turn to be slight at high Reynolds numbers.     

Developing a physical influence upwind scheme for pressure-based cell-centered finite volume methods

In the framework of a cell-centered finite volume method (FVM), the advection scheme plays the most important role in developing FVMs to solve complicated fluid flow problems for a wide range of Reynolds numbers. Advection schemes have been widely developed for FVMs employing pressure-velocity coupling methodology in the incompressible flow limit. In this regard, the physical influence upwind scheme (PIS) is developed for a cell-centered finite volume coupled solver (FVCS) using a pressure-weighted interpolation method for linking the pressure and velocity fields. The well-known exponential differencing scheme and skew upwind differencing scheme are also deployed in the current FVCS and their numerical results are presented. The accuracy and convergence of the present PIS are evaluated solving flow in a lid-driven square cavity, a lid-driven skewed cavity, and over a backward-facing step (BFS). The flow within the lid-driven square cavity is numerically solved at Reynolds numbers from 400 to 10 000 on a relatively coarse mesh with respect to other reported solutions. The lid-driven skewed cavity test case at Reynolds number of 1000 demonstrates the numerical performance of the present PIS on nonorthogonal grids. The flow over a BFS at Reynolds number of 800 is numerically solved to examine capabilities of current FVCS employing the current PIS in inlet-outlet flow computations. The numerical results obtained by the current PIS are in excellent agreement with those of benchmark solutions of corresponding test cases. Incorporating implicit role of pressure terms in a pressure-weighted interpolation method and development of PIS provides satisfactory solution convergence alongside the numerical accuracy for the current FVCS. A particular numerical verification is performed for the V velocity calculation within the BFS flow field, which confirms the reliability of present PIS.     

Lattice Boltzmann simulation of natural convection in open end cavity with inclined hot wall

Natural convection in an open end cavity with a hot inclined wall is simulated based on the lattice Boltzmann method (LBM). The physics of flow and energy transfer in open end cavities are addressed when the hot wall is inclined. The combination of the two topics (open cavity and inclined walls) is the main novelty of the present study. The effects of the angle of the hot inclined wall on the flow field and heat transfer are thoroughly investigated. The Prandtl number is fixed to 0.71 (air). The Rayleigh number and the angle of the hot inclined wall are varied in the range of 10⁴ to 10⁶ and 60? to 85?, respectively. The results are presented for two different aspect ratios, i.e., A = 1 and 2. The results obtained with the LBM are also compared with those of the finite volume method (FVM). The predicted results of the LBM conform to those of the FVM. The results show that by increasing the angle of the hot inclined wall and the aspect ratio of the cavity, the average Nusselt number decreases. The trend of the local Nusselt number on the inclined wall is also discussed.     

Multiple-relaxation-time lattice Boltzmann method for study of two-lid-driven cavity flow solution multiplicity

As a fundamental subject in fluid mechanics, sophisticated cavity flow patterns due to the movement of multi-lids have been routinely analyzed by the computational fluid dynamics community. Unlike those reported computational studies that were conducted using more conventional numerical methods, this paper features employing the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) to numerically investigate the two-dimensional cavity flows generated by the movements of two adjacent lids. The obtained MRT-LBM results reveal a number of important bifurcation flow features, such as the symmetry and steadiness of cavity flows at low Reynolds numbers, the multiplicity of stable cavity flow patterns when the Reynolds number exceeds its first critical value, as well as the periodicity of the cavity flow after the second critical Reynolds number is reached. Detailed flow characteristics are reported that include the critical Reynolds numbers, the locations of the vortex centers, and the values of stream function at the vortex centers. Through systematic comparison against the simulation results obtained elsewhere by using the lattice Bhatnagar–Gross–Krook model and other numerical schemes, not only does the MRT-LBM approach exhibit fairly satisfactory accuracy, but also demonstrates its remarkable flexibility that renders the adjustment of its multiple relaxation factors fully manageable and, thus, particularly accommodates the need of effectively investigating the multiplicity of flow patterns with complex behaviors.     

Investigation of incompressible flow within ½ circular cavity using lattice Boltzmann method

A wall‐driven incompressible viscous flow in a ½ circular cavity is simulated, based on the lattice Boltzmann method (LBM). The treatment of curved boundary with second‐order accuracy is used. The force evaluation is based on the momentum‐exchange method. The streamlines and vorticity contours and the velocity component along the central line of a semi‐circular cavity are obtained for different Reynolds numbers. The numerical results show that the LBM can capture the formation of primary, secondary and tertiary vortices exactly as the Reynolds number increases and has a great agreement with those of current literatures. Copyright © 2008 John Wiley & Sons, Ltd.     

Forced convection heat transfer due to different inclination angles of splitter behind square cylinder

A numerical investigation is carried out to study the effect of splitter’s inclination angle behind an inclined square cylinder on the forced convection heat transfer in a plan channel using the lattice Boltzmann method (LBM). The simulations are conducted for the pertinent parameters in the following ranges: the Reynolds number Re=50–300, the gap ratio G/d = 2, and the splitter’s inclination angle θ = 0 ^?–90^?. The results show that with the increase in the angle of the splitter, the drag coefficient initially decreases and then increases. Moreover, the time-averaged Nusselt number at a certain angle increases noticeably.     

Lattice Boltzmann methods for global linear instability analysis

Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier–Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.     

Numerical study of the properties of the central moment lattice Boltzmann method

Central moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify the collision process and forcing, and thereby naturally maintaining Galilean invariance, an important characteristic of fluid flows. When the different central moments are relaxed at different rates like in a standard multiple relaxation time (MRT) formulation based on raw moments, it is endowed with a number of desirable physical and numerical features. Because the collision operator exhibits a cascaded structure, this approach is also known as the cascaded LBM. While the cascaded LBM has been developed sometime ago, a systematic study of its numerical properties, such as the accuracy, grid convergence, and stability for well‐defined canonical problems is lacking, and the present work is intended to fulfill this need. We perform a quantitative study of the performance of the cascaded LBM for a set of benchmark problems of differing complexity, viz., Poiseuille flow, decaying Taylor–Green vortex flow, and lid‐driven cavity flow. We first establish its grid convergence and demonstrate second‐order accuracy under diffusive scaling for both the velocity field and its derivatives, that is, the components of the strain rate tensor, as well. The method is shown to quantitatively reproduce steady/unsteady analytical solutions or other numerical results with excellent accuracy. The cascaded MRT LBM based on the central moments is found to be of similar accuracy when compared with the standard MRT LBM based on the raw moments, when a detailed comparison of the flow fields are made, with both reproducing even the small scale vortical features well. Numerical experiments further demonstrate that the central moment MRT LBM results in significant stability improvements when compared with certain existing collision models at moderate additional computational cost. Copyright © 2015 John Wiley & Sons, Ltd.     

Resolution sensitivity of momentum‐exchange and immersed boundary methods for solid–fluid interaction in the lattice Boltzmann method

In the lattice Boltzmann method (LBM), the mechanism of fluid–solid interaction can be effectively captured by appropriately enforcing the no‐slip conditions in shear direction, and bounce‐back of the non‐equilibrium distribution portion in the normal direction at fluid–solid interfaces. Among various solid–fluid interaction schemes being proposed for LBM in recent decades, two simple fluid–solid interaction methods—the momentum exchange algorithm (MEA) and the immersed boundary scheme (IBS)—were developed based on the above concept. In this paper, MEA and IBS are implemented in a D2Q9 LBGK system and applied to measure the wall correction factors of drag force upon a stationary circular particle midway in the Poiseuille channel flow at very low Reynolds number and drag coefficients at low to moderate Reynolds numbers. MEA and IBS are also employed to compare the fluid‐induced torque over the cylinder in the Taylor–Couette flow, and the steady velocity of a particle settling under the influence of gravity inside a tube. The above experiments show that IBS seems to be more accurate and less demanding on lattice resolution. Copyright © 2010 John Wiley & Sons, Ltd.