Comparative study of lattice‐Boltzmann and finite volume methods for the simulation of laminar flow through a 4:1 planar contraction

In the present paper, a comparative study of numerical solutions for Newtonian fluids based on the lattice‐Boltzmann method (LBM) and the classical finite volume method (FVM) is presented for the laminar flow through a 4:1 planar contraction at a Reynolds number of value one, Re=1. In this study, the stress field for LBM is directly obtained from the distribution function. The calculations of the stress based on the FVM‐data use the evaluations of velocity gradients with finite differences. The stress field for both LBM and FVM is expressed in the present study in terms of the shear stress and the first normal stress difference. The lateral and axial profiles of the velocity, the shear stress and the first normal stress difference for both methods are investigated. It is shown that the LBM results for the velocity and the stresses are in excellent agreement with the FVM results. Copyright © 2004 John Wiley & Sons, Ltd.     

Simulation of gravity currents using the thermal lattice Boltzmann method

The lattice Boltzmann method (LBM) is becoming an effective numerical technique of computational fluid dynamics (CFD). In this study, with some new thermal LBM schemes being proposed, the LBM is used to simulate the gravity current prior to backdraft (a particular and hazardous phenomenon in compartment fire) within laminar restrictions. The dimensionless time for gravity current traveling from the opening to the rear wall of a bench‐scale compartment is calculated under different opening geometries, respectively, including: full end opening, upside‐slot end opening, middle‐slot end opening, downside‐slot end opening, and slot ceiling opening. The application is very successful and the results show that the dimensionless time under the slot ceiling opening is the longest. Among the slot end openings, similar dimensionless time has been obtained for the upside‐slot and middle‐slot end openings, which is shorter than the downside‐slot end opening. For the full end opening, the shortest dimensionless time is obtained. Finally, some valuable advices are given for fire protection engineering. Copyright © 2010 John Wiley & Sons, Ltd.     

Lattice Boltzmann method for simulating particle–fluid interactions

The lattice Boltzmann method （LBM） has gained increasing popularity in the last two decades as an alternative numerical approach for solving fluid flow problems. One of the most active research areas in the LBM is its application in particle-fluid systems, where the advantage of the LBM in efficiency and parallel scalability has made it superior to many other direct numerical simulation （DNS） techniques. This article intends to provide a brief review of the application of the LBM in particle-fluid systems. The numerical techniques in the LBM pertaining to simulations of particles are discussed, with emphasis on the advanced treatment for boundary conditions on the particle-fluid interface. Other numerical issues, such as the effect of the internal fluid, are also briefly described. Additionally, recent efforts in using the LBM to obtain closures for particle-fluid drag force are also reviewed.     

Development of a lattice Boltzmann method for two‐layered shallow‐water flow

In this paper the dynamics of a two‐layered liquid, made of two immiscible shallow‐layers of different density, has been investigated within the framework of the lattice Boltzmann method (LBM). The LBM developed in this paper for the two‐layered, shallow‐water flow has been obtained considering two separate sets of LBM equations, one for each layer. The coupling terms between the two sets have been defined as external forces, acted on one layer by the other. Results obtained from the LBM developed in this paper are compared with numerical results obtained solving the two‐layered, shallow‐water equations, with experimental and other numerical results published in literature. The results are interesting. First, the numerical results obtained by the LBM and by the shallow‐water model can be considered as equivalent. Second, the LBM developed in this paper is able to simulate motion conditions on nonflat topography. Third, the agreement between the LBM (and also shallow‐water model) numerical results and the experimental results is good when the evolution of the flow does not depend on the viscosity, that is, during the initial phase of the flow, dominated by gravity and inertia forces. When the viscous forces dominate the evolution of the flow the agreement between numerical and experimental results depends strongly on the viscosity; it is good if the numerical LBM viscosity has the same order of magnitude of the liquid's kinematic viscosity. Copyright © 2012 John Wiley & Sons, Ltd.     

基于格子-波尔兹曼法的流体能耗求解

格子-波尔兹曼法是近年来新兴的一种计算流体力学数值方法。随着这种方法的不断发展,人们将它用于流体的仿真、优化等不同场合。与此同时,一些与流场流速和压强相关的物理量(如能耗)的求解也成为关注的焦点。本文介绍了能耗这一流体宏观量的格子-波尔兹曼法求解及其实现。与传统的有限差分法不同,本文在求解有关的速度梯度时使用了格子-波尔兹曼-矩法,这种方法不但能够避免有限差分法在边界处失效的缺点,而且计算简单,算法局部性好,适合大规模并行计算。本文在分析其数值解精度的基础上,使用这种方法进行了以能耗极小为目标的直通道内椭圆挡块的参数优化。这些分析和算例分别定量和定性地说明了本文算法的准确性。     

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．     

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.     

THE RESEARCH PROGRESS OF LATTICE BOLTZMANN METHOD IN NON-NEWTONIAN FLUID FLOW

格子玻尔兹曼方法（lattice Boltzmann method,LBM）能够直接计算局部剪切速率并可以达到二次精度,因此在非牛顿流动数值模拟中展现出一定优势。尽管已证实LBM 对于非牛顿流动的适用性,但是LBM 需要通过即时调节BGK（Bhatnagar-Gross-Krook）碰撞项中的松弛时间来实时反映黏度改变,当松弛时间接近1/2 时,迭代会出现数值不稳定现象。该文对LBM 在非牛顿流体研究中的进展进行了总结,介绍了增加数值稳定性的方法并对结果的精度进行了比较,在此基础上对LBM 在非牛顿研究中的进一步发展进行了展望。     

Numerical and experimental study on the motion characteristics of single bubble in a complex channel

This paper is an extended study from previous work. In this study, the focus is paid to the dynamics of bubble rising and deformation in a complex channel, while the previous work is in straight channel. For this purpose, a three-dimensional lattice Boltzmann method (LBM) is employed to simulate the dynamics behaviour of a bubble rising in a complex channel consisting of three half-round throats. To validate the numerical method, a visual experiment was carried out by means of a high-speed digital camera and computer image processing technology. The behaviour of the rising bubble through glycerine solution in a complex channel was recorded. Some physical parameters such as rising velocities, trajectory and shapes of the bubble were calculated and processed based on the experimental data. In the same conditions, the trajectory, shapes and rising velocities of the bubble were simulated during its rising process by the proposed LBM. The numerical results are in good agreement with the experimental results. It demonstrates that LBM used in this work is feasible for simulating two-phase flow in such a complex channel.     

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.     

Numerical rheometry of bulk materials using a power law fluid and the lattice Boltzmann method

In the present study, the flow of bulk materials is characterised as a non-Newtonian fluid and modelled using the lattice Boltzmann method. A power law and a Bingham model is implemented in the LBM, which is hydrodynamically coupled to the discrete element method (DEM) for structural interaction. The performance of both non-Newtonian models is assessed, both qualitatively and quantitatively, in benchmark problems. The validated, non-Newtonian LBM–DEM framework is then applied to the geometry of a cylindrical Couette rheometer to numerically determine the constitutive response of a sample of Leighton Buzzard sand. The numerical results, which employ the power law, are compared with experimental data, and a number of other synthetic soil samples are defined using the presented process of numerical rheometry. Finally, the numerical stress–strain rate response of the synthetic soil samples is interpreted within the context of a regularised Bingham model, and the similarities discussed.     

Application of the Lattice-Boltzmann Method for Particle-laden Flows: Point-particles and Fully Resolved Particles

The Lattice-Boltzmann-Method (LBM) is a powerful and robust approach for calculating fluid flows over or through complex geometries. This method was further developed for allowing the calculation of several problems relevant to dispersed particle-laden flows. For that purpose two approaches have been developed. The first approach concerns the coupling of the LBM with a classical Lagrangian procedure where the particles are considered as point-masses and hence the particles and the flow around them are numerically not resolved. As an example of use, the flow through a single pore representing a single element of a filter medium was considered and the deposition of nano-scale particles was simulated. The temporal evolution of the deposit structures is visualised and both the filtration efficiency and the pressure drop are simulated and compared with measurements. In the second developed LBM-approach, the particles are fully resolved by the numerical grid whereby the flow around particles is also captured and it is possible to effectively calculate forces on complex particles from the bounce-back boundary condition. As a case study the flow around spherical agglomerates consisting of poly-sized spherical primary particles with sintering contact is examined. Using local grid refinement and curved wall boundary condition, accurate simulations of the drag coefficient of such complex particles were performed. Especially the effect of porosity on the drag was analysed. Moreover, the flow about very porous fractal flocks, generated by a random process, was simulated for different flock size and fractal dimension. The drag coefficients resulting from LBM simulations were compared to theoretical results for Stokes flow. Finally, scenarios with moving particles were considered. First, the sedimentation of a single particle towards a plane wall was simulated and compared with measurements for validation. Secondly, the temporal sedimentation of a cluster of 13 particles was studied. Here, the primary particles were allowed to stick together and form agglomerates. This research will be the basis for further analysing agglomerate formation in laminar and turbulent flows.     

Coupling of finite volume method and thermal lattice Boltzmann method and its application to natural convection

On the basis of the existing density distribution function reconstruction operator, the temperature distribution operator was derived to calculate heat transfer by coupling the lattice Boltzmann method (LBM) with the finite volume method. The present coupling model was validated by two‐dimensional natural convection flows with and without an isolated internal vertical plate. The results from the coupling model agree well with those from the pure‐finite volume method, pure‐LBM and references, and all the physical quantities cross the coupled interface smoothly. On the basis of residual history curves, it is likely that the convergence property and the numerical stability of the present model are better than those of the pure‐LBM at fine grid numbers and high Rayleigh numbers. Copyright © 2011 John Wiley & Sons, Ltd.     

Implicit–explicit finite‐difference lattice Boltzmann method with viscid compressible model for gas oscillating patterns in a resonator

Difficulties for the conventional computational fluid dynamics and the standard lattice Boltzmann method (LBM) to study the gas oscillating patterns in a resonator have been discussed. In light of the recent progresses in the LBM world, we are now able to deal with the compressibility and non‐linear shock wave effects in the resonator. A lattice Boltzmann model for viscid compressible flows is introduced firstly. Then, the Boltzmann equation with the Bhatnagar–Gross–Krook approximation is solved by the finite‐difference method with a third‐order implicit–explicit (IMEX) Runge–Kutta scheme for time discretization, and a fifth‐order weighted essentially non‐oscillatory (WENO) scheme for space discretization. Numerical results obtained in this study agree quantitatively with both experimental data available and those using conventional numerical methods. Moreover, with the IMEX finite‐difference LBM (FDLBM), the computational convergence rate can be significantly improved compared with the previous FDLBM and standard LBM. This study can also be applied for simulating some more complex phenomena in a thermoacoustics engine. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

A new cross-scaling method to deal with the porous flow problem

The finite volume method (FVM) and the lattice Boltzmann method (LBM) are coupled with each other to construct a new cross-scaling method to deal with the porous flow problem. To check the effectiveness of our developed cross-scaling LBM—FVM, the above mentioned problem is also solved by the well known LBM—LBM. Based on the data checking of the published data and the results of LBM—FVM and LBM—LBM, good agreement is observed.     

A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast

A hybrid phase field multiple relaxation time lattice Boltzmann method (LBM) is presented in this paper for simulation of multiphase flows with large density contrast. In the present method, the flow field is solved by a lattice Boltzmann equation. Concurrently, the interface of two fluids is captured by solving the macroscopic Cahn‐Hilliard equation using the upwind scheme. To be specific, for simulation of the flow field, an lattice Boltzmann equation (LBE) model developed in Shao et al. (Physical Review E, 89 (2014), 033309) for consideration of density contrast in the momentum equation is used. Moreover, in the present work, the multiple relaxation time collision operator is applied to this LBE to enable simulation of problems with large viscosity contrast or high Reynolds number. For the interface capturing, instead of solving another set of LBE as in many phase field LBMs, the macroscopic Cahn‐Hilliard equation is directly solved by using a weighted essentially non‐oscillatory scheme. In this way, the present hybrid phase field LBM shares full advantages of the phase field LBM while enhancing numerical stability. The ability of the present method to simulate multiphase flow problems with large density contrast is demonstrated by several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

An IB-LBM study of continuous cell sorting in deterministic lateral displacement arrays

The deterministic lateral displacement(DLD) is an important method used to sort particles and cells of different sizes. In this paper, the flexible cell sorting with the DLD method is studied by using a numerical model based on the immersed boundary-lattice Boltzmann method(IB-LBM). In this model, the fluid motion is solved by the LBM, and the cell membrane–fluid interaction is modeled with the LBM.The proposed model is validated by simulating the rigid particle sorted with the DLD method, and the results are found in good agreement with those measured in experiments. We first study the effect of flexibility on a single cell and multiple cells continuously going through a DLD device. It is found that the cell flexibility can significantly affect the cell path,which means the flexibility could have significant effects on the continuous cell sorting by the DLD method. The sorting characteristics of white blood cells and red blood cells are further studied by varying the spatial distribution of cylinder arrays and the initial cell–cell distance. The numerical results indicate that a well concentrated cell sorting can be obtained under a proper arrangement of cylinder arrays and a large enough initial cell–cell distance.     

过渡区气体微尺度流动的格子Boltzmann模拟

采用格子Boltzmann方法(LBM)对过渡区内的微尺度气体流动进行了模拟研究. 在已有滑移区微流动LBM模型中引入Knudsen层速度修正,选取合适的修正函数表达式并依据动理论确定了可调参数的合理取值. 在边界条件的处理格式上,采用了适合过渡区模拟的高阶滑移边界的替代格式来捕捉过渡区微流动的滑移速度,避免了直接求解高阶速度导数项的数值困难. 通过对两类不同的微流动进行模拟的结果表明:与数值解吻合得较好,尤其是对Kn>0.5微流动滑移速度的预测,与已有LBM的模拟结果相比有明显的提高.