AN EVALUATION OF THE BOUNCE-BACK BOUNDARY CONDITION FOR LATTICE BOLTZMANN SIMULATIONS

The bounce-back boundary condition for lattice Boltzmann simulations is evaluated for flow about an infinite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltemann method and with finite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0·1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder. The bounce-back boundary condition is shown to yield accurate lattice Boltzmann simulations with reduced computational requirements for computational grids of 170×170 or finer, a relaxation time less than 1·5 and any Reynolds number from 0·1 to 100. For this range of parameters the root mean square error in velocity and the relative error in drag coefficient are less than 1 per cent for the octagonal cylinder and 2 per cent for the circular cylinder. © 1997 John Wiley & Sons, Ltd.     

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.     

Lattice Boltzmann modeling of shallow water flows over discontinuous beds

Numerical modeling of shallow water flows over discontinuous beds is presented. The flows are described with the shallow water equations and the equations are solved using the lattice Boltzmann method (LBM) with single relaxation time (Bhatnagar–Gross–Krook‐LBM (BGK‐LBM)) and the multiple relaxation time (MRT‐LBM). The weighted centered scheme for force term together with the bed height for a bed slope is described to improve simulation of flows over discontinuous bed. Furthermore, the resistance stress is added to include the local head loss caused by flow over a step. Four test cases, one‐dimensional tidal over regular bed and steps, dam‐break flows, and two‐dimensional shallow water flow over a square block, are considered to verify the present method. Agreements between predictions and analytical solutions are satisfactory. Furthermore, the performance and CPU cost time of BGK‐LBM and MRT‐LBM are compared and studied. The results have shown that the lattice Boltzmann method is simple and accurate for simulating shallow water flows over discontinuous beds. This demonstrates the capability and applicability of the lattice Boltzmann method in modeling shallow water flows on bed topography with a discontinuity in practical hydraulic engineering. Copyright © 2014 John Wiley & Sons, Ltd.     

A high‐order compact finite‐difference lattice Boltzmann method for simulation of steady and unsteady incompressible flows

A high‐order compact finite‐difference lattice Boltzmann method (CFDLBM) is proposed and applied to accurately compute steady and unsteady incompressible flows. Herein, the spatial derivatives in the lattice Boltzmann equation are discretized by using the fourth‐order compact FD scheme, and the temporal term is discretized with the fourth‐order Runge–Kutta scheme to provide an accurate and efficient incompressible flow solver. A high‐order spectral‐type low‐pass compact filter is used to stabilize the numerical solution. An iterative initialization procedure is presented and applied to generate consistent initial conditions for the simulation of unsteady flows. A sensitivity study is also conducted to evaluate the effects of grid size, filtering, and procedure of boundary conditions implementation on accuracy and convergence rate of the solution. The accuracy and efficiency of the proposed solution procedure based on the CFDLBM method are also examined by comparison with the classical LBM for different flow conditions. Two test cases considered herein for validating the results of the incompressible steady flows are a two‐dimensional (2‐D) backward‐facing step and a 2‐D cavity at different Reynolds numbers. Results of these steady solutions computed by the CFDLBM are thoroughly compared with those of a compact FD Navier–Stokes flow solver. Three other test cases, namely, a 2‐D Couette flow, the Taylor's vortex problem, and the doubly periodic shear layers, are simulated to investigate the accuracy of the proposed scheme in solving unsteady incompressible flows. Results obtained for these test cases are in good agreement with the analytical solutions and also with the available numerical and experimental results. The study shows that the present solution methodology is robust, efficient, and accurate for solving steady and unsteady incompressible flow problems even at high Reynolds numbers. Copyright © 2014 John Wiley & Sons, Ltd.     

Lattice Boltzmann simulation of non-Newtonian flows past confined cylinders

A second-order lattice Boltzmann algorithm is used for Power-Law non-Newtonian flow simulation. The shear dependent behavior of the fluid is implemented through calculating the shear locally from the lattice distribution functions. A step by step verification procedure is taken to ensure the accuracy and the physical correctness of the numerical simulation. The flow past a series of tandem arrangement of two cylinders is computed in a confined domain. The effects of Reynolds number, the Power-Law index, and the distance between two cylinders on both the flow field and the drag coefficients of the cylinders are examined in detail.     

Unstructured lattice Boltzmann method in three dimensions

Over the last decade, the lattice Boltzmann method (LBM) has evolved into a valuable alternative to continuum computational fluid dynamics (CFD) methods for the numerical simulation of several complex fluid‐dynamic problems. Recent advances in lattice Boltzmann research have considerably extended the capability of LBM to handle complex geometries. Among these, a particularly remarkable option is represented by cell‐vertex finite‐volume formulations which permit LBM to operate on fully unstructured grids. The two‐dimensional implementation of unstructured LBM, based on the use of triangular elements, has shown capability of tolerating significant grid distortions without suffering any appreciable numerical viscosity effects, to second‐order in the mesh size. In this work, we present the first three‐dimensional generalization of the unstructured lattice Boltzmann technique (ULBE as unstructured lattice Boltzmann equation), in which geometrical flexibility is achieved by coarse‐graining the lattice Boltzmann equation in differential form, using tetrahedrical grids. This 3D extension is demonstrated for the case of 3D pipe flow and moderate Reynolds numbers flow past a sphere. The results provide evidence that the ULBE has significant potential for the accurate calculation of flows in complex 3D geometries. Copyright © 2005 John Wiley & Sons, Ltd.     

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。     

A Lattice Boltzmann study of non-newtonian flow in digitally reconstructed porous domains

In the present study, the Lattice Boltzmann Method (LBM) is applied to simulate the flow of non-Newtonian shear-thinning fluids in three-dimensional digitally reconstructed porous domains. The non-Newtonian behavior is embedded in the LBM through a dynamical change of the local relaxation time. The relaxation time is related to the local shear rate in such a way that the power law rheology is recovered. The proposed LBM is applied to the study of power-law fluids in ordered sphere packings and stochastically reconstructed porous domains. A linear relation is found between the logarithm of the average velocity and the logarithm of the body force with a curve slope approximately equal to the inverse power-law index. The validity of the LBM for the flow of shear thinning fluids in porous media is also tested by comparing the average velocity with the well known semi-empirical Christopher–Middleman correlation. Good agreement is observed between the numerical results and the Christopher–Middleman correlation, indicating that the LBM combined with digital reconstruction constitutes a powerful tool for the study of non-Newtonian flow in porous media.     

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.     

Efficient viscosity contrast calculation for blood flow simulations using the lattice Boltzmann method

The lattice Boltzmann method (LBM) combined with the immersed boundary method is a common tool to simulate the movement of red blood cel ls (RBCs) through blood vessels. With very few exceptions, such simulations neglect the difference in viscosities between the hemoglobin solution inside the cells and the blood plasma outside, although it is well known that this viscosity contrast can severely affect cell deformation. While it is easy to change the local viscosity in LBM, the challenge is to distinguish whether a given lattice point is inside or outside the RBC at each time step. Here, we present a fast algorithm to solve this issue by tracking the membrane motion and computing the scalar product between the local surface normal and the distance vector between the closest LBM lattice point and the surface. This approach is much faster than, for example, the ray-casting method. With the domain tracking applied, we investigate the shape transition of a RBC in a microchannel for different viscosity contrast and validate our method by comparing with boundary-integral simulations.     

Lattice Boltzmann method for polymer kinetic theory

The purpose of this work is to extend the applicability of the lattice Boltzmann method (LBM) to the field of polymer kinetic theory or more generally suspensions that could be described in the Fokker–Planck formalism. This method has been, in a first time, used for gas kinetic theory, where the resolution space corresponds to the physical space coordinate. In a second time is has been generalized to be applied to fluid flow involving different behaviours: turbulence, porous media, multiphase flow, etc. However this powerful, parallel, and efficient algorithm has not been applied for solving Fokker–Planck equations widely used to describe suspension kinetic theory. In this scale, molecular models involve a high computational costs because of the multidimensionality of the fully coupled micro–macro complex flow. The originality of this work consists to apply the lattice Boltzmann technique for solving Fokker–Planck equation based on a discretization of the configuration space where the resolution coordinates correspond to the microscopic configuration space (and not the physical coordinates). The result of this work emphasizes the optimality of the used technique that, in addition to its parallel ability, gathers the simplicity of the stochastic simulation and the robustness of the traditional fixed mesh support (such as the finite element method). Accuracy and convergence of the LBM will be compared to the stochastic and the finite element techniques for homogeneous shear flow.     

一种新的玻尔兹曼方程可计算模型构造与分析

临近空间飞行器因各部件尺寸差异较大, 在高空高马赫数条件下飞行会出现多流区共存的多尺度复杂非平衡流动现象, 流场中的气体分子速度分布函数与当地位置、流场分子速度、气体密度、流动速度、温度、热流矢量、应力张量等相关. 通过分析玻尔兹曼方程的一阶查普曼?恩斯科近似解, 构造了一种同时考虑热流矢量和应力张量影响、满足玻尔兹曼方程高阶碰撞矩的跨流域统一可计算模型方程, 并在数学上分析了其守恒性、H定理等基本属性, 证明了新模型方程与玻尔兹曼方程的相容性, 给出了新模型与现有模型如沙克霍夫(Shakhov)模型等的递进关系, 基于碰撞动力学确定了各流域统一气体分子碰撞松弛参数表达式. 在气体动理论统一算法中采用新建模型及现有模型模拟了一维激波结构、二维近空间飞行环境平板和多体圆柱干扰流动, 并与直接模拟蒙特卡洛方法对比分析, 结果表明在流场中粘性效应显著的区域新建模型能更好地捕捉激波位置, 尤其是在激波内部新模型模拟的宏观参数分布与直接模拟蒙特卡洛方法结果符合更好, 验证了新模型的有效性和可靠性, 同时说明在非平衡显著的流动区域碰撞松弛模型受多参数共同作用的影响.      

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。     

Investigation on Heat and Mass Transfer in a Evaporator of a Capillary-Pumped Loop with the Lattice Boltzmann Method: Pore Scale Simulation

A two-dimensional transient numerical model based on the lattice Boltzmann method (LBM) for the global evaporator of a capillary-pumped loop (CPL) is proposed to describe heat and mass transfer with evaporation in the porous wick, heat conduction in the cover plate, and heat transfer in the vapor groove. To indicate the stochastic phase distribution characteristics of most porous wick, the quartet structure generation set (QSGS) is introduced for generating more realistic microstructures of porous media. By using the present lattice Boltzmann algorithm along with the porous structure, the heat and mass transfer of an evaporator on pore scale can be predicted without resorting to any empirical parameters determined case by case. The energy equations for entire evaporator are solved as a conjugate problem, which are solved by means of a spatially varying relaxation time in the lattice Boltzmann model and the liquid flow is driven via the interfacial mass flux. A convective boundary condition considering the latent heat during the evaporation on the interface is introduced into the lattice Boltzmann model based on the nonequilibrium extrapolation rule. Especially, the bounce-back rule and the equilibrium rule of the LBM are, respectively, introduced to deal with the momentum boundary conditions inside the porous wick and on the evaporation interface in order to ensure the stability and the efficiency of the LBM model. Numerical results corresponding to different working conditions and different working fluids are presented, which provide guidance for the evaporator design of a CPL system.     

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.     

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.     

LBM simulation of fluid flow in fractured porous media with permeable matrix

To analyze and depict complicated fluid behaviors in fractured porous media with variably permeable matrix, an integrated discrete computational algorithm is proposed based on lattice Boltzmann method (LBM). This paper combines with the external force model and statistical material physics to effectively describe the feature changes while the fluid passes through the fractures within the permeable matrix. As an application example, a two dimensional rock sample is reconstructed using the digital image and characterized with different feature values at each LBM grid to distinguish pores, impermeable and permeable matrix by stating its local physical property. Compared with the conventional LBM, the results demonstrate the advantages of proposed algorithm in modeling fluid flow phenomenon in fractured porous media with variably permeable matrix.     

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．