多孔介质中流体流动及扩散的耦合格子Boltzmann模型

多孔介质中高Péclet数和大黏性比下混溶流体的流动和扩散广泛存在于二氧化碳驱油、化工生产等工业过程中.用数值方法对该问题进行研究时,关键在于如何正确描述高Péclet数和大黏性比下多孔介质内流体的行为.为此,提出了一种基于多松弛模型和格子动理模型的耦合格子Boltzmann模型.通过Chapman-Enskog分析,证明该模型能有效求解不可压Navier-Stokes方程和对流扩散方程.数值结果表明,该模型不仅具有二阶精度和良好的稳健性,而且对于高Péclet数和大黏性比的问题具有良好的数值稳定性,为模拟此类问题提供了有效工具.     

An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation

The lattice Boltzmann method (LBM) for two-phase flow simulation is often hindered by insufficient resolution at the interface. As a result, the LBM simulation of bubbles in bubbling flows is commonly limited to spherical or slightly deformed bubble shapes. In this study, the adaptive mesh refinement method for the LBM is developed to overcome such a problem. The approach for this new method is based on the improved interaction potential model, which is able to maintain grid-independent fluid properties in the two-fluid phases and at the interface. The LBM–AMR algorithm is described, especially concerning the LBM operation on a non-uniform mesh and the improved interaction potential model. Numerical simulations have been performed to validate the method in both single phase and multiphase flows. The 2D and 3D simulations of the buoyant rise of bubbles are conducted under various conditions. The agreement between the simulated bubble shape and velocity with experiments illustrates the capability of the LBM–AMR approach in predicting bubble dynamics even under the large bubble deformation conditions. Further, the LBM–AMR technique is capable of simulating a complex topology change of the interface. Integration of LBM with AMR can significantly improve the accuracy and reduce computation cost. The method developed in this study may appreciably enhance the capability of LBM in the simulation of complex multiphase flows under realistic conditions.     

On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.     

Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

<正>In this paper,an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface,where the surface tension is implemented.The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid,an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface,and an indicator function is introduced to update the fluid properties accurately.The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points,and then the surface tension is directly computed by using the normal vector and curvature of the interface.Two benchmark problems,including Laplace’s law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation.Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.     

基于总能形式的耦合的双分布函数热晶格玻尔兹曼数值方法

双分布函数热晶格玻尔兹曼数值方法在微尺度热流动系统中得到广泛的应用. 本文基于晶格玻尔兹曼平衡分布函数低阶Hermite展开式, 创新性地提出了包含黏性热耗散和压缩功的耦合的双分布函数热晶格玻尔兹曼数值方法, 将能量场内温度的变化以动量源的形式引入晶格波尔兹曼动量演化方程, 实现了能量场与动量场之间的耦合. 研究了考虑黏性热耗散和压缩功的和不考虑的两种热自然对流模型, 重点分析了不同瑞利数和普朗特数下流场内的流动情况以及温度、速度和平均努赛尔数的变化趋势. 本文实验结果与文献结果一致, 验证了本文数值方法的可行性和准确性. 研究结果表明: 随着瑞利数和普朗特数的增大, 方腔内对流传热作用逐渐增强, 边界处形成明显的边界层; 考虑黏性热耗散和压缩功的模型对流作用相对增强, 黏性热耗散和压缩功对自然对流的影响在微尺度流动过程中不能忽略.     

Embedding sharp interfaces within the lattice Boltzmann method for fluids with arbitrary density ratios

Current lattice Boltzmann methods for simulating two fluids create a diffuse interface between the fluids. In this work, we develop a novel technique for embedding sharp interfaces between fluids with unbounded density ratios for the LB method. Distribution functions streamed across an interface are transformed so that the receiving node is passed information corresponding to its fluid phase. Two different methods are employed to determine the transformation. The first uses analytical distribution functions from steady Poiseuille flow to determine the jump in moments of the distribution functions across the interface. The second uses approximate expansions of distribution functions to determine jumps in distribution functions. The accuracy and stability of the methods are examined in simulations of Poiseuille-Couette flows with an interface parallel to the walls. Both methods show linear convergence to the analytical solution.     

A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio

This paper reports a new numerical scheme of the lattice Boltzmann method for calculating liquid droplet behaviour on particle wetting surfaces typically for the system of liquid–gas of a large density ratio. The method combines the existing models of Inamuro et al. [T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198 (2004) 628–644] and Briant et al. [A.J. Briant, P. Papatzacos, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion in a liquid–gas system, Philos. Trans. Roy. Soc. London A 360 (2002) 485–495; A.J. Briant, A.J. Wagner, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: I. Liquid–gas systems. Phys. Rev. E 69 (2004) 031602; A.J. Briant, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: II. Binary fluids, Phys. Rev. E 69 (2004) 031603] and has developed novel treatment for partial wetting boundaries which involve droplets spreading on a hydrophobic surface combined with the surface of relative low contact angles and strips of relative high contact angles. The interaction between the fluid–fluid interface and the partial wetting wall has been typically considered. Applying the current method, the dynamics of liquid drops on uniform and heterogeneous wetting walls are simulated numerically. The results of the simulation agree well with those of theoretical prediction and show that the present LBM can be used as a reliable way to study fluidic control on heterogeneous surfaces and other wetting related subjects.     

Lattice Boltzmann Simulation of Shear-Thinning Fluids

It is shown how shear-thinning flow can be simulated without the need for numerical differentiation by following a lattice Boltzmann approach. The basic idea of is to combine the Cross model of viscosity with a 3D multiple relaxation time lattice Boltzmann method and to extract the required velocity derivatives from intrinsic quantities of the lattice Boltzmann scheme. Computational results are presented for a simple benchmark and for the simulation of liquid composite moulding.     

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiplerelaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time(SRT) lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations,it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version.     

An improved bounce-back scheme for complex boundary conditions in lattice Boltzmann method

In recent years, the lattice Boltzmann method (LBM) has been widely adopted to simulate various fluid systems, and the boundary treatment has been an active topic during the LBM development. In this paper, we present a novel approach to improve the bounce-back boundary treatment for moving surfaces with arbitrary configurations. We follow the framework originally proposed by Ladd [A.J.C. Ladd, Numerical simulations of particulate suspensions via a discretized Boltzman equation. Part 1. Theoretical foundation, Journal of Fluid Mechanics 271 (1994) 285–309]; however, the adjustment in the density distribution during the bouncing-back process at the boundary is calculated using the midpoint velocity inter-/extrapolated from the boundary and fluid velocities, instead of the real boundary velocity in the Ladd method. This modification ensures that the bouncing-back process and the density distribution adjustment both take place at a same location: the midpoint of a boundary lattice link, and thus removes the discrepancy of bouncing-back at the midpoint but density distribution adjustment at the boundary point in the original Ladd method. When compared with other existing boundary models, this method involves a simpler algorithm and exhibits a comparable or even better accuracy in describing flow field and flow-structure interaction, as demonstrated by several test simulations. Therefore, this boundary method could be considered as a competitive alternative for boundary treatment in LBM simulations, especially for particulate and porous flows with large fluid–solid interfacial areas.     

Simulations of complex fluids by mixed lattice Boltzmann—finite difference methods

We present the numerical results of simulations of complex fluids under shear flow. We employ a mixed approach which combines the lattice Boltzmann method for solving the Navier–Stokes equation and a finite difference scheme for the convection–diffusion equation. The evolution in time of shear banding phenomenon is studied. This is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow.     

Permeative flows in cholesteric liquid crystals

We use lattice Boltzmann simulations to solve the Beris-Edwards equations of motion for a cholesteric liquid crystal subjected to Poiseuille flow along the direction of the helical axis (permeative flow). The results allow us to clarify and extend the approximate analytic treatments currently available. We find that if the cholesteric helix is pinned at the boundaries there is an enormous viscosity increase. If, instead, the helix is free the velocity profile is flattened, but the viscosity is essentially unchanged. We highlight the importance of secondary flows, and, for higher flow velocities, we identify a flow-induced double twist structure in the director field--reminiscent of the texture characteristic of blue phases.     

Consistent lattice Boltzmann method

Lack of energy conservation in lattice Boltzmann models leads to unrealistically high values of the bulk viscosity. For this reason, the lattice Boltzmann method remains a computational tool rather than a model of a fluid. A novel lattice Boltzmann model with energy conservation is derived from Boltzmann's kinetic theory. Simulations demonstrate that the new lattice Boltzmann model is the valid approximation of the Boltzmann equation for weakly compressible flows and microflows.     

Lattice Boltzmann computational fluid dynamics in three dimensions

The recent development of the lattice gas method and its extension to the lattice Boltzmann method have provided new computational schemes for fluid dynamics. Both methods are fully paralleled and can easily model many different physical problems, including flows with complicated boundary conditions. In this paper, basic principles of a lattice Boltzmann computational method are described and applied to several three-dimensional benchmark problems. In most previous lattice gas and lattice Boltzmann methods, a face-centered-hyper-cubic lattice in four-dimensional space was used to obtain an isotropic stress tensor. To conserve computer memory, we develop a model which requires 14 moving directions instead of the usual 24 directions. Lattice Boltzmann models, describing two-phase fluid flows and magnetohydrodynamics, can be developed based on this simpler 14-directional lattice. Comparisons between three-dimensional spectral code results and results using our method are given for simple periodic geometries. An important property of the lattice Boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency, while all other methods, including the spectral method, are unable to model complicated geometries efficiently.     

A lattice Boltzmann method for nonlinear disturbances around an arbitrary base flow

In this paper we address the problem of the time evolution of a perturbation around a steady base flow with the use of the lattice Boltzmann method (LBM). This approach, named base flow lattice Boltzmann method, is of great interest in particular for aeroacoustic fields where the acoustic perturbation, on the one hand, is almost exclusively influenced by the large scale average structures of the underlying flow, and on the other hand, has a low effect on the large structures. The method is implemented for weakly compressible flows and the results of the base flow lattice Boltzmann are compared with the standard single relaxation time LBM. The boundary conditions for the base flow lattice Boltzmann method are discussed, as well as the implementation of outflow conditions for acoustic waves.     

格子Boltzmann亚格子模型的研究

为了将格子Boltzmann法应用于大雷诺数流动的模拟,本文将Smagorinsky亚格子模型和LBGK模型相结合,并对该亚格子LBM模型进行了研究。利用该亚格子LBM模型,对二维顶盖驱动流进行了模拟,得到了若干大雷诺数下流线图和方腔中心线上无量纲速度分布。计算结果与基准解进行比较,两者相互吻合。     

Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows

Is the lattice Boltzmann method suitable to investigate numerically high-Reynolds-number magneto-hydrodynamic (MHD) flows? It is shown that a standard approach based on the Bhatnagar–Gross–Krook (BGK) collision operator rapidly yields unstable simulations as the Reynolds number increases. In order to circumvent this limitation, it is here suggested to address the collision procedure in the space of central moments for the fluid dynamics. Therefore, an hybrid lattice Boltzmann scheme is introduced, which couples a central-moment scheme for the velocity with a BGK scheme for the space-and-time evolution of the magnetic field. This method outperforms the standard approach in terms of stability, allowing us to simulate high-Reynolds-number MHD flows with non-unitary Prandtl number while maintaining accuracy and physical consistency.     

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier–Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.     

Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.