Lattice Boltzmann Solid Particles in a Lattice Boltzmann Fluid

We define a lattice Boltzmann model of solid, deformable suspensions immersed in a fluid itself described in terms of the lattice Boltzmann method. We discuss the rules governing the internal dynamics of the solid object as well as the rules specifying the interaction between solid and fluid particle. We perform a numerical drag experiment to validate the model. Finally we consider the case of a population of flexible chains in suspension in a shear stress flow and study the influence on the velocity profile.     

Three-dimensional lattice Boltzmann method for simulating blood flow in aortic arch

The three-dimensional （3D） lattice Boltzmann models, 3DQ15, 3DQ19 and 3DQ27, under different wall boundary conditions and lattice resolutions have been investigated by simulating Poiseuille flow in a circular cylinder for a wide range of Reynolds numbers. The 3DQ19 model with improved Fillippova and Hanel （FH） curved boundary condition represents a good compromise between computational efficiency and reliability. Blood flow in an aortic arch is then simulated as a typical haemodynamic application. Axial and secondary fluid velocity and effective wall shear stress profiles in a 180° bend are obtained, and the results also demonstrate that the lattice Boltzmann method is suitable for simulating the flow in 3D large-curved vessels.     

Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method

The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in a wide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation are presented in detail The flow separation zones revealed with increase of Reynolds number are located in the areas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particular blood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmann method is adaptive to simulating the flow in larger vessels under a high Reynolds number.     

Influence of erythrocyte aggregation on leukocyte margination in postcapillary expansions: A lattice Boltzmann analysis

Leukocyte rolling on the vascular endothelium requires initial contact between the circulating leukocytes in the blood and the vessel wall. Although specific adhesion mechanisms are involved in leukocyte–endothelium interactions, adhesion patterns in vivo suggest other rheological mechanisms are involved as well. Previous studies have proposed that the abundance of leukocyte rolling in postcapillary venules is due to interactions between red blood cells and leukocytes as they enter capillary expansions as well as red blood cell (RBC) aggregation. We have established a lattice Boltzmann approach to analyze the interactions of RBC aggregates and leukocytes as they flow through a postcapillary expansion. The lattice Boltzmann technique provides the complete solution of the flow field and quantification of the particle–particle forces. Our results show that RBC aggregation strongly influences leukocyte–endothelium interactions.     

Lattice Boltzmann method for three-dimensional moving particles in a Newtonian fluid

A lattice Boltzmann method is developed to simulate three-dimensional solid particle motions in fluids. In the present model, a uniform grid is used and the exact spatial location of the physical boundary of the suspended particles is determined using an interpolation scheme. The numerical accuracy and efficiency of the proposed lattice Boltzmann method is demonstrated by simulating the sedimentation of a single sphere in a square cylinder. Highly accurate simulation results can be achieved with few meshes, compared with the previous lattice Boltzmann methods. The present method is expected to find applications on the flow systems with moving boundaries, such as the blood flow in distensible vessels, the particle－flow interaction and the solidification of alloys.     

三维方腔温盐双扩散的格子Boltzmann方法数值模拟

研究了温盐双扩散系统的多组分格子Boltzmann方法.通过对二维方腔的温盐双扩散系统的数值模拟，检验了方法的可行性及有效性，所得到的结果与差分法结果符合良好，继而将此方法推广到三维，建立了三维温盐双扩散系统的格子Boltzmann方法，对三维方腔双扩散问题进行了模拟和分析，并与差分法模拟的结果进行了比较，结果令人满意.最后，分析了格子Boltzmann方法在模拟双扩散对流问题时存在的局限性. 关键词： 格子Boltzmann方法 温盐双扩散 Boussinesq近似 数值模拟     

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.     

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.     

Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows

A lattice Boltzmann flux solver (LBFS) is presented in this work for simulation of incompressible viscous and inviscid flows. The new solver is based on Chapman-Enskog expansion analysis, which is the bridge to link Navier-Stokes (N-S) equations and lattice Boltzmann equation (LBE). The macroscopic differential equations are discretized by the finite volume method, where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. LBFS is validated by its application to simulate the viscous decaying vortex flow, the driven cavity flow, the viscous flow past a circular cylinder, and the inviscid flow past a circular cylinder. The obtained numerical results compare very well with available data in the literature, which show that LBFS has the second order of accuracy in space, and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.     

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.     

A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young–Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.     

A lattice Boltzmann method for a two-phase flow containing solid bodies with viscoelastic membranes

A lattice Boltzmann method (LBM) for two-phase flows containing solid bodies with viscoelastic membranes is proposed. The method is based on the two-phase LBM, in which one phase is regarded as the solid phase. In the present model, the membrane is assumed to be composed of identical particles that are connected to their neighboring particles by elastic springs to take account of stretching and compression effects. The method is applied to two representative problems, namely the behavior of a viscoelastic body under shear flow and the motion of a viscoelastic body in a Poiseuille flow. Tank-tread motion and axial migration, which are both characteristic of the motion of viscoelastic bodies, are simulated by using the method. These results indicate that the method is capable of simulating the complex behavior of viscoelastic bodies in capillaries, such as the motion of red blood cells in blood flows.     

Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows

We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows. The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions, eddy viscosity, wind shear stresses and Coriolis forces. The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation. The dispersion of free-surface temperature is modelled by an advection-diffusion equation. Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure. Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations. In addition, the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms. We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.     

Extended Lattice Boltzmann Model

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.     

Deformation of Two-Dimensional Nonuniform-Membrane Red Blood Cells Simulated by a Lattice

To study two-dimensional red blood cells deforming in a shear flow with the membrane nonuniform on the rigidity and mass, the membrane is discretized into equilength segments. The fluid inside and outside the red blood cell is simulated by the D2Q9 lattice Boltzmann model and the hydrodynamic forces exerted on the membrane from the inner and outer of the red blood cell are calculated by a stress-integration method. Through the global deviation from the curvature of uniform-membrane, we find that when the membrane is nonuniform on the rigidity, the deviation first decreases with the time increases and implies that the terminal profile of the red blood cell is static. To a red blood cell with the mass nonuniform on the membrane, the deviation becomes more large, and the mass distribution affects the profile of the two sides of the flattened red blood cell in a shear flow.     

基于速度源修正的浸入边界-晶格玻尔兹曼法研究仿生微流体驱动模型

浸入边界—晶格波尔兹曼法在流固耦合等复杂的流体系统中得到广泛的应用.本文采用基于速度源修正的浸入边界—晶格玻尔兹曼法,建立了仿生微流体驱动模型,创新性地将波动弹性体的速度引入晶格玻尔兹曼方程,避免了传统浸入边界—晶格玻尔兹曼法中浸入边界速度-结构变形-力之间的转换,提高了计算效率和准确率.研究了行波波动细丝对流场内流动速度和压力的影响,重点分析了驱动模型各项参数对微流体的驱动效果.研究结果表明:细丝长度、频率、振幅的增加引起出口处流量的增加;波长、流体粘滞系数以及细丝位置与出口处流量呈复杂的非线性关系.     

Lees–Edwards Boundary Conditions for Lattice Boltzmann

Lees–Edwards boundary conditions (LEbc) for Molecular Dynamics simulations⁽¹⁾ are an extension of the well known periodic boundary conditions and allow the simulation of bulk systems in a simple shear flow. We show how the idea of LEbc can be implemented in isothermal lattice Boltzmann simulations and how LEbc can be used to overcome the problem of a maximum shear rate that is limited to less then 1/L _y (with L _y the transverse system size) in traditional lattice Boltzmann implementations of shear flow. The only previous Lattice Boltzmann implementation of LEbc⁽²⁾ requires a specific fourth order equilibrium distribution. In this paper we show how LEbc can be implemented with the usual quadratic equilibrium distributions.     

用晶格玻尔兹曼方法研究微结构表面的疏水性能

将固体表面分别近似为具有简单的周期性矩形、三角形和半圆形微粗糙结构表面,建立了两相流的晶格玻尔兹曼模型.通过测量不同微粗糙结构表面上液滴的接触角,探讨微结构形状和尺寸的改变对固体材料表面疏水性能的影响.最后,由流体在各种糙壁管中的速度滑移,验证了结论的正确性.     

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.     

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.