Capillary filling with pseudo-potential binary Lattice-Boltzmann model

We present a systematic study of capillary filling for a binary fluid by using a mesoscopic lattice Boltzmann model for immiscible fluids describing a diffusive interface moving at a given contact angle with respect to the walls. The phenomenological way to impose a given contact angle is analysed. Particular attention is given to the case of complete wetting, that is contact angle equal to zero. Numerical results yield quantitative agreement with the theoretical Washburn’s law, provided that the correct ratio of the dynamic viscosities between the two fluids is used. Finally, the presence of precursor films is experienced and it is shown that these films advance in time with a square-root law but with a different prefactor with respect to the bulk interface.     

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.     

Lattice Boltzmann method for the generalized Kuramoto-Sivashinsky equation

In this paper, a lattice Boltzmann model with an amending function is proposed for the generalized Kuramoto-Sivashinsky equation that has the form u_t+uu_x+αu_xx+βu_xxx+γu_xxxx=0. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. It is found that the numerical results agree well with the analytical solutions.     

Lattice Boltzmann method with the cell-population equilibrium

The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman--Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.     

Lattice Boltzmann method with the cell-population equilibrium

The central problem of the lattice Boltzmann method （LBM） is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non- negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman-Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.     

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 equation method in electrohydrodynamic problems

A consistent lattice Boltzmann equation (LBE) model for simulating different electrohydrodynamic (EHD) phenomena is developed. The model includes fluid dynamics, electric charge transport via advection and conduction currents, and action of electric forces upon space charges in liquid. Problems with different thermodynamic phases (liquid and gaseous) and phase transitions, and with inhomogeneous and density-dependent electric permittivity and conductivity can also be simulated, as well as charge injection and recombination. Deformations and breakup of conductive vapor bubbles, bubble deformation due to electrostriction, dynamics of drops with different electric permittivity were simulated. Simulations show the great potential of the method especially for problems with free boundaries (systems with vapor bubbles and multiple components with different electric properties).     

Lattice Boltzmann simulations of capillary filling: Finite vapour density effects

Numerical simulations of two-dimensional capillary filling using the pseudo-potential lattice Boltzmann model for multiphase fluids are presented. It is shown that whenever the density of the light-phase exceeds about ten percent of the dense phase, the front motion proceeds through a combined effect of capillary advection and condensation.     

Lattice Boltzmann simulation of solid particles suspended in fluid

The lattice Boltzmann method, an alternative approach to solving a fluid flow system, is used to analyze the dynamics of particles suspended in fluid. The interaction rule between the fluid and the suspended particles is developed for real suspensions where the particle boundaries are treated as no-slip impermeable surfaces. This method correctly and accurately determines the dynamics of single particles and multi-particles suspended in the fluid. With this method, computational time scales linearly with the number of suspensions,N, a significant advantage over other computational techniques which solve the continuum mechanics equations, where the computational time scales asN ³. Also, this method solves the full momentum equations, including the inertia terms, and therefore is not limited to low particle Reynolds number.     

用晶格玻尔兹曼方法研究螺旋波的产生机制和演化行为

采用五速正方晶格玻尔兹曼模型，由晶格玻尔兹曼方程推导得到了反应扩散方程.分析了Selkov反应扩散系统螺旋波的形成机制.零流边界条件下计算机数值模拟螺旋波的形成和破碎过程，发现Selkov反应扩散系统的失稳属于Doppler失稳.改变参数模拟系统的演化行为，发现不同的参数下系统可能到达三种不同的状态：均匀定态、混沌状态和螺旋波. 关键词： 晶格玻尔兹曼方法 螺旋波 计算机模拟     

Lattice Boltzmann method on quadtree grids for simulating fluid flow through porous media: A new automatic algorithm

During the past two decades, the lattice Boltzmann (LB) method has been introduced as a class of computational fluid dynamic methods for fluid flow simulations. In this method, instead of solving the Navier Stocks equation, the Boltzmann equation is solved to simulate the flow of a fluid. This method was originally developed based on uniform grids. However, in order to model complex geometries such as porous media, it can be very slow in comparison with other techniques such as finite differences and finite elements. To eliminate this limitation, a number of studies have aimed to formulate the lattice Boltzmann on the unstructured grids. This paper deals with simulating fluid flow through a synthetic porous medium using the LB method and on the quadtree grid structure. To this end, the LB method was used on nonuniform grids coupled with a technique for image reconstruction which resulted in the quadtree grids for simulation of fluid flow through porous media. Accuracy and efficiency of this algorithm is compared against the conventional LB method based on uniform grids. While the decrease in computational time in the proposed LB method on nonuniform grids is found to be significant regarding the size of the initial and reconstructed images, the same level of accuracy is obtained when compared with the conventional LB method on uniform grids.     

Modelling capillary filling dynamics using lattice Boltzmann simulations

We investigate the dynamics of capillary filling using two lattice Boltzmann schemes: a liquid-gas model and a binary model. The simulation results are compared to the well-known Washburn's law, which predicts that the filled length of the capillary scales with time as l ∝ t ^1/2. We find that the liquid-gas model does not reproduce Washburn's law due to condensation of the gas phase at the interface, which causes the asymptotic behaviour of the capillary penetration to be faster than t ^1/2. The binary model, on the other hand, captures the correct scaling behaviour when the viscosity ratio between the two phases is sufficiently high.     

Incorporation of smooth spherical bodies in the Lattice Boltzmann method

A method to simulate bodies suspended in a Lattice Boltzmann solvent is proposed. It is based on a generalized reaction force that enforces no-slip boundary conditions at the fluid–body interface as the limiting case of an iterative procedure. A smooth version of the Heaviside function allows to treat spherical particles of arbitrary size and produces smooth hydrodynamic forces as particles move in the continuum. Numerical tests demonstrate the accuracy of the method in reproducing the hydrodynamic field around a single particle and the fluid-mediated forces between pairs of particles. The drag force experienced by a particle moving in a straight channel and at various Reynolds numbers is studied as a non-trivial testcase.     

Lattice Boltzmann method for n-dimensional nonlinear hyperbolic conservation laws with the source term

It is important for nonlinear hyperbolic conservation laws (NHCL) to own a simulation scheme with high order accuracy, simple computation, and non-oscillatory character. In this paper, a unified and novel lattice Boltzmann model is presented for solving n-dimensional NHCL with the source term. By introducing the high order source term of explicit lattice Boltzmann method (LBM) and the optimum dimensionless relaxation time varied with the specific issues, the effects of space and time resolutions on the accuracy and stability of the model are investigated for the different problems in one to three dimensions. Both the theoretical analysis and numerical simulation validate that the results by the proposed LBM have second-order accuracy in both space and time, which agree well with the analytical solutions.     

Lattice Boltzmann simulation of transverse wave travelling in Maxwell viscoelastic fluid

A nine-velocity lattice Boltzmann method for Maxwell viscoelastic fluid is proposed. Travelling of transverse wavein Maxwell viscoelastic fluid is simulated. The instantaneous oscillating velocity, transverse shear speed and decay rateagree with theoretical results very well.     

椭圆柱体在牛顿流体中运动的格子Boltzmann方法模拟

用格子Boltzmann方法建立了椭圆柱体的二维动力学模型，利用所建立的模型，数值模拟了 牛顿流体中不同形状的椭圆柱体在相同初始条件下的运动和同一椭圆柱体在不同初始条件下 的运动，并通过比较相同条件下圆柱体的运动，讨论了椭圆柱体二维运动的特征，得到了一 些有意义的结果. 关键词： 格子Boltzmann方法 椭圆柱体 牛顿流体     

Lattice Boltzmann Simulation for the Spiral Wave Dynamics

We investigated the dynamics of the simple spiral waves of the Se/kov reaction-diffusion system with the Lattice Boltzmann method. The results of computer simulation lead to the conclusion that the trajectory of the spiral tip is a small circle, the wavelength and the period decay exponentially when the value of parameter b increases; and the relation between the wavelength and the period is λ ∝ T1/2, which is qualitatively the same as that obtained by Ou-Yang Qi from Belousov-Zhabotinsky reaction system.