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In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon.

This study constructs a new diffuse-domain (DD) lattice Boltzmann (LB) method for two-phase flows in complex geometries. We first coupled the DD method with the consistent and conservative phase-field (CCPF) method which can be described by the DD-CC Navier--Stokes--Cahn--Hilliard (NSCH) equations with the consistency of reduction, the consistency of mass and momentum transport, and the consistency of mass conservation. Then we conducted a matched asymptotic analysis and found that the DD-CCNSCH equations would converge to the CCNSCH equations as the thickness of the DD interface approaches to zero. Since the boundary conditions imposed on the complex geometries are incorporated into the DD-CCNSCH equations as the source terms, the system can be implemented more readily in a large and regular domain, and there is no need to treat the complex boundary conditions specially. We further developed a DD-CCPFLB method, and through the Chapman--Enskog analysis, the DD-CCPFLB method can correctly recover the DD-CCNSCH equations for two-phase flows in complex geometries. To quantitatively validate the DD-CCPFLB method, three benchmark problems are considered, and the numerical results are in agreement with those obtained through directly solving the CCNSCH equations combined with the original boundary conditions, the analytical solution, or the reported data. Finally, the present method is used to study the problems of two-phase flows in complex geometries, including the droplet dynamics in the Y-shaped channel and a droplet passing through cylindrical obstacles. The effects of the wettability and viscosity ratio are mainly investigated, and it is found that these two factors have significant impacts on the droplet dynamics. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann method is used for examining the gaseous flow in a microchannel with surface roughness that is modeled by an array of rectangular modules. The surface roughness effect is important with the decrease of the Knudsen number because the rarefaction has reduced the interaction between the gas molecules and the channel walls, thus reducing the surface roughness effect.

The lattice Boltzann method (LBM) is used for studying the electro-osmotic flow (EOF) in microchannels packed with a variable porosity medium. The results have shown that variations of porosity, particle size and tortuosity have affected the flow pattern and also the variation of the porosity near the wall has a vital affect on the velocity profile.

Deregulation of miR-186 and Twist1 has been identified to be involved in the progression of multiple cancers. However, the detailed molecular mechanisms underlying miR-186-involved cholangiocarcinoma (CCA) are still unknown. In this study, we found that miR-186 was downregulated in CCA tissues and cell lines, and negatively correlated with the expression of Twist1 protein. In vitro assays demonstrated that miR-186 mimics repressed cell proliferation, in vivo tumor formation, and caused cell cycle arrest. miR-186 mimics also inhibited the migration and invasion of CCLP1 and SG-231 cells. Mechanistically, the 3'-untranslated region (3'-UTR) of Twist1 mRNA is a direct target of miR-186. Further, miR-186 inhibited the expressions of Twist1, N-cadherin, vimentin, and matrix metallopeptidase 9 (MMP9) proteins, whereas it increased the expression of E-cadherin in CCLP1 and SG-231 cells. Silencing of Twist1 expression enhanced the inhibitory effects of miR- 186 on the proliferation, migration, and invasion of CCLP1 and SG-231 cells. In conclusion, miR-186 inhibited cell proliferation, migration, invasion, and epithelial-mesenchymal transition (EMT) through targeting Twist1 in human CCA. Thus, miR-186/Twist1 axis may benefit the development of therapies for CCA. [ABSTRACT FROM AUTHOR]

In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation and the other is applied for saturation evolution described by the convection-diffusion equation with a source term. We first performed a Chapman-Enskog analysis and show that the macroscopic nonlinear equations for pressure and saturation can be recovered correctly from the present LB model. Then in the framework of the LB method, we adopted a local scheme developed in some previous works for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal second-order finite-difference schemes. We also performed some numerical simulations, and the results show that the developed LB model and local scheme for velocity are accurate and also have a second-order convergence rate in space. Finally, compared to the available pore-scale LB models for two-phase flow in porous media, the present LB model has more potential in the study of large-scale problems. [ABSTRACT FROM AUTHOR]

In this paper, a regularized lattice Boltzmann model l'or a class of nonlinear convection-diffusion equations with variable coefficients is proposed. The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments. The Chapman-Enskog analysis shows that the nonlinear convection-diffusion equations can be recovered correctly. Numerical tests, including Fokker-Planck equations, Buckley-Leverett equation with discontinuous initial function, nonlinear convection-diffusion equation with anisotropic diffusion, are carried out to validate the present model, and the results show that the present model is more accurate than some available lattice Boltzmann models. It is also demonstrated that the present model is more stable than the traditional single-relaxation-time model for the nonlinear convection-diffusion equations. [ABSTRACT FROM AUTHOR]

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 1012). [ABSTRACT FROM AUTHOR]

In this paper, a general bounce-back scheme is proposed to implement concentration or thermal boundary conditions of convection-diffusion equation with the lattice Boltzmann method (LBM). Using this scheme, the general concentration boundary conditions, i.e., b1 &dgr;Cw/&dgr;n + b2Cw = b3, can be easily implemented at boundaries with complex geometry structure like that in porous media. The numerical results obtained using the present scheme are in excellent agreement with the analytical solutions of flows with both stationary and moving interfaces. Furthermore, to better understand the halfway bounce-back scheme, an analytical study of the concentration jump is presented. The studies of theoretical analysis and numerical experiments demonstrate that the proposed scheme has second-order accuracy. [ABSTRACT FROM AUTHOR]

Based on the chaotic oscillator, a method for weak signal detection using information fusion technology is proposed in this paper. On the one hand, various methods are employed to the amplitude detection of the same weak periodic signal, then the detection outcomes are fused by the adaptive weighted fusion method. On the other hand, during the detection course, information entropy, statistic distance, and Walsh transform are, respectively, used in the state recognition of chaotic oscillator from the viewpoint of time domain or frequency domain, then the recognition results are fused by the k/l fusion method. Numerical results show that the proposed approach detects signal more precisely, identifies state more accurately, and represents information more completely compared with traditional methods. [ABSTRACT FROM AUTHOR]

A unified thermal Lattice Bhatnagar-Gross-Krook (LBGK) model for the Boussinesq incompressible fluids is introduced. In the model, the velocity and temperature fields are solved by two independent LBGK equations which are combined into a coupled one for the whole system. Numerical simulations of three-dimensional natural convection flow in rectangular enclosures with differentially heated vertical walls are performed at Rayleigh numbers 1.5 x 10³ - 7.5 x 104 and Prandtl numbers 0.015 and 0.025. The numerical results are compared with those of a previous study. [ABSTRACT FROM AUTHOR]

In this paper, a general propagation lattice Boltzmann model is proposed for nonlinear advection-diffusion equations (NADEs), and the Chapman-Enskog analysis shows that the NADEs with variable coefficients can be recovered correctly from the present model. We also perform some simulations of the linear advection-diffusion equation, nonlinear heat conduction equation, NADEs with anisotropic diffusion, and variable coefficients to test the present model, and find that the numerical results agree well with the corresponding analytical solutions. Moreover, it is also shown that by properly adjusting the two free parameters introduced into the propagation step, the present model could be more stable and more accurate than the standard lattice Bhatnagar-Gross-Krook model. [ABSTRACT FROM AUTHOR]

An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation-based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second order (or lower order) of accuracy in the time-splitting scheme as in the conventional high-order Runge-Kutta-based kinetic methods, the present method solves the original Boltzmann equation, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows. [ABSTRACT FROM AUTHOR]

Outflow boundary condition (OBC) is a critical issue in computational fluid dynamics. As a type of numerical method for fluid flows, the lattice Boltzmann equation (LBE) method has gained much success in a variety of complex flows, and certain OBCs have been suggested for the LBE in simulating simple single-phase flows. However, very few discussions on the OBCs have been made for the two-phase LBE method. In this work, three types of OBCs that are widely used in the LBE for single-phase flows, i.e., the Neumann boundary condition, the convective boundary condition, and the extrapolation boundary condition, are extended to a two-phase LBE method and their performances are investigated. The comprehensive results of several two-phase flows show that these boundary conditions behave quite differently in the simulations of two-phase flows. Specifically, it is found that the Neumann boundary condition and the extrapolation boundary condition give rather poor predictions, while the type of convective boundary conditions work well, although the choice of the convection velocity has some slight influences on the results. We also apply these OBC schemes to some other two-phase models, and similar observations are found. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann equation (LBE) method has been shown to be a promising tool for microscale gas flows. However, few works focus on the microtube flows, and there still are some fundamental problems for the LBE to such flows. In this paper, a recently proposed axisymmetric LBE with three kinetic boundary conditions, i.e., the combination of bounceback and specular reflection scheme, the combination of the Maxwell and specular-reflection scheme, and the combination of the Maxwell and bounceback scheme, have been investigated in detail. By analyzing the micro-Hagen-Poiseuille flow, we observed the discrete boundary condition effect and provided a revised boundary scheme to overcome such effect near the slip flow regime. Some numerical tests for the micro-Hagen-Poiseuille have been carried out to validate the analysis, and the numerical results of the revised boundary schemes agree well with the analytic solutions which confirmed our theoretical analysis. In addition, we also applied the revised combination of the Maxwell and bounceback scheme to microtube flow with sudden expansion and contraction, the numerical results of the pressure distribution and normalized slip velocity agree well with the theoretical ones. [ABSTRACT FROM AUTHOR]

As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model. [ABSTRACT FROM AUTHOR]

The capability of modeling and simulating complex interfacial dynamics of multiphase flows has been recognized as one of the main advantages of the lattice Boltzmann equation (LBE). A basic feature of two-phase LBE models, i.e., the force balance condition at the discrete lattice level of LBE, is investigated in this work. An explicit force-balance formulation is derived for a flat interface by analyzing the two-dimensional nine-velocity (D2Q9) two-phase LBE model without invoking the Chapman-Enskog expansion. The result suggests that generally the balance between the interaction force and the pressure does not hold exactly on the discrete lattice due to numerical errors. It is also shown that such force imbalance can lead to some artificial velocities in the vicinity of phase interface. [ABSTRACT FROM AUTHOR]

In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs. [ABSTRACT FROM AUTHOR]

In this paper, we present a numerical study on the deformation and breakup behavior of liquid droplet past a solid circular cylinder by using an improved interparticle-potential lattice Boltzmann method. The effects of the eccentric ratio β, viscosity ratio between the droplet and the surrounding fluid, surface wettability, and Bond number (Bo) on the dynamic behavior of the liquid droplet are considered. The parameter β represents the degree that the solid cylinder deviates from the center line, and Bo is the ratio between the inertial force and capillary force. Numerical results show that there are two typical patterns, i.e., breakup and no breakup, which are greatly influenced by the aforementioned parameters. When β increases to a critical value βc, the droplet can pass the circular cylinder without a breakup, otherwise, the breakup phenomenon occurs. The critical eccentric ratio βc increases significantly with increasing Bo for case with >1, while for the case with <1, the viscosity effects on the βc is not obvious when Bo is large. For the breakup case, the amount of deposited liquid on the tip of the circular cylinder is almost unaffected by β. In addition, the results also show that the viscosity ratio and wettability affect the deformation and breakup process of the droplet. For case with <1, the viscosity ratio plays a minor role in the thickness variations of the deposited liquid, which decreases to a nonzero constant eventually; while for >1, the increase of the viscosity ratio significantly accelerates the decrease of the deposited liquid, and finally no fluid deposits on the cylinder. In term of the wettability, there occurs continuous gas phase trapped by the wetting droplet, but this does not happen for nonwetting droplet. Besides, for <1, the time required to pass the cylinder (tp) decreases monotonically with decreasing contact angle, while a nonmonotonic decrease appears for >1. It is also found that tp decreases monotonically with increasing Bo and is less sensitive to at a large Bo. [ABSTRACT FROM AUTHOR]

In this paper, we develop an efficient and alternative lattice Boltzmann (LB) model for simulating immiscible incompressible N-phase flows (N≥2) based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the N-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, (N-1) LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible N-phase fluid flows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four fluid phases and dynamics of droplets and interfaces for five fluid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among N (N≥2) immiscible incompressible flows. [ABSTRACT FROM AUTHOR]

In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes. [ABSTRACT FROM AUTHOR]

Within the phase-field framework, we present an accurate and robust lattice Boltzmann (LB) method for simulating contact-line motion of immiscible binary fluids on the solid substrate. The most striking advantage of this method lies in that it enables us to handle two-phase flows with mass conservation and a high density contrast of 1000, which is often unavailable in the existing multiphase LB models. To simulate binary fluid flows, the present method utilizes two LB evolution equations, which are respectively used to solve the conservative Allen-Cahn equation for interface capturing, and the incompressible Navier-Stokes equations for hydrodynamic properties. Besides, to account for the substrate wettability, two popular contact angle models including the cubic surface-energy model and the geometrical one are incorporated into the present method, and their performances are numerically evaluated over a wide range of contact angles. The contact-angle hysteresis effect, which is inherent to a rough or chemically inhomogeneous substrate, is also introduced in the present LB approach through the strategy proposed by Ding and Spelt [J. Fluid Mech. 599, 341 (2008)]. The present method is first validated by simulating droplet spreading and capillary intrusion on the ideal or smooth pipes. It is found that the cubic surface-energy and geometrical wetting schemes both offer considerable accuracy for predicting a static contact angle within its middle region, while the former is more stable at extremely small contact angles. Besides, it is shown that the geometrical wetting scheme enables us to obtain better accuracy for predicting dynamic contact points in capillary pipe. Then we use the present LB method to simulate the droplet shearing processes on a nonideal substrate with contact angle hysteresis. The geometrical wetting model is found to be capable of reproducing four typical motion modes of contact line, while the surface-energy wetting scheme fails to predict the hysteresis behaviors in some cases. At last, a complex contact-line dynamic problem of three-dimensional microscale droplet impact on a wettable solid is simulated, and it is found that the numerical results for droplet shapes agree well with the experimental data. [ABSTRACT FROM AUTHOR]

The phenomena of diffusion in multicomponent (more than two components) mixtures are universal in both science and engineering, and from the mathematical point of view, they are usually described by the Maxwell-Stefan (MS)-theory-based diffusion equations where the molar average velocity is assumed to be zero. In this paper, we propose a multiple-relaxation-time lattice Boltzmann (LB) model for the mass diffusion in multicomponent mixtures and also perform a Chapman-Enskog analysis to show that the MS continuum equations can be correctly recovered from the developed LB model. In addition, considering the fact that the MS-theory-based diffusion equations are just a diffusion type of partial differential equations, we can also adopt much simpler lattice structures to reduce the computational cost of present LB model. We then conduct some simulations to test this model and find that the results are in good agreement with the previous work. Besides, the reverse diffusion, osmotic diffusion, and diffusion barrier phenomena are also captured. Finally, compared to the kinetic-theory-based LB models for multicomponent gas diffusion, the present model does not include any complicated interpolations, and its collision process can still be implemented locally. Therefore, the advantages of single-component LB method can also be preserved in present LB model. [ABSTRACT FROM AUTHOR]

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ + ∑k=1m αk∂xkΠk(ϕ) = 0(1 ≤ k ≤ m ≤ 6), αk are constant coefficients, Πk(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009); H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)] for high-order nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]