Lattice Boltzmann Model Research Articles

Numerical Simulation for the Wave of the Variable Coefficient Nonlinear Schrödinger Equation Based on the Lattice Boltzmann Method

The variable coefficient nonlinear Schrödinger equation has a wide range of applications in various research fields. This work focuses on the wave propagation based on the variable coefficient nonlinear Schrödinger equation and the variable coefficient fractional order nonlinear Schrödinger equation. Due to the great challenge of accurately solving such problems, this work considers numerical simulation research on this type of problem. We innovatively consider using a mesoscopic numerical method, the lattice Boltzmann method, to study this type of problem, constructing lattice Boltzmann models for these two types of equations, and conducting numerical simulations of wave propagation. Error analysis was conducted on the model, and the convergence of the model was numerical validated. By comparing it with other classic schemes, the effectiveness of the model has been verified. The results indicate that lattice Boltzmann method has demonstrated advantages in both computational accuracy and time consumption. This study has positive significance for the fields of applied mathematics, nonlinear optics, and computational fluid dynamics.

Numerical study of magnesium dendrite microstructure under convection: Change of dendrite symmetry

Besides diffusion and capillary, convection which is unavoidable under terrestrial condition has remarkable effects on the microstructure evolution during solidification. In this study, a phase-field lattice-Boltzmann model, accelerated by state-of-the-art parallel-adaptive mesh refinement algorithm, is solved to investigate the morphological evolution of the Mg-Gd dendrite under convection. The lengths of the dendrite primary arms are quantified to analyze the asymmetric dendrite patterns under convection. The effects of the multiple factors including the orientation angle, the flow intensity, and the undercooling are elucidated, and the relation between the length ratios and the three independent factors is established through multiple regression analysis. The upstream-downstream arm length difference and the included angle between the primary arms are characterized to illustrate the effect of convection on the evolution of the Mg-Gd dendrite. The 3D morphological selection, together with algorithm performance tests, is further discussed to elucidate the change of morphological symmetry under different growth conditions and to demonstrate the robustness of the numerical scheme. Deep understanding of the synergy between convection-induced solute transport and undercooling-driven growth, which largely determines the morphological selection, can assist guidance for the prediction and control of the magnesium alloy microstructures.

Energy evolution of a droplet impacting a nonuniform chemically patterned fuel cell surface

A three-dimensional nonorthogonal lattice Boltzmann model is employed to simulate a single droplet impacting a nonuniform wettable surface at the bottom of a proton exchange membrane fuel cell. The effects of nonuniform surface wettability differences in the flow channel, the impact Weber number, and the central stripe width on the energy evolution during the spreading stage are investigated. Qualitative and quantitative comparisons between the numerical simulations and experimental results indicate that the main energy loss during the initial spreading stage is attributable to momentum redistribution, while viscous dissipation is caused by shear stress and vorticity in the rim. A larger wettability difference leads to a higher net unbalanced Young’s force, resulting in stronger shear and viscous dissipation near the wettability contrast line. For smaller Weber numbers, in the early impact stage, the main loss of kinetic energy is caused by the redistribution of momentum; in the later spreading stage, the increase in surface energy is the main sink of kinetic energy. The unbalanced Young’s force hinders the spreading of the droplet at larger stripe widths, leading to a larger vortex intensity within the rim.

Multi-phase-field lattice Boltzmann modeling and simulations of semi-solid simple shear deformation

Semi-solid deformation is a versatile phenomenon that occurs during the solidification of alloys. Semi-solid simple shear deformation is simulated using the multi-phase-field lattice Boltzmann (MPF-LB) method, which has been originally devised to capture polycrystalline solidification accompanied with melt flow and solid motion. MPF-LB simulations of semi-solid simple shear deformation, with variations in solid fractions, reveal the transition from a liquid-like behavior to a solid-like one. Especially, the shear band formed via dilatancy effects is thoroughly examined in the high solid fraction region. The relationship between grain rearrangement and mechanical behaviors during the formation process of the shear band is investigated in detail. In addition, the effect of domain size and initial grain arrangement on shear band formation is evaluated. Finally, the mechanism of shear band formation is clarified. The developed MPF-LB simulation method is promising for comprehensive evaluations of semi-solid deformation.

A Thread-Safe Lattice Boltzmann Model for Multicomponent Turbulent Jet Simulations

In this work an optimized multicomponent lattice Boltzmann (LB) model is deployed to simulate axisymmetric turbulent jets of a fluid evolving in a quiescent, immiscible environment over a wide range of dynamic regimes. The implementation of the multicomponent LB code achieves peak performance on graphic processing units (GPUs) with a significant reduction of the memory footprint, retains the algorithmic simplicity inherent to standard LB computing, and, being based on a high-order extension of the thread-safe LB algorithm, allows us to perform stable simulations at vanishingly low viscosities. The proposed approach opens attractive prospects for high-performance computing simulations of realistic turbulent flows with interfaces on GPU-based architectures.

Dynamics of droplet adsorption by liquid film on a grooved surface

Understanding the dynamics of droplet adsorption by liquid film on a grooved surface is of great significance for the possible manipulation of dropwise condensation on the grooved surface. In this study, an improved phase-field lattice Boltzmann model is proposed to describe the process of droplet adsorption from the ridge to the liquid film within the channel. The results indicate that the leading edge of the droplet undergoes two accelerations during the adsorption process, obeying the power law of and , respectively. The adsorption process between droplets with different sizes and the liquid film exhibits self-similarity characteristics including the same first peak velocity, the similar droplet displacement-time curve and the equal dimensionless spreading length of . Decreasing the contact angle of the droplet from to accelerates the displacement of the leading edge and extends the spreading length. These findings may help reveal the mechanics of droplet adsorption by the liquid film on the grooved surface and thus manipulate the condensation behavior for the heat transfer enhancement.

Level-set lattice Boltzmann method for interface-resolved simulations of immiscible two-phase flow.

A lattice Boltzmann (LB) scheme for a level-set equation is proposed to capture interface and is coupled with the LB model for incompressible fluid to simulate immiscible two-phase flows. The reinitialization of a level-set field is achieved directly by adding a source term to LB equation, which avoids solving an additional partial differential equation as required in traditional level-set methods. Compared to the classical phase-field lattice Boltzmann method, the proposed approach demonstrates significantly reduced errors in solving interface motion and deformation. Furthermore, GPU parallel computation is implemented for the level-set lattice Boltzmann method (LS-LBM) to enhance computational efficiency. To validate the LS-LBM, it is employed to simulate four benchmark problems: static droplet, layered Poiseuille flow, rising bubble, and Rayleigh-Taylor instability. Numerical results show that LS-LBM exhibits good stability, accuracy and high efficiency, demonstrating its feasibility for accurate simulations of immiscible two-phase flows, even with large density ratios or high Reynolds numbers.

Pore-scale modeling of wettability alteration coupled two-phase flow in carbonate porous media

The Middle East marine carbonate reservoirs are the primary targets for global crude oil exploration and production. In contrast to the clastic rock reservoirs, the marine carbonate reservoirs have undergone more complicated deposition, diagenesis and transformation, and the rock surface tends to be oil-wet or mixed-wet. One of the most effective methods for enhancing oil recovery in marine carbonate reservoirs is the use of an ion matched (IM)-surfactant (S) system to alter the wettability of rock surfaces. In this paper, we propose a microscale mathematical model of wettability alteration-coupled fluid flow by considering oil–water two-phase flow, wettability alteration, solute advection- diffusion and surfactant adsorption. The proposed microscale mathematical model is solved using the multi-component lattice Boltzmann model, and its accuracy is further verified. Finally, the effects of displacing fluid, ion-matched water concentration and surfactant concentration on oil mobilization at pore-scale are studied. Results show that, ion-matched water has a positive effect on wettability alteration, and typically shifts the cross-point of oil–water relative permeability curve to the right. The concentration of ion-matched water primarily affects fluid morphology of the wetting-phase and has little effect on phase permeability. After adding surfactant to the ion-matched water, the Euler coefficient of oil-phase gradually increases as the displacement continues, a large amount of remaining oil is gradually dispersed into scattered oil droplets and the oil-phase relative permeability is further improved.

Lattice Boltzmann modeling of forced imbibition dynamics in dual-wetted porous media

Forced imbibition dynamics are critical for enhancing recovery rates in reservoirs, as efficient fluid displacement directly impacts resource extraction. This study employs the Zou-He velocity boundary condition and a modified convective boundary condition (mCBC) within the multi-component Shan-Chen lattice Boltzmann method (LBM), thus facilitating unobstructed flow of multi-component fluids at the outlet while maintaining constant outlet pressure. The model's validity was established through outflow tests of immiscible droplets in channels. Its accuracy was further confirmed by comparing results from forced imbibition dynamics tests in dual-wetted pores with theoretical predictions. A symmetrical porous medium was constructed using the stacking method, achieving dual wettability by fixing the contact angle in the upper region and varying it in the lower region. We performed 20 simulation sets under unfavorable viscosity ratios and varying capillary numbers, focusing on overall displacement efficiency before and after breakthrough, and employing energy balance equations to evaluate the dominant forces. Results reveal that capillary forces predominantly dictate forced imbibition dynamics in low capillary number scenarios. In strongly wetted regions, the invading fluid fully occupies pore spaces; however, in weakly wetted regions, displacement efficiency significantly declines as wettability approaches neutrality, even nearing zero. As capillary numbers increase, viscous forces become more prominent, controlling dynamics and leading to fingering and trapping of defending fluids. In weakly wetted areas, the increasing influence of viscous forces enhances fluid displacement, resulting in significant improvements in overall displacement efficiency compared to conditions dominated by capillary forces.

A pore-scale investigation of viscous coupling effect on immiscible two-phase flow in porous media

Viscous coupling effect plays a significant role in immiscible two-phase flow within porous media, while its influence on relative permeability remains uncertain. In this paper, an improved MRT-based viscosity-modified multicomponent multiphase (MCMP) pseudopotential lattice Boltzmann model, capable of handling high viscosity ratio, is employed to simulate two-phase flow with different viscosities in a cross-array circular structure and a real rock structure, respectively. The applicability of this model for two-phase flow with various viscosity ratios has been verified by some typical tests. Systematically, the effects of viscosity ratio, structural configuration, and wetting condition on the relative permeability curves are investigated in conjunction with their component distributions and velocity fields at different two-phase saturations. These results indicate that due to the two-phase flow competition under different structural conditions, the viscous coupling effect has varying degrees of impacts on the mobility of thin phase and viscous phase. Further, the mechanism of two-phase lubricating effect is also discussed under different wetting conditions at Darcy flow regime.

An Allen-Cahn-based lattice Boltzmann model for two-phase flows with surfactants

An Allen-Cahn-based lattice Boltzmann model for two-phase flows with surfactants

Lattice Boltzmann Model for Rarefied Gaseous Mixture Flows in Three-Dimensional Porous Media Including Knudsen Diffusion

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures’ effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived.

Enhancement of pool boiling under reduced gravity by the synergistic effect of non-uniform surface structure and electric field: A lattice Boltzmann study

In this paper, a novel non-uniformly structured surface with primary and secondary pillars is conceived to be coupled with the action of an electric field to enhance pool boiling under reduced gravity. On the surface, the secondary pillars are distributed diagonally. A three-dimensional thermal lattice Boltzmann (LB) model combined with an electric field model is employed to investigate the boiling heat transfer performance on the non-uniformly pillar-structured surface and the associated boiling enhancement mechanism. It is found that the synergistic effect of the non-uniform surface structure and the electric field leads to a non-equilibrium electric force that causes the bubbles to be pushed away from the center of the heating surface, which promotes an earlier departure of the bubbles and provides more paths for the fresh liquid replenishment. As a result, the boiling performance under reduced gravity can be significantly enhanced by utilizing such a synergistic effect, with both the critical heat flux (CHF) and the maximum heat transfer coefficient (HTC) on the non-uniformly pillar-structured surface exceeding those on a uniformly pillar-structured surface under normal gravity. Moreover, the influences of the distribution of the secondary pillars on the boiling performance under reduced gravity are also studied. It is shown that the non-uniformly pillar-structured surface whose secondary pillars are distributed diagonally performs much better than those with the secondary pillars being distributed crossly and centrally, and the synergistic effect of the non-uniform surface structure and the electric field results from tuning the distribution of the non-uniform electric force.

Pore-scale study of [formula omitted] desublimation in a contact liquid

Cryogenic carbon capture (CCC) designed to operate in a contact liquid is an innovative technology for capturing CO2 from industrial flue gases, helping mitigate climate change. Understanding CO2 desublimation properties in a contact liquid is crucial to optimizing CCC, but is challenging due to the complex physics involved. In this work, a multiphysics lattice Boltzmann (LB) model is developed to investigate CO2 desublimation in a contact liquid for various operating conditions, with the multiple and fully-coupled physics being incorporated (i.e., two-phase flow, heat transfer across three phases, CO2 transport between the gas and liquid, homogeneous and heterogeneous desublimation of CO2, and solid CO2 generation). The CO2 desublimation process in a contact liquid is well reproduced. Moreover, parametric studies and quantitative analyses are set out to identify optimal conditions for CCC. The decreasing liquid temperature (Tl) and flue gas temperature (T0) are found to accelerate the CO2 desublimation rate and enhance the CO2 capture velocity (vc). However, excessively low Tl and T0 values should be avoided. These conditions increase the energy consumption of cooling while only marginally improving vc, due to the limited CO2 supply. The CCC system performs effectively when purifying flue gases with high CO2 content (Y0). This is because the large Y0 accelerates the CO2 desublimation rate and enhances the overall CO2 capture efficiency. A high gas injection velocity (or Pe) is beneficial for amplifying vc by increasing the gas–liquid interfaces and enhancing the CO2 supply. Nevertheless, too high a Pe should be avoided, as it hinders the transport of CO2 to the liquid or solid CO2 surfaces, ultimately restricting the amount of CO2 available for desublimation and inhibiting the enhancement of vc. This study develops a viable LB methodology to investigate CO2 desublimation in a contact liquid for varying conditions, which advances the knowledge base of CCC and facilitates its industrial applications.

A lattice Boltzmann model with sharp interface tracking for the motion and growth of dendrites in non-equilibrium solidification of alloys

A lattice Boltzmann model (LBM) with sharp interface tracking is developed to simulate the motion and growth of dendrites in non-equilibrium solidification of alloys. The model is validated through comparative analysis with the drafting-kissing-tumbling (DKT) phenomena of two and three particles and the continuous growth model (CGM), and demonstrates its computational efficiency advantage without compromising accuracy by comparison with the multi-phase field (MPF) model. Subsequently, the model is utilized to investigate the dendrite morphology transition and primary dendritic arm spacing (PDAS). It is found that the velocity dependent solute partition and the resulting changes in constitutional undercooling strongly influence the estimated morphology region and PDAS. Moreover, the segregation and microstructure evolution during the rapid solidification were studied. And the results revealed that free dendrites lead to significant changes in microstructure and segregation under the influence of non-equilibrium effects. This work illustrates the great potential of the proposed model in simulating dendrites and microstructure evolution under a wide range of solidification conditions. Its suitability for extreme conditions and non-equilibrium solidification can contribute to the understanding of microstructure formation patterns and solute segregation in rapid solidification.

Progress in theory and simulations of lattice Boltzmann method for heat transfer enhancement on phase change

As a general phenomenon in science and engineering, phase change has appeared and been applied in many aspects. However, there is a sufficient necessity to enhance the heat transfer in the phase change process due to the low heat transfer efficiency of the phase change material. In order to improve the efficiency of heat transfer during the phase change process, theory and numerical simulations based on computational fluid dynamics, especially the lattice Boltzmann (LB) method, are reviewed. The LB method has become a strong numerical method for heat and mass transfer and fluid dynamics because of its mesoscopic nature and a series of unique merits brought by this nature. In this article, progress in theory and simulations of the LB method for heat transfer enhancement on phase change is reviewed. This review first introduces the basic theories and models of the LB method for flow field and temperature field. Afterward, the development of the LB models for tracing the phase interface is reviewed. The application of the LB method for phase change and investigations of the heat transfer enhancement in the phase change process are also discussed. Finally, future developments in the LB method for phase change problems are prospected.

Evaluating the effectiveness of the modified multi-scale multi-physics coupled model for solid oxide fuel cells: A comparative analysis

A multi-scale multi-physics coupling numerical model serves as an effective tool to study the performance and improve the efficiency of solid oxide fuel cells (SOFCs) and provides the theory and data support for optimizing SOFC structure and operational strategy. To improve the accuracy and reliability of the model, this work established a modified simulation model that considers the effect of operational, structural, and physical parameters of SOFCs. First, the electrochemical kinetics equation, multi-component diffusion lattice Boltzmann (LB) model, and heat transfer LB model are modified by incorporating the reaction gas molar fraction, gas mixture concentration, temperature, and other parameters. Second, a regional hierarchical modeling strategy is proposed, and the multi-scale coupling model is modified by coupling mass and heat transfer. Third, considering the effect of carbon monoxide molar fraction, temperature difference, concentration change and porosity on electrochemical, mass, and heat transfer processes, the effectiveness of modification model is analyzed and validated. Results demonstrate that the modified model considerably improves the numerical simulation to handle the complex operational conditions of SOFCs. The modified model's predictions show better accuracy compared with experimental data, while maintaining consistency with the trends predicted by the original numerical models.

Lattice Boltzmann modeling of individual and collective cell dynamics in the presence of fluid flows

Lattice Boltzmann modeling of individual and collective cell dynamics in the presence of fluid flows

Three-dimensional central-moment pseudopotential lattice Boltzmann model with improved discrete additional term

In this work, a three-dimensional central-moment pseudopotential lattice Boltzmann model is developed to simulate a two-phase flow and wetting phenomena. In this model, an improved discrete additional term is proposed to regulate the thermodynamic consistency and surface tension. Different from the discrete additional terms in previous models where only low-order terms are derived at the macroscopic Navier–Stokes equation level, high-order terms are correctly constructed at the mesoscopic lattice Boltzmann equation level in the present improved discrete additional term so that the high-order central moments can be modified in the collision step. With the improved discrete additional term, the simple relationship between the interaction force and the pseudopotential functions is well preserved. On this basis, a simplified wetting boundary scheme is further proposed, which eliminates the complex process for choosing proper characteristic vectors and interpolation. Numerical simulations demonstrate that the proposed model can achieve better performance in thermodynamic consistency, Galilean invariance, numerical stability and computational efficiency, and have great ability to simulate two-phase flow and wetting phenomena on realistic conditions.

Examining a Conservative Phase-Field Lattice Boltzmann Model for Two-Phase Flows

In this study, a conservative phase-field lattice Boltzmann model is examined for simulating immiscible two-phase flows with large density and viscosity ratios. This model is built upon the Allen–Cahn equation, incorporating a filtered collision operator and high-order corrections in the equilibrium distribution functions. The numerical model is also integrated with the volumetric boundary scheme and the immersed boundary method to achieve various stationary and moving boundary conditions on arbitrary geometries for different application scenarios. A comprehensive evaluation of this phase-field solver is conducted through a range of academic and industrial cases. First, droplet splashing cases at different Reynolds numbers are studied. The phase-field LB model effectively captures the surface wave motion and splashing of the droplet, although some smearing of small structures is observed due to the diffused interface property of the numerical model. Second, a tuned liquid damper is simulated, accurately capturing sloshing forces on solid walls. In the simulation of a dam-breaking case, predicted gauge pressure and free-surface elevation time histories compare well with experimental data. Lastly, a gearbox case under dip lubrication is simulated, with both the gearbox churning loss and oil distribution being well predicted across a range of rotating speeds. The validation studies demonstrate the effectiveness of the present phase-field lattice Boltzmann model in simulating immiscible two-phase flows with large and realistic density and viscosity ratios. The strengths, limitations, and weaknesses of the conservative phase-field LB model are discussed, and suggestions for the development and application of this numerical model are provided.