Lattice Boltzmann Method Model Research Articles

A comparative study on the Lattice Boltzmann Method and the VoF-Continuum method for oxygen transport in the anodic porous transport layer of an electrolyzer

The optimization of Polymer Electrolyte Membrane (PEM) electrolyzers necessitates an intimate knowledge of the oxygen flows within the anodic porous transport layers (PTLs) to determine any possible reduction in performance. In this field, as experimental studies are cumbersome and expensive, numerical modeling has arisen as a viable alternative for studying the oxygen transport within the Anodic PTLs of a PEM electrolyzer. Amongst the various numerical modeling techniques, the Lattice Boltzmann Method (LBM) is gaining prominence for its effectiveness in analyzing fluid transport within porous media due to its mesoscopic nature and ease of implementation. This study utilizes the Shan-Chen LBM methodology to model the flow of oxygen within the Anodic PTL of a PEM electrolyzer and compares it against the Volume-of-Fluid-based Continuum Model. The results show that LBM can not only replicate the experimental studies accurately, but can also maintain its high accuracy at progressively shrinking length scales of PTLs, even at length scales where the VoF-based Continuum Model would run into accuracy issues. The high accuracy of the LBM model, combined with the simplicity of the LB algorithm makes LBM a powerful technique for simulating the microfluidic flows such as the flow of oxygen within the Anodic PTL of a PEM electrolyzer.

Numerical investigation of saline gravity currents with different water depth and salinity based on the lattice Boltzmann method

In this paper, we used Lattice Boltzmann Method (LBM) to simulate the motion of saline gravity currents, considering different cases of water depth and salinity, aiming to evaluate the reliability of the LBM model and investigate the longitudinal properties of the gravity currents. The study in this paper was divided into two phases. The first phase explained the basic principles and the implementation process of the numerical model. By comparing the simulation results with laboratory experimental data, it was found that the simulation results were in good agreement with the laboratory experiments. The second phase of the study simulated the saline gravity currents with different water depths and salinities. It was observed that, due to the increasing density gradient, the front velocity of dense current increased with rising water depth and saltwater salinity, and the intensity of turbulence at the interface was enhanced.

Equation-of-state-based lattice Boltzmann model of multicomponent adsorption onto fluid–fluid interfaces

In diffuse interface models, such as the lattice Boltzmann method (LBM), interfacial physics plays an important role. An example of an important interfacial phenomenon is adsorption onto a fluid–fluid interface. In the context of LBM, adsorption studies have traditionally only focused on adsorption onto a solid surface. The studies on adsorption onto fluid–fluid interfaces have been qualitative in nature, suffer from restrictions on the number of components, or are based on simple thermodynamic models designed for fully immiscible phases. Our recently published fugacity-based LBM model introduces a platform for the accurate modeling of multiphase fluids unrestricted by the number of components, and governed through accurate equations of state (Soomro and Ayala, 2023). In this study, we utilize the fugacity-based LBM to capture interfacial adsorption. This paper begins by simulating adsorption in a binary system with a flat interface, and shows that the amount of adsorption, quantified by relative adsorption measures, is in exact agreement with Gibbs theory. Next, the analysis is continued for a ternary system with two species adsorbing onto the interface. The binary and ternary simulations are then repeated for the case of a droplet and finally a five component case is presented. The study shows that the fugacity-based LBM can capture adsorption in full agreement with Gibbs adsorption theory. This provides a path for a generalized LBM model for adsorption, based on robust thermodynamic models for the fluids and unrestricted by the number of components, marking a significant contribution to the LBM literature.

Numerical Analysis of Narrow-gap Underfill Flow in the Flip-chip Process Using the Lattice Boltzmann Method

Flip-chip packaging is a first-level interconnect technology, and to predict its melt front of capillary driven underfill analytical models have been made. Using the Analytical models, prediction of the melt front can be efficiently done, however it is difficult to reflect the flow resistance resulting from complex solder bump arrangement. Therefore, 3D numerical analysis is required. In this study, Lattice Boltzmann method (LBM) is used for observing the micro void generation that occurs in a underfill process with a height of several tens of microns. LBM statistically expresses the motion of the molecule, to solve the mass transfer of the microscale. In particular, LBM has strengths in multiphase flow analysis of several microscales that cannot be solved by continuum assumption. In this paper, underfill process of several tens of micro scales, which was not covered in previous 3D numerical analysis studies, was simulated using LBM. The improvement of the new LBM model, which more accurately simulates the resistance due to pressure by considering collisions between air and molten mold molecules, is introduced. With the hydraulic diameter greatly reduced due to the narrow gap, it is observed how the solder bump pitch affects the micro void generation. And it is observed whether the air ventilation could change significantly according to the ambient pressure.

Impact of nanoparticle agglomeration on thermal conductivity of molten salt based nanofluids: Insights from molecular dynamics and lattice Boltzmann methods

The nanoparticle aggregation has significant influence on heat transfer properties. The contradictions between different researches exist and the underlying mechanisms of heat conduction remain unclear. To address these issues, the thermal conductivity of solar salt-SiO2 nanofluids in the non-aggregated and aggregated states was investigated, based on the combination of the advantages of molecular dynamics (MD) in revealing physical insights and lattice Boltzmann method (LBM) in simulating properties for complex structures. LBM models were simplified on the basic of MD results. Different heat transfer physics in nanofluids at nanoscale and mesoscale were compared. The results show that the thermal conductivity of aggregated nanofluid is higher than the non-aggregated nanofluid. By analyzing the diffusion coefficient, number density and vibrational density of states, we found that the previous hypotheses (such as Brownian motion, interfacial layer and interfacial thermal resistance) cannot explain the enhanced thermal conductivity induced by the nanoparticle agglomeration. The heat transfer mechanisms of aggregated nanofluid were further analyzed from new perspectives, i.e., the contributions of different material components and fluctuation modes to heat flux. It is found that the nanoparticle aggregation leads to the nanoparticle contribution increase, indicating the formation of low thermal resistance channels within the aggregates. The heat conduction contributed by collision decreases in the aggregated state, while that contributed by potential energy increases. Moreover, the thermal conductivity of aggregated nanofluid is negatively correlated with temperature, aggregate size and fractal dimension of agglomerates, and positively correlated with mass fraction of nanoparticles, degree of agglomeration, and backbone length of each aggregate.

A new three dimensional cumulant phase field lattice Boltzmann method to study soluble surfactant

Surfactants play a critical role in the physics of paint and coating formulations, affecting key rheological properties such as viscosity, yield stress, and thixotropy. This paper proposes a new three-dimensional phase-field model that uses the cumulant lattice Boltzmann method (LBM) to simulate soluble surfactants. Although current phase-field models commonly use Langmuir's relationship, they cannot calculate interfacial tension analytically, or the LBM models used are unstable when viscosities are low. However, the proposed method overcomes these limitations through two main features. First, the main parameters for modeling and controlling the surfactant's strength and interaction with other phases are directly obtained from a given initial interfacial tension and bulk surfactant, eliminating the need for trial-and-error simulations. Second, a new equilibrium distribution function in the moment space that includes diagonal and off diagonal elements of the pressure tensor is used to minimize Galilean invariance violation. Additionally, there is no need to use an external force to recover multiphase flows, which could break mass conservation. Furthermore, this method has significant potential for parallelization since only one neighbor's cell is used for discretization. The method shows Langmuir relation behavior and is validated with analytical solutions for various interfacial tensions and surfactant concentrations. Moreover, the paper demonstrates the influence of interfacial tension and surfactants on spurious velocities, indicating the method's stability at low viscosities. The dynamics of droplets in the presence of the surfactants is studied in spinodal decomposition and under various external forces. The method accurately simulates the breaking-up and coalescence for these cases. Furthermore, the method successfully simulates the breakage of a liquid thread at a high viscosity ratio.

Pore-scale modelling of water sorption in nanopore systems of shale

Water vapor sorption in nanoporous media with complex pore structures, like shale, is not well understood. To address this, a pseudopotential lattice Boltzmann method (LBM) is developed to investigate water sorption behavior. The LBM model incorporates long-range molecular forces using a modified Shan-Chen model based on the Carnahan-Starling equation of state. The simulation results show that the presence of water films in nanopores can create a liquid pressure difference of up to 100 MPa between confined and free states. The adsorption theories based on simple pore shapes are not applicable to nanoporous systems with complex pore geometries. Additionally, when the relative humidity exceeds 1, water vapor condenses inside hydrophobic nanostructures while being attracted by neighboring liquid, leading to cluster formation. In water-wet nanoporous media, capillary condensation occurs progressively from small throats to large pores, and the sorption curves vary smoothly with pressure variation. In mixed-wet nanoporous media, the sorption curves exhibit no hysteresis in the early desorption stage, where the adsorption and desorption processes occur in the region around the hydrophobic particles and are reversible. Overall, this study provides valuable insights into water sorption behavior in nanopore systems of shale and sets the foundation for modelling liquid-vapor distribution in nanoporous media at the pore scale.

Modeling the Impacts of Structural Heterogeneities on the Reaction-Transport Coupling in Porous Electrodes of Lithium-Ion Batteries Using Lattice Boltzmann Method

Structural optimization of porous electrodes has been a practical route to improve the performance of lithium-ion batteries (LIBs). Currently, this relies mainly on the structure-featureless pseudo-two-dimension (P2D) model in the theoretical aspect, which is inherently contradictory to the emphasis on the importance of electrode structure. Herein, a 2D pore-scale LIBs model based on the lattice Boltzmann method (LBM) and the galvanostatic simulation scheme are established. The model is used to investigate the effects of physical structures on the coupling between ions transport and electrochemical reactions in porous electrodes, and the results are compared with a P2D model on the same electrode. The results show that for battery systems composed of homogeneously distributed structures, the LBM model gives nearly identical results to that of the P2D model. However, for battery systems with heterogeneously structured electrodes, obvious difference from the prediction of P2D model are obtained, especially at high C-rates. The P2D model significantly underestimates the structure-sensitive transport-reaction coupling and the non-uniform utilization of active materials, even when using the physical tortuosity based on electrode structure. These results emphasize the significance of developing a pore-scale model of LIBs based on realistic physical structure for the design of LIBs with satisfactory performance.

Study of single-component two-phase free energy lattice Boltzmann models using various equations of state

In single-component two-phase flow simulations by the lattice Boltzmann method (LBM), one key topic of interest is the equation of state (EOS), which has been studied more in the pseudo-potential approach but much less in the free energy approach. Here, we conducted fair assessment of several popular non-ideal gas EOS in free energy LBM. The inability to independently tune the surface tension and interface thickness was identified for existing free energy formulation using most EOS. A simple modification was proposed and incorporated into three free energy LBM models, including the pressure tensor model, Lee–Fischer's model, and Guo's well-balanced model. Good compatibility with all of them was demonstrated by numerical simulations. In addition, a piecewise-linear (PWL) EOS proposed in pseudo-potential LBM was found to be also feasible in free energy LBM. Extensive numerical experiments on diverse problems (some containing contact lines) revealed that the influence of EOS was rather limited when key parameters are nearly the same (easily achievable with the proposed modification). The capability of the Lee–Fischer and well-balanced models to reduce the spurious currents down to machine accuracy (for static drop tests) was found to be independent of the EOS (including the customized PWL EOS). Overall, the pressure tensor LBM is associated with larger spurious currents and deviations in the density and chemical potential, thus less accurate than the other two. However, it is less sensitive to the relaxation parameter and grid number, thus more robust.

Improved boundary conditions for lattice Boltzmann modeling of pool boiling at low temperature

The pseudopotential lattice Boltzmann method (LBM) becomes popular in simulating the boiling heat transfer problems. By using the interaction force determined from an equation of state, the boiling phenomenon can occur spontaneously according to the thermodynamics, which avoids using empirical models for boiling. However, this pseudopotential interaction model also brings additional cause of instability, which becomes severe at high density ratios. Therefore, most of its previous boiling simulations are conducted at high saturated temperatures with low density ratios. Since the instability usually stems from the disturbance at the interfaces, we investigated the scheme of computing the solid pseudopotential for the solid–fluid interaction and proposed using the average surrounding fluid properties as the virtual solid temperature in addition to density. Droplet evaporation and film boiling problems at high saturated temperatures are simulated, and very good agreement is obtained when compared with the available numerical and analytical solutions, respectively. We then applied the pseudopotential LBM model to simulate droplet evaporation and pool boiling at a low reduced temperature of Tr=0.592 with a density ratio of 1000, as demonstrations of the improved numerical stability. Different boiling regimes are observed by varying the superheat imposed at the bottom wall.

Experimental and LBM simulation study on the bubble dynamic behaviors in subcooled flow boiling

Bubble dynamic behavior is a fundamental issue in comprehending flow boiling process. In this paper, the bubble characteristics are studied in depth through experiment in conjunction with the Lattice Boltzmann method (LBM). Firstly, the visualized experiment in rectangular channels with double heating plates is performed during subcooled flow boiling. High-speed camera is employed to directly capture the macroscopic bubble dynamic behaviors under different working conditions. Furthermore, LBM model with a novel hybrid boundary scheme is developed to investigate mesoscopic bubble characteristics, including contact diameter, microlayer thickness profile and superheated layer thickness. The bubble diameter from LBM model is compared to experimental data with a mean relative error of 10.8%. The results of the current research find that the bubbles nucleating on the inside channel have smaller contact diameter ratio and larger inclined angle. Finally, combining macroscopic experiments and mesoscopic LBM studies, a model of the bubble growth rate is proposed for predicting bubble growth behavior. In the process of model development, three aspects for deciding the bubble growth rate are considered, including microlayer evaporation, heat diffusion from the superheated liquid layer, and condensation at bubble dome caused by subcooled flow boiling. The prediction model agrees well with the experimental results, with a mean relative error of 14.7%. The established bubble growth model will help to predict the heat transfer process during flow boiling.

Prediction and Validation of Flow Properties in Porous Lattice Structures

Abstract High-porosity metal foams have been extensively studied as an attractive candidate for efficient and compact heat exchanger design. With the advancements in additive manufacturing, such foams can be manufactured with controlled topology to yield highly tailorable mechanical and transport properties. In this study, a lattice Boltzmann method (LBM)-based pore-scale model is implemented to simulate the fluid flow in additively manufactured (AM) metal foams with unit cell topologies of Cube, Face Diagonal (FD)-Cube, Tetrakaidecahedron (TKD), and Octet lattices. The pressure gradient versus average velocity profiles predicted by the LBM model were validated against in-house measurements on the AM lattice samples with the same unit cell topologies. Based on the simulation results, a novel hybrid model is proposed to accurately predict the volume averaged flow properties (permeability and inertial coefficients) of the four structures. Specifically, the linear LBM (neglecting inertial forces) is first implemented to obtain the intrinsic permeability, and then the standard LBM is applied to obtain the inertial coefficient. Convenient correlations for those flow properties as a function of porosity and fiber diameter are constructed. The effects of the AM print qualities on the flow properties are also discussed. The advantages of the hybrid model compared to the polynomial fitting approach for determining flow properties are discussed and compared quantitatively. The hybrid model and presented results are valuable for flow and thermal transport evaluation when designing new metal foams for specific applications and with different materials and topologies. The presented correlations based on pore-scale simulations can also be conveniently used in volume-averaged models to predict the macroscale flow behavior in such complex structures.

SIMULATION OF THE COLD-END TEMPERATURE AND THE OPTIMAL CURRENT OF THERMOELECTRIC COOLER WITH VARIABLE SEMICONDUCTOR CROSS SECTION USING LATTICE BOLTZMANN METHOD

In order to evaluate the effects of variable semiconductor cross section on the cold-end temperature of thermoelectric cooler (TEC), the numerical model of the cold-end temperature field of TEC with variable semiconductor cross section was established using the lattice Boltzmann method (LBM) in this work, Firstly, the Chapman-Enskog expansion method was used to derive the LBM model and build the parameter connection between the continuous equation and the discrete model. Secondly, nine different types of cross section of TECs were designed to calculate cold-end temperature field at different electric current. Finally, it is found that increasing the cross-sectional area of the cold end will decrease the minimum cold-end temperature, but increase the optimal current. While maintaining the same cross-sectional area of the cold end, decreasing the hot-end cross-sectional area has less effect on the minimum cold-end temperature but decreases the optimal current. In order to increase the cooling capacity, the cross-sectional area of the cold end can be appropriately larger. TEC of type 2# with a larger cross section at the cold end reduces the cooling temperature by 15.38 K at the cost of a coefficient of performance reduction of 0.021.

A dual-lattice hydrodynamic-thermal MRT-LBM model implemented on GPU for DNS calculations of turbulent thermal flows

PurposeThe purpose of this paper is to present a fast and bare bones implementation of a numerical method for quickly simulating turbulent thermal flows on GPUs. The work also validates earlier research showing that the lattice Boltzmann method (LBM) method is suitable for complex thermal flows.Design/methodology/approachA dual lattice hydrodynamic (D3Q27) thermal (D3Q7) multiple-relaxation time LBM model capable of thermal DNS calculations is implemented in CUDA.FindingsThe model has the same computational performance compared to earlier publications of similar LBM solvers. The solver is validated against three benchmark cases for turbulent thermal flow with available data and is shown to be in excellent agreement.Originality/valueThe combination of a D3Q27 and D3Q7 stencil for a multiple relaxation time -LBM has, to the authors’ knowledge, not been used for simulations of thermal flows. The code is made available in a public repository under a free license.

Development and assessment of the interface lattice Boltzmann flux solvers for multiphase flows

Unlike the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS) is free from the limitation of uniform meshes, coupled time step and mesh spacing, and high memory cost. Specifically, the existing interface LBFS (LBFS-CH0) is reconstructed by locally applying the Cahn–Hilliard-based (CH-based) LBM with additional artificial terms. In the framework of LBM, the influence of the additional artificial terms has been assessed. Besides, the comparative study of the CH-based and the Allen–Cahn-based (AC-based) LBM shows that the latter has higher accuracy and stability. Though the LBFS is originated from the LBM, their performances may not be exactly the same. In this study, the AC-based and CH-based LBFS (LBFS-AC and LBFS-CH1) models which can accurately recover the phase field equations are developed from the interface LBM models without any additional terms. The gradient term in the LBFS-AC is discretized by the second-order central difference method. Compared with the LBFS-CH0, the LBFS-CH1 can eliminate the additional terms and recover the true CH equation. Then these interface LBFS models are compared to evaluate their performance and the influence of the additional terms. Different from the LBM, it is found that the CH-based LBFS is superior to the AC-based one in terms of the numerical accuracy and stability. In addition, numerical results show that the additional terms have minor effect on the ability to model the phase interface. This study can provide guidance to ensure the accuracy and stability of interface modeling. Taking into account the accuracy, stability and simplicity, we can conclude that the LBFS-CH0 model could be the first choice to simulate the phase interface in the framework of LBFS.

Multiscale modeling of gas flow behaviors in nanoporous shale matrix considering multiple transport mechanisms.

This study proposes a multiscale model combining molecular simulation and the lattice Boltzmann method (LBM) to explore gas flow behaviors with multiple transport mechanisms in nanoporous media of shale matrix. The gas adsorption characteristics in shale nanopores are first investigated by molecular simulations, which are then integrated and upscaled into the LBM model through a local adsorption density parameter. In order to adapt to high Knudsen number and nanoporous shale matrix, a multiple-relaxation-time pore-scale LBM model with a regularization procedure is developed. The combination of bounce-back and full diffusive boundary condition is adopted to take account of gas slippage and surface diffusion induced by gas adsorption. Molecular simulation results at the atomic scale show that gas adsorption behaviors are greatly affected by the pressure and pore size of the shale organic nanopore. At the pore scale, the gas transport behaviors with multiple transport mechanisms in nanoporous shale matrix are explored by the developed multiscale model. Simulation results indicate that pressure exhibits more significant influences on the transport behaviors of shale gas than temperature does. Compared with porosity, the average pore size of nanoporous shale matrix plays a more significant role in determining the apparent permeability of gas transport. The roles of the gas adsorption layer and surface diffusion in shale gas transport are discussed. It is observed that under low pressure, the gas adsorption layer has a positive influence on gas transport in shale matrix due to the strong surface diffusion effect. The nanoporous structure with the anisotropy characteristic parallel to the flow direction can enhance gas transport in shale matrix. The obtained results may provide underlying and comprehensive understanding of gas flow behaviors considering multiple transport mechanisms in shale matrix. Also, the proposed multiscale model can be considered as a powerful tool to invesigate the multiscale and multiphysical flow behaviors in porous media.

Mesoscopic Fluid-Particle Flow and Vortex Structural Transmission in a Submerged Entry Nozzle of Continuous Caster.

Understanding the essence of the flow oscillations within a submerged-entry nozzle (SEN) is essential to control flow patterns in the continuous casting mold and consequently increase the superficial quality of steel products. A numerical study of the mesoscopic fluid-particle flow in a bifurcated pool-type SEN under steady operating conditions is conducted using the lattice Boltzmann method (LBM) coupled with the large eddy simulation (LES) model. The accuracy of the model has been verified by comparing vortex structures and simulated velocities with published experimental values. The LBM modeling is also verified by comparing the “stair-step” jet patterns observed in the experiment. The geometrical parameters and operational conditions of physical experiments are reproduced in the simulations. By comparing the time-averaged velocities of Reynolds-averaged Navier–Stokes equations (RANS) with LBM models, transient mesoscopic fluid-particles and related vortex structures can be better reproduced within the SEN. The visualization of internal flow within the SEN is illustrated through the mass-less Discrete Phase Model (DPM) model. The trajectories show that the LBM–LES–DPM coupled model is good at predicting the transient vortical flow within the SEN. A large vortex is found inside the exit port and continuously changes in shape and size therein. The monitoring points and lines within the SEN are selected to illustrate the velocity variations and effective viscosity, which can reflect the oscillating characteristics even under stable operating conditions without changes at the exit from the SEN. Furthermore, the formation, development, diffusion, and dissipation of the vortex structures from the exit port of the SEN are also investigated using the Q criteria. The comparison of the power spectrum with high-frequency components along the exit port indicates that the flow oscillations must originate from within the SEN and are intensified in the exit port. The mesoscopic LBM model can replicate the fluid-particle flow and vortex structure transmission as well as their turbulence effects inside the SEN in detail.

Lattice Boltzmann method modeling and experimental study on liquid water characteristics in the gas diffusion layer of proton exchange membrane fuel cells

Water transport through the gas diffusion layer (GDL) is vital to proton exchange membrane fuel cells (PEMFCs), especially under flooding conditions. In this paper, a two-dimensional (2D) lattice Boltzmann method (LBM) is applied to reveal the water dynamic characteristics in GDL, and the computational domain is reconstructed based on the experiment. In-situ experiments, including I–V performance and electrochemical impedance spectroscopy (EIS) tests under flooding conditions, are carried out and analyzed. It is found that the porosity distribution inside the GDL is a crucial factor in water dynamic behavior research. The horizontal liquid water saturation (HSw) under the channel of real GDL (with porosity distribution) at 0.4 relative thickness are 3.2 times, 2.1 times and 3.4 times higher than the ideal GDL (without porosity distribution) in the case of 0.8 mm, 1.2 mm and 2.0 mm, respectively. The numerical simulation and experimental study show that water dynamic characteristics under the rib influence cell performance directly. In our LBM model, the GDL water distribution inconsistency (Varw) under 2.0 mm width rib is 43.1% and 28.0% higher than that under the 0.8 mm and 1.2 mm rib, respectively. With the rib wider from 0.8 mm to 2.0 mm, some parts of cell impedance such as Rmt, Rct, and Lmt increase 64.22%, 98.89%, and 47.46%, respectively. However, GDL under the channel shows no influence on water transport process.

Research on heavy metal release with suspended sediment in Taihu Lake under hydrodynamic condition.

Heavy metals are often stored in the sediment of lakes or reservoirs and are easily released to the overlying water in the case of strong wind, which greatly affects the water environment of lakes or reservoirs. The conventional investigation of heavy metals in lakes has been relatively extensive, but there is no numerical model for heavy metals released into overlying water with suspended sediment under hydrodynamic action. In this paper, laboratory experiments were carried out, and it is found that the concentration of heavy metals (Cr, Cu, Cd) often begins to stabilize after the concentration of total suspended solids (TSS) reaches a stable level. With the increase of flow velocity (3.2 to 14cm/s), the final equilibrium concentration of TSS, Cr, Cu, and Cd will also increase from 174 to 1102mg/L, 0.72 to 1.14μg/L, 2.34 to 10.45μg/L, and 0.13 to 0.35μg/L, respectively. Based on lattice Boltzmann method (LBM), a numerical model of heavy metal released into overlying water under hydrodynamic conditions is established. Compared the simulated data with measured data, the average [Formula: see text] of LBM model can be reached at 0.827, higher than 0.711 of traditional simulation model. The development of the numerical model is conducive to the prediction of lake or reservoir environment and also provides a theoretical basis for heavy metal treatment in reservoirs.

LBM modeling of solid particle dynamics in a viscous medium

This article discusses the mathematical and computer modeling of single solid particle dynamics in a viscous medium. The results of the study were obtained using a 3D numerical algorithm implemented on the basis of the D3Q19 model of the lattice Boltzmann method (LBM). The moving «liquid-solid» interface is accounted for using an interpolated bounce back (IBB) scheme. The velocity of a solid particle motion and the trajectory of a particle at Re = 1,56 are obtained. The results are in good agreement with the experimental and numerical results of other authors.