Lattice Boltzmann Research Articles

Reaction-limited evaporation for the color-gradient lattice Boltzmann model.

We propose a reaction-limited evaporation model within the color-gradient lattice Boltzmann (LB) multicomponent framework to address the lack of intrinsic evaporation mechanisms. Unlike diffusion-driven approaches, our method directly enforces mass removal at the fluid interface in a reaction-limited manner while maintaining numerical stability. Using the inherent color-gradient magnitude and a single adjustable parameter, evaporation sites are chosen in a computationally efficient way with seamless mass exchange between the components, with no change to the core algorithm. Extensive validation across diverse interface geometries and evaporation flux magnitudes demonstrates high accuracy, with errors below 5% for unit density ratios. For density contrasts, the method remains robust in the limit of smaller evaporation flux magnitudes and density ratios. Our approach extends the applicability of the color-gradient LB model to scenarios involving reaction-limited evaporation, such as droplet evaporation on heated substrates, vacuum evaporation of molten metals, and drying processes in porous media.

Volumetric lattice Boltzmann method for thermal particulate flows with conjugate heat transfer

Volumetric lattice Boltzmann method for thermal particulate flows with conjugate heat transfer

Deep LBLS: Accelerated Sky Region Segmentation Using Hybrid Deep CNNs and Lattice Boltzmann Level-Set Model

Accurate segmentation of the sky region is crucial for various applications, including object detection, tracking, and recognition, as well as augmented reality (AR) and virtual reality (VR) applications. However, sky region segmentation poses significant challenges due to complex backgrounds, varying lighting conditions, and the absence of clear edges and textures. In this paper, we present a new hybrid fast segmentation technique for the sky region that learns from object components to achieve rapid and effective segmentation while preserving precise details of the sky region. We employ Convolutional Neural Networks (CNNs) to guide the active contour and extract regions of interest. Our algorithm is implemented by leveraging three types of CNNs, namely DeepLabV3+, Fully Convolutional Network (FCN), and SegNet. Additionally, we utilize a local image fitting level-set function to characterize the region-based active contour model. Finally, the Lattice Boltzmann approach is employed to achieve rapid convergence of the level-set function. This forms a deep Lattice Boltzmann Level-Set (deep LBLS) segmentation approach that exploits deep CNN, the level-set method (LS), and the lattice Boltzmann method (LBM) for sky region separation. The performance of the proposed method is evaluated on the CamVid dataset, which contains images with a wide range of object variations due to factors such as illumination changes, shadow presence, occlusion, scale differences, and cluttered backgrounds. Experiments conducted on this dataset yield promising results in terms of computation time and the robustness of segmentation when compared to state-of-the-art methods. Our deep LBLS approach demonstrates better performance, with an improvement in mean recall value reaching up to 14.45%.

Two-component lattice Boltzmann model for solute transport in bubbly flows

A free energy lattice Boltzmann model has been developed to describe a binary system consisting of a nonideal solvent and a gaseous ideal solute. A free energy functional to describe this mixture has been derived, and it is used to determine the driving forces for two lattice Boltzmann equations, one for each component. The well-balanced lattice Boltzmann method is used to avoid discretization errors, which allows correct thermodynamic equilibrium to be achieved for both components as well as high density ratios. In this model, the distribution of the solute between the liquid and vapor phases of the solvent follows Henry's law due to the contributions of the two components to the free energy density. The momenta of the two components are coupled through the use of a mixture velocity in the equilibrium distributions of both components. The model also includes surface tension due to gradients of the solvent density and diffusion due to an added mobility term. The effects of model parameters on phase composition, surface tension, and the rate of solute transport are characterized, with examples of static gas bubbles and flat interfaces demonstrated. Mass transfer of the soluble component in the liquid phase of the nonideal component is characterized, and an equation for the solute diffusion coefficient is provided. Published by the American Physical Society 2025

Numerical study of fractal-tree-generated non-equilibrium turbulence

Self-similar fractal tree models are numerically investigated to elucidate the drag coefficient, non-equilibrium dissipation behaviour and various turbulence statistics of fractal trees. For the simulation, a technique based on the lattice Boltzmann method with a cumulant collision term is used. Self-similar fractal tree models for aerodynamic computations are constructed using parametric L-system rules. Computations across a range of tree-height-based Reynolds numbers $Re_H$ , from 2500 to 120 000, are performed using multiple tree models. As per the findings, the drag coefficients ( $C_D$ ) of these models match closely with those of the previous literature at high Reynolds numbers ( $Re_H \geqslant 60\,000$ ). A normalization process that collapses the turbulence intensity across various tree models is formulated. For a single tree model, a consistent centreline turbulence intensity trend is maintained in the wake region beyond a Reynolds number of 60 000. The global and local isotropy analysis of the turbulence generated by fractal trees indicates that, at high Reynolds numbers ( $Re_H \geqslant 60\,000$ ), the distant wake can be considered nearly locally isotropic. The numerical results confirm the non-equilibrium dissipation behaviour demonstrated in previous studies involving space-filling fractal square grids. The non-dimensional dissipation rate $C_\epsilon$ does not remain constant; instead, it becomes approximately inversely proportional to the local Taylor-microscale-based Reynolds number, $C_\epsilon \propto 1/Re_\lambda$ . We find significant one-point inhomogeneity, production and transverse transport of turbulent kinetic energy within the non-equilibrium dissipation near wake region.

Evaporation of Non-Isothermal Wall Microlayer Based on the Lattice Boltzmann Method

In the process of boiling heat transfer, the microlayer is not only a crucial medium for enhancing heat transfer but also directly determines the heat flux distribution, dry zone expansion, and overall heat transfer efficiency through its morphological evolution and evaporation behavior. Building on this, this study employs the Lattice Boltzmann Method (LBM) with a single-component multiphase model to numerically simulate the evaporation process of microlayers on non-isothermal walls. The results show that, due to the uneven velocity distribution in the flow field, the microlayer exhibits significant contraction behavior during evaporation, particularly at the three-phase contact point, where velocity differences lead to fluid accumulation and the formation of a “cap-like” structure. The initial growth of the dry zone follows a linear trend, but its growth rate gradually decreases as the microlayer thickness increases, while near-wall density effects result in residual thickness within the dry zone. Additionally, the microlayer height first increases and then decreases over time, accompanied by a noticeable time lag. Heat flux analysis reveals that, during the formation of the dry spot, the lowest heat flux occurs at the three-phase contact point, followed by a sudden increase. A cold air ring forms above the dry zone, expanding and splitting as it moves with the dry spot. Higher temperatures promote microlayer evaporation, with the evaporation volume exhibiting nearly linear growth and the total fluid mass decreasing linearly.

The Frequency‐Domain Lattice Boltzmann Method (FreqD‐LBM): A Versatile Tool to Predict the QCM Response Induced by Structured Samples

AbstractThe quartz crystal microbalance with dissipation monitoring (QCM‐D) is routinely used to investigate structured samples. Here, a simulation technique is described, that predicts the shifts of frequency and half bandwidth, Δfn and ΔΓn, of a quartz resonator operating on different overtone orders, n, induced by structured samples in contact with the resonator surface in liquid. The technique, abbreviated as FreqD‐LBM, solves the Stokes equation in the frequency domain. The solution provides the complex amplitude of the area‐averaged tangential stress at the resonator surface, from which Δfn and ΔΓn are derived. Because the dynamical variables are complex amplitudes, the viscosity can be complex, as well. The technique naturally covers viscoelasticity. Limitations are linked to the grid resolution and to problems at large viscosity. Validation steps include viscoelastic films, rough surfaces, an oscillating cylinder in a viscous medium, and a free‐floating sphere above the resonator. Application examples are soft adsorbed particles, stiff adsorbed particles, and a large, immobile spherical cap above the resonator, which allows to study the high‐frequency properties of the material in the gap. FreqDLBM runs on an office PC and does not require expert knowledge of numerical techniques. It is accessible to an experimentalist.

Darcy number effects on natural convection around a porous cylinder in L-shaped enclosure using Lattice Boltzmann method

This study numerically evaluates fluid flow and natural convection heat transfer of a porous square cylinder in an L-shaped enclosure using the Lattice Boltzmann method. Three layouts along vertical and horizontal centrelines are explored, investigating the effects of Rayleigh number (Ra) (103 ≤ Ra ≤ 106), Darcy number (Da) (10−6 ≤ Da ≤ 10−2), and cylinder size. Results show that increasing Rayleigh numbers enhances heat transfer, with higher Mean Nusselt number (NuMean) values observed. Doubling the cylinder’s width at Da = 10−6 increases NuMean by 46.5%, and tripling the width results in a 118% enhancement. Higher Rayleigh values enhance buoyant forces’ intensity, improving heat transfer; for example, at Ra = 105 and Da = 10–2, there is a 42% increase in Nu mean for a cylinder with a 0.6 L side length compared to Ra = 103. Optimal cylinder orientation significantly maximizes convective heat transfer, especially at high Rayleigh and Darcy numbers. This study provides valuable insight for optimizing the orientation of electronic blocks in compact L-shaped enclosures for better thermal management.

Three-Dimensional Modeling of Non-Newtonian Fluids Flow in the Mixing Section of Extruder Using the Two-Relaxation-Time Lattice Boltzmann Method

Three-Dimensional Modeling of Non-Newtonian Fluids Flow in the Mixing Section of Extruder Using the Two-Relaxation-Time Lattice Boltzmann Method

Modeling Lithium Adsorption in Column Chromatography Applications with Granulated Li/Al-LDH: A Lattice Boltzmann Modeling Approach

Abstract Given a crucial role of lithium (Li) on clean energy transition through effective decarbonization of various energy sectors, enhancing and diversifying the source of Li is regarded as an urgent priority. Producing Li from formation brines is a promising solution due to their abundant resources and environmental friendlessness to extract. In this study, we focus on Li extraction with ion sieve method utilizing Li/Aluminum-Layered Double Hydroxide Chlorides (Li/Al-LDH), by its significant stability, great scalability, and favorable techno-economic feasibility. In this regard, we set our goal to numerically quantify the adsorption performance of granulated Li/Al-LDH adsorbent for Li+ by quantitatively analyzing the impacts of controlling factors. To achieve the goal, we develop our numerical capability of addressing brine injection, fluid flow, component transport, and adsorption in column chromatography application, based on Lattice Boltzmann Method (LBM) modeling. To quantify the impact of operational conditions of Li+ adsorption performance with granulated Li/Al-LDH adsorbent, various values of porosity and radius of granule, Li+ concentration in injected brine, and brine injection velocity are considered. From the numerical simulations and coupled local sensitivity analysis, radius of adsorbent granule is found to be most influential on the adsorption performance, followed by granule porosity, concentration of Li+ in injected brine, and injection velocity. This study provides the conceptual and essential information of quantified impact of various operational conditions on Li+ adsorption performance that can be used to optimize the design of Li/Al-LDH adsorbent granule and column chromatography strategy, as achieving the techno-economically feasible Li+ extraction from formation brines.

Study of thermal convection in liquid metal using modified lattice Boltzmann method

Purpose This study aims to extend the application of the lattice Boltzmann method (LBM) to solve solid-to-liquid phase transition problems involving low Prandtl number (Pr) materials. It provides insight about the flow instability in a cavity undergoing melting. This work further report interface development and thermal transport against the Boussinesq number. Design/methodology/approach This study modifies the lattice Bhatnagar–Gross–Krook model by including correction components in the energy and density distribution functions. To prevent numerical instability, a tuning parameter in the flow domain is set in the range of 0.15–0.7 for the range of Rayleigh number and Prandtl number. To the best of the authors’ knowledge, the modified LBM is being used for the first time to examine the low Pr domain melting behavior of liquid metals. Findings The interaction with complicated flow structure with natural convection, studied in a square enclosure, has a significant impact on the melting of metals in the low Pr range. Results show that the melting rate and the length of the interface between two phases are significantly influenced by the Boussinesq number (Bo), the product of Pr and Rayleigh number (Ra). For changing Ra, the maximum interface length is almost constant in the in the Boussinesq number range up to 100 and beyond this range the interface length increases with Bo. Originality/value The effects of Pr on melting rate, Ra and Pr together on the length of the solid–liquid interface and the thermofluidic behavior in the melt zone are explained. This work also includes mapping the maximum melt interface size with Bo.

Intermittent swimmers optimize energy expenditure with flick-to-flick motor control

Abstract Intermittent swimming behaviour is commonly observed in larval zebrafish, often attributed to energy-saving mechanisms. In this study, we utilize a hybrid approach combining deep reinforcement learning and the immersed boundary–lattice Boltzmann method to train a larval zebrafish-like swimmer to reach a target with minimized energy expenditure. We find that when the tail-beat period is fixed, continuous swimming emerges as the optimal strategy. However, when the tail-beat period is allowed to vary, intermittent swimming proves superior in energy performance, achieved through reductions in tail-beat amplitude and frequency. Our detailed analysis reveals that intermittent swimmers employ rapid backward tail flicks to attain high speeds, coupled with slower forward tail flicks and coasting phases to conserve energy. Furthermore, we derive scaling laws governing the swimming performance of trained fish. These results offer valuable insights into the intermittent swimming patterns of fish, with implications for understanding bio-inspired locomotion and informing the design of energy-efficient aquatic systems.

Surface wettability analysis using a microdroplet: a numerical approach

Analysis of hydrophobicity is essential for learning about the characteristics of molecules, surfaces, and materials that reject water. Using a two-dimensional (2D) pseudo-potential multiphase lattice Boltzmann approach with a D2Q9 model, this work examines the influence of solid-fluid interaction strength on wettability and hydrophobicity of smooth surfaces. To ascertain the contact angle and assess the accuracy of the numerical model, the study considers the equilibrium state of a water droplet on a smooth surface. In a 200×200 lattice unit domain, droplets having a radius of 60 lattice units are used to assess the hydrophobicity of smooth surfaces. According to the research, there is a large rise in the contact area between solid walls and water droplets when the solid-fluid interaction parameter is raised, which leads to a greater degree of hydrophobicity. By measuring the contact angle between the solid and fluid-vapor interface for different surfaces, it is observed that as G_ads becomes more negative, the contact angle decreases, indicating increased surface hydrophobicity, and the effect on droplet spreading is also highlighted in the research.

Derivation of the incompressible Navier–Stokes equations from the lattice Boltzmann equation: difference between the Chapman–Enskog expansion and the Sone expansion

Abstract We derive the incompressible Navier–Stokes equations from the lattice Boltzmann equation using the Chapman–Enskog expansion and the Sone expansion and clarify the differences between the two approaches. In the Chapman–Enskog expansion, we first derive the compressible Navier–Stokes equations on the multiple time scales (the acoustic and diffusive time scales). Then the incompressible Navier–Stokes equations are derived under the conditions of low Mach number flows and small density variations on the diffusive time scale. If the acoustic time scale remains in the analysis of the derived macroscopic equations, the incompressible Navier–Stokes equations are recovered with only the first-order spatial accuracy. On the other hand, in the Sone expansion we can derive the incompressible Navier–Stokes equations under the condition of low Mach number flows on the diffusive time scale. Despite some differences between the two approaches, we obtain the same result that the flow velocity and the pressure satisfy the incompressible Navier–Stokes equations with the second-order spatial accuracy in low Mach number flows on the diffusive time scale. The accuracy is verified through simulating a generalized Taylor–Green problem.

On the Invalidity of the Extended Navier-Stokes Equations to Compute Rarefied Gas Flows in a Cylinder Array

On the Invalidity of the Extended Navier-Stokes Equations to Compute Rarefied Gas Flows in a Cylinder Array

A voxel-based approach for simulating microbial decomposition in soil: Comparison with LBM and improvement of morphological models.

This paper deals with the computational modeling of biological dynamics in soil using an exact micro-scale pore space description from 3D Computed Tomography (CT) images. Within this context, computational costs and storage requirements constitute critical factors for running simulations on large datasets over extended periods. In this research, we represent the pore space by a graph of voxels (Voxel Graph-Based Approach, VGA) and model transport in fully saturated conditions (two-phase system) using Fick's law and coupled diffusion with biodegradation processes to simulate microbial decomposition in soil. To significantly decrease the computational time of our approach, the diffusion model is solved by means of Euler discretization schemes, along with parallelization strategies. We also tested several numerical strategies, including implicit, explicit, synchronous, and asynchronous schemes. To validate our VGA, we compare it with LBioS, a 3D model that integrates diffusion (via the Lattice Boltzmann method) with biodegradation, and Mosaic, a Pore Network Geometrical Modelling (PNGM) which represents the pore space using geometrical primitives. Our method yields result similar to those of LBioS in a quarter of the computing time. While slower than Mosaic, it is more accurate and requires no calibration. Additionally, we show that our approach can improve PNGM-based simulations by using a machine-learning approach to approximate diffusional conductance coefficients.

Elucidating the Effect of the Catalyst Layer Morphology on the Growth and Detachment of Bubbles in Water Electrolysis via Lattice Boltzmann Modeling.

The performance of water electrolysis is profoundly influenced by the behavior of the gas bubbles generated at the electrode surface. In order to improve the efficiency of bubble transportation, various nanostructures for the catalyst layer (CL), such as nanorods (NRs) or nanoparticles (NPs), have been proposed. However, there is still a lack of complete understanding about the relationship between the catalyst layer morphology and bubble evolution, which has a considerable impact on bubble transport. This study examines the effect of the catalyst layer morphology on the growth and detachment of bubbles in water electrolysis by employing the Lattice Boltzmann (LB) model. The performance of three different catalyst layer morphologies, namely, nanorods, nanoparticles, and hierarchical nanostructures, on bubble dynamics is estimated. The results suggest that the catalyst layer morphology is characterized by two factors: the bubble contact area and the electrochemically active surface area, which varies the bubble diameter, detachment time, and, subsequently, the bubble coverage. As a result, the energy efficiency of water electrolysis is influenced, aligned with experimental data that show a voltage differential of 148 mV at a current density of 0.65 A/cm2. This study highlights the significance of improving the structure of the catalyst layer to boost the efficiency of water electrolysis systems.

GPU‐Accelerated Lattice Boltzmann Simulations of Power‐Law Non‐Newtonian Fluid Flow in a Diagonally Driven Cavity Using D3Q27 MRT‐LBM

ABSTRACTThe study examines the flow dynamics of power‐law non‐Newtonian fluids in a cubic cavity with a top lid‐driven diagonally‐driven diagonally using the D3Q27 multiple‐relaxation‐time (MRT) lattice Boltzmann method (LBM). This situation frequently occurs in both natural and industrial processes. Utilizing CUDA C++ programming on a graphics processing unit (GPU) speeds up the simulations, enabling effective investigation of intricate fluid dynamics. Non‐Newtonian behaviors, such as shear‐thinning and shear‐thickening properties, are frequently found in many real‐world fluid systems and are captured by the power‐law rheology model. LBM provides a mesoscopic method that makes handling intricate geometries easier and scales effectively on GPUs and other parallel computing architectures. The simulations investigate how Reynolds numbers () and power‐law indices () affect non‐Newtonian fluid flow characteristics like streamlines, velocity profiles, viscosity distributions, iso‐surfaces, and helicity (twistiness). GPU acceleration makes faster simulations and parametric research possible, improving computational efficiency. These findings provide information for non‐Newtonian fluid engineering applications in the food industry, biomedical engineering, and polymer processing. Because of their decreased viscosity, shear‐thinning fluids have higher helicity than shear‐thickening fluids. The numerical results of the study offer applicable standards for evaluating 3D codes for fluids with non‐Newtonian power laws. The uniqueness is that a D3Q27 multiple‐relaxation‐time lattice Boltzmann method (MRT‐LBM) framework with GPU acceleration can be used to model an underexplored situation, revealing fluid dynamics and rheological features with unprecedented detail and computing efficiency. We also examine how the power‐law index influences vortex generation, helicity, and flow stability in a diagonally driven cavity. Additionally, a comparison of the D3Q19 and D3Q27 MRT‐LBM models is provided, emphasizing how they handle complex fluid behaviors differently.

Numerical prediction of permeability and effective thermal conductivity in simple cubic and body-centered truss structures

Abstract The lattice Boltzmann method (LBM) is utilized to numerically investigate the permeability and effective thermal conductivity of simple cubic and body-centered truss structures. The key objective of this paper is to analyze how different geometric parameters affect the macroscopic properties of these truss structures that are increasingly used in advanced engineering applications due to their unique thermal-fluid characteristics. Simple cubic and body-centered cubic (SC-BCC) lattice structures are modeled, and the simulations are performed to determine their permeability and effective thermal conductivity. The findings highlight that the rod diameter and simple-cubic diameter significantly influence porosity, permeability, and thermal conductivity. Larger rod diameters generally result in higher porosity and permeability but may reduce thermal conductivity. Conversely, smaller simple-cubic diameters tend to enhance thermal conductivity. These results can optimize the design and application of truss structures in heat exchangers, cooling systems, and other areas where efficient thermal management and fluid flow are critical. The study concludes that LBM is an effective tool for predicting the thermal-fluid behavior of complex porous structures, providing valuable insights for the engineering design of advanced materials.

Quantum unitary matrix representation of the lattice Boltzmann model for low Reynolds fluid flow simulation

We propose a quantum algorithm for the lattice Boltzmann (LB) method to simulate fluid flows in the low Reynolds number regime. First, we encode the particle distribution functions (PDFs) as probability amplitudes of the quantum state and demonstrate the need to control the state of the ancilla qubit during the initial state preparation. Second, we express the LB algorithm as a matrix-vector product by neglecting the quadratic non-linearity in the equilibrium distribution function, wherein the vector represents the PDFs, and the matrix represents the collision and streaming operators. Third, we employ classical singular value decomposition to decompose the non-unitary collision and streaming operators into a product of unitary matrices. Finally, we show the importance of having a Hadamard gate between the collision and the streaming operations. Our approach has been tested on linear/linearized flow problems such as the advection-diffusion of a Gaussian hill, Poiseuille flow, Couette flow, and lid-driven cavity problems. We provide counts for two-qubit controlled-NOT and single-qubit U gates for test cases involving 9–12 qubits with grid sizes ranging from 24 to 216 points. While the gate count aligns closely with theoretical limits, the high number of two-qubit gates on the order of 107 necessitates careful attention to circuit synthesis.