Lattice Boltzmann Method Framework Research Articles

Numerical simulation of the flow and output of a Savonius hydraulic turbine using the lattice Boltzmann method

The flow and output of a Savonius hydraulic turbine rotor were simulated using the lattice Boltzmann method (LBM). The rotor, characterized by a configuration featuring two semi-circular arc-shaped blades, operated at a Reynolds number of 1.1 × 105. The simulations were conducted in a two-dimensional domain, focusing on the incompressible flow within the cross-sectional area of the rotor perpendicular to its rotational axis. The LBM approach was coupled with a rotor rotation analysis. In the LBM framework, the non-orthogonal central moment model was employed for the precise computation of particle collisions. Additionally, the direct forcing method was used to consider the rotating blades and shaft. Consequently, the torque exerted on both advancing and returning blades and rotor output was successfully simulated. These simulations unveiled the inherently unsteady rotational behavior of the rotor, stemming from the variable torque acting upon the blades. Moreover, the computational results exhibited a notable agreement between the simulated flow pattern around the rotor and the experimental visualization. Furthermore, an approximately identical correlation between the rotor speed and power output was established, mirroring the experimental results. These findings underscore the robust applicability of LBM in facilitating the design and operational analysis of Savonius hydraulic turbines.

A thermal lattice Boltzmann model for evaporating multiphase flows

Modeling thermal multiphase flows has become a widely sought methodology due to its scientific relevance and broad industrial applications. Much progress has been achieved using different approaches, and the lattice Boltzmann method is one of the most popular methods for modeling liquid–vapor phase change. In this paper, we present a novel thermal lattice Boltzmann model for accurately simulating liquid–vapor phase change. The proposed model is built based on the equivalent variant of the temperature governing equation derived from the entropy balance law, in which the heat capacitance is absorbed into transient and convective terms. Then a modified equilibrium distribution function and a proper source term are elaborately designed in order to recover the targeting equation in the incompressible limit. The most striking feature of the present model is that the calculations of the Laplacian term of temperature, the gradient term of temperature, and the gradient term of density can be simultaneously avoided, which makes the formulation of the present model is more concise in contrast to all existing lattice Boltzmann models. Several benchmark examples, including droplet evaporation in open space, droplet evaporation on a heated wall, and nucleate boiling phenomenon, are carried out to assess numerical performance of the present model. It is found that the present model effectively improves the numerical accuracy in solving the interfacial behavior of liquid–vapor phase change within the lattice Boltzmann method framework.

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

This study analyses an approach to consistently recover the second-order convergence of the lattice Boltzmann method (LBM), which is frequently degraded by an improper discretisation of the required source terms. The current work focuses on advection-diffusion models, in which the source terms are dependent on the intensity of transported fields. Such terms can be observed in reaction-type equations used in heat and mass transfer problems or multiphase flows. The investigated scheme is applicable to a wide range of formulations within the LBM framework. All considered source terms are interpreted as contributions to the zeroth-moment of the distribution function. These account for sources in a scalar field, such as density, concentration, temperature or a phase field. Further application of this work can be found in the method of manufactured solutions or in the immersed boundary method. This paper is dedicated to three aspects regarding proper inclusion of the source term in LBM schemes. Firstly, it identifies the differences observed between the ways in which source terms are included in the LBM schemes present in the literature. The algebraic manipulations are explicitly presented in this paper to clarify the observed differences, and to identify their origin. Secondly, it analyses in full detail, the implicit relation between the value of the transported macroscopic field, and the sum of the LBM densities. This relation is valid for any source term discretization scheme. It is a crucial ingredient for preserving the second-order convergence in the case of complex source terms. Moreover, three equivalent forms of the second-order accurate collision operator are presented. Finally, closed form solutions of this implicit relation are shown for a variety of common models, including general linear and second order terms; population growth models, such as the Logistic or Gompertz model and the Allen-Cahn equation. The second-order convergence of the proposed LBM schemes is verified on both linear and non-linear source terms. The pitfalls of the commonly used acoustic and diffusive scalings are identified and discussed. Furthermore, for a simplified case, the competing errors are shown visually with isolines of error in the space of spatial and temporal resolutions.

Droplet impact on a heated porous plate above the Leidenfrost temperature: A lattice Boltzmann study

In the past few decades, the droplet impact on a heated plate above the Leidenfrost temperature has attracted immense research interest. The strong hydrophobicity caused by the Leidenfrost effect leads to the droplet bouncing from a flat plate at a given contact time predicted by the classical Rayleigh theory. Numerous investigations were conducted to break the theoretical Rayleigh's limit to reduce the interfacial contact time. Recently, a droplet was observed to form a pancake shape and bounce as it impacted nanotube or micropost surfaces above the Leidenfrost temperature. This led to a significant reduction in droplet contact time. However, this unique bouncing phenomenon is still not fully understood, such as the influence of the plate configuration and the relationship between the droplet rebound time and evaporation mass loss. In this study, we carry out a numerical study of the droplet impact dynamics on a heated porous plate above the Leidenfrost temperature, using a multiphase thermal lattice Boltzmann model. Our model is constructed within the unified lattice Boltzmann method framework and is first validated based on theoretical and experimental results. Then, a comprehensive parametric study is performed to investigate the effects of the impact Weber number, the plate temperature, and the plate configurations on the droplet bouncing dynamics. Results show that higher plate temperature, larger Weber number, and smaller pore intervals can accelerate the droplet rebound and promote the droplet pancake bouncing. We demonstrate that the occurrence of the pancake bouncing is attributed to the additional lift force provided by the vapor pressure due to the evaporation of liquid inside the pores. Moreover, the droplet maximum spreading time and maximum spreading factor can be described by a power law function of the impact Weber number. The droplet evaporation mass loss increases linearly with the impingement Weber number and the plate opening fractions. This study provides new insights into the Leidenfrost droplet impingement on porous plates, which may potentially facilitate the design of novel engineering surfaces and devices.

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.

ProLB: A Lattice Boltzmann Solver of Large‐Eddy Simulation for Atmospheric Boundary Layer Flows

AbstractA large‐eddy simulation tool is developed for simulating the dynamics of atmospheric boundary layers (ABLs) using lattice Boltzmann method (LBM), which is an alternative approach for computational fluid dynamics and proved to be very well suited for the simulation of low‐Mach flows. The equations of motion are coupled with the global complex physical models considering the coupling among several mechanisms, namely basic hydro‐thermodynamics and body forces related to stratification, Coriolis force, canopy effects, humidity transport, and condensation. Mass and momentum equations are recovered by an efficient streaming, collision, and forcing process within the framework of LBM while the governing equations of temperature, liquid, and vapor water fraction are solved using a finite volume method. The implementation of wall models for ABL, subgrid models, and interaction terms related to multiphysic phenomena (e.g., stratification, condensation) is described, implemented, and assessed in this study. An immersed boundary approach is used to handle flows in complex configurations, with application to flows in realistic urban areas. Applications to both wind engineering and atmospheric pollutant dispersion are illustrated.

On the use of conservative formulation of energy equation in hybrid compressible lattice Boltzmann method

Effect of density variations on mass conservation properties is widely recognized in the lattice Boltzmann method (LBM), thus non-conservative form of scalar transport equation was commonly adopted within the framework of hybrid LBM. Focusing on the compressible hybrid LBM, mass conservation and its effect on energy conservation equation are studied in this paper. Starting from the analysis on mass conservation law recovered by LBM, the consistency between conservative and non-conservative formulations of energy conservation equation based on various thermodynamic variables and lattice Boltzmann equation is addressed. Driven by the theoretical analysis, a set of modified consistent energy equations in entropy and internal energy form is derived to reduce the error terms and improve the consistency. The theoretical analysis and modified energy equations are intensively evaluated by several numerical test cases, e.g., the isentropic vortex convection, three-dimensional compressible Taylor-Green vortex and shock-vortex interaction.

A pseudopotential based lattice Boltzmann modeling of electro wetting-on-dielectric for droplet operations

Droplet based digital microfluidics and its related studies are contemplated for many useful applications including lab-on-chip. The dynamics of such multiphase, multiphysics studies can be analyzed by lattice Boltzmann method (LBM). In this work, a pseudopotential based LBM framework for implementing EWOD actuation of droplet is explored by coupling the droplet and electrohydrodynamics.The effect of viscosity over the droplet spreading, merging, splitting is reported. The presented result can be useful in designing transportation, merging and splitting of the droplets. The results presented here shows that the modified pseudopotential-LBM can be used effectively for modeling EWOD and lab-on-chip applications.

Analysis and assessment of the no-slip and slip boundary conditions for the discrete unified gas kinetic scheme.

The discrete unified gas kinetic scheme (DUGKS) with a force term is a finite volume solver for the Boltzmann equation. Unlike the standard lattice Boltzmann method (LBM), DUGKS can be applied on nonuniform grids. For both the LBM and DUGKS, the boundary conditions need to be processed through the density distribution function. So researchers introduced the boundary conditions from the LBM frame into the DUGKS. However, the accuracy of these boundary conditions in the DUGKS has not been studied thoroughly. Through strict theoretical deduction, we find that the bounce-back (BB) scheme leads to a different dependence of the numerical error term in the DUGKS as compared to the LBM. The error term is influenced by the relaxation time and the body force. And it can be reduced by lowering the kinetic viscosity. Unlike the BB scheme, the nonequilibrium bounce-back scheme has the ability to implement real no-slip boundary condition. Furthermore, two slip boundary conditions incorporated with Navier's slip model are introduced from the LBM framework into the DUGKS. The tangential momentum change-based (TMAC) scheme can be used directly in the DUGKS because it generates no numerical error term in the DUGKS. For the combination of the bounce-back and specular reflection schemes (BSR), the relation between the slip length and the combination parameter should be modified in accordance with the numerical error term. Analysis shows that the TMAC scheme can simulate a wider range of slip length than the BSR scheme. Numerical simulations of the Couette flow and the Poiseuille flow confirm our theoretical analysis.

Axisymmetric compact finite-difference lattice Boltzmann method for blood flow simulations.

An axisymmetric compact finite-difference lattice Boltzmann method is proposed to simulate both Newtonian and non-Newtonian flow of blood through a lumen. The curvature of the arteries could be accurately resolved using body-fitted mesh owing to the proposed finite-difference formulation. The axisymmetric nature of the flow, as well as the non-Newtonian nature of blood, are incorporated into the lattice Boltzmann equation using separate source terms. Using Chapman-Enskog expansion it is shown that the resulting lattice Boltzmann equation with these additional source terms recovers the macroscopic axisymmetric hydrodynamic equations. The solver is verified for (1) steady inflow of a Newtonian fluid through a stenosed lumen, (2) temporally developing pulsatile flow (Womersley flow) through a straight lumen with Newtonian fluid, and (3) steady inflow of a non-Newtonian fluid through a straight lumen. The solver is then applied to simulate the steady flow of a non-Newtonian fluid through a stenosed lumen, and it was found that a smaller recirculation zone and lower WSS values are obtained when compared with the flow of a Newtonian fluid. The capability of the solver to simulate spatially developing (velocity-driven) pulsatile flow is then demonstrated by simulating physiological pulsatile flow through an axisymmetric abdominal aortic aneurysm. From this simulation, the cycle-averaged wall shear stress is observed to have a steep gradient going from a minimum (negative) to a maximum (positive) value towards the distal end of the aneurysm, which is prone to the risk of rupture. An iterative procedure to select the geometric and flow parameters for unsteady inflow condition in the lattice Boltzmann method framework is demonstrated that accurately resolves all the timescales to achieve incompressibility. Overall, the present solver seems to be promising to simulate axisymmetric flow of blood with steady and pulsatile inflows while considering the blood rheology.

Direct simulation of pore-scale two-phase visco-capillary flow on large digital rock images using a phase-field lattice Boltzmann method on general-purpose graphics processing units

We describe the underlying mathematics, validation, and applications of a novel Helmholtz free-energy—minimizing phase-field model solved within the framework of the lattice Boltzmann method (LBM) for efficiently simulating two-phase pore-scale flow directly on large 3D images of real rocks obtained from micro-computed tomography (micro-CT) scanning. The code implementation of the technique, coined as the eLBM (energy-based LBM), is performed in CUDA programming language to take maximum advantage of accelerated computing by use of multinode general-purpose graphics processing units (GPGPUs). eLBM’s momentum-balance solver is based on the multiple-relaxation-time (MRT) model. The Boltzmann equation is discretized in space, velocity (momentum), and time coordinates using a 3D 19-velocity grid (D3Q19 scheme), which provides the best compromise between accuracy and computational efficiency. The benefits of the MRT model over the conventional single-relaxation-time Bhatnagar-Gross-Krook (BGK) model are (I) enhanced numerical stability, (II) independent bulk and shear viscosities, and (III) viscosity-independent, nonslip boundary conditions. The drawback of the MRT model is that it is slightly more computationally demanding compared to the BGK model. This minor hurdle is easily overcome through a GPGPU implementation of the MRT model for eLBM. eLBM is, to our knowledge, the first industrial grade–distributed parallel implementation of an energy-based LBM taking advantage of multiple GPGPU nodes. The Cahn-Hilliard equation that governs the order-parameter distribution is fully integrated into the LBM framework that accelerates the pore-scale simulation on real systems significantly. While individual components of the eLBM simulator can be separately found in various references, our novel contributions are (1) integrating all computational and high-performance computing components together into a unified implementation and (2) providing comprehensive and definitive quantitative validation results with eLBM in terms of robustness and accuracy for a variety of flow domains including various types of real rock images. We successfully validate and apply the eLBM on several transient two-phase flow problems of gradually increasing complexity. Investigated problems include the following: (1) snap-off in constricted capillary tubes; (2) Haines jumps on a micromodel (during drainage), Ketton limestone image, and Fontainebleau and Castlegate sandstone images (during drainage and subsequent imbibition); and (3) capillary desaturation simulations on a Berea sandstone image including a comparison of numerically computed residual non-wetting-phase saturations (as a function of the capillary number) to data reported in the literature. Extensive physical validation tests and applications on large 3D rock images demonstrate the reliability, robustness, and efficacy of the eLBM as a direct visco-capillary pore-scale two-phase flow simulator for digital rock physics workflows.

A thermal LBM-LES model in body-fitted coordinates: Flow and heat transfer around a circular cylinder in a wide Reynolds number range

In order to apply the lattice Boltzmann method (LBM) for modeling passive heat transfer at high Reynolds numbers, a number of models were proposed by introducing the large eddy simulation (LES) into the LBM framework to improve numerical stability. Our study finds that the generalized form of interpolation-supplemented LBM (GILBM), likewise, can locally modify the dimensionless relaxation time, thus enhancing the numerical stability at high Reynolds numbers. Given additional advantages of the GILBM in dealing with complicated geometries and improving computing accuracy, a thermal LBM-LES model in body-fitted coordinates is established in this paper. Numerical validation is performed by investigating the flow and heat transfer around a circular cylinder over a wide range of Reynolds numbers. The obtained results agree well with both experimental and numerical data in the previous work. Meanwhile, the effects of Reynolds number and Prandtl number on thermodynamic features of flow past a circular cylinder are revealed. It is found out that when the Reynolds number exceeds the critical value, the local Nusselt number fluctuates rapidly in a specific region of the rear cylinder surface affected by the Prandtl number. In the near-wake region, the temperature field exhibits significant dependence on the Prandtl number at moderate Reynolds numbers, while such effects turn to be slight at high Reynolds numbers.

Massively Parallel GPU Implementation of the Lattice-Boltzmann Method for the Simulation of Coupled Aero-Thermodynamic Systems

The automotive industry is showing high demand for efficient design of cooling systems in electric vehicles. The development of complex aero-thermodynamic systems requires reliable, high-fidelity simulations of high Reynolds number flows. We implemented a numerical solver based on the double-distribution lattice-Boltzmann method (LBM). The main advantage of the LBM, compared to the Navier-Stokes-based solvers, is its computational efficiency and intrinsic parallelism, which allows for execution on massively parallel architectures (GPUs). We have validated our GPU implementation by simulating a natural convection flow and a heated cylinder in an enclosed cavity. Both cases show very good agreement with published literature. In the future, we aim to extend the usage of the LBM framework to industry-relevant cases like the simulation of various packaging concepts for electric vehicles.

A numerical tool for the study of the hydrodynamic recovery of the Lattice Boltzmann Method

We investigate the hydrodynamic recovery of Lattice Boltzmann Method (LBM) by analyzing exact balance relations for energy and enstrophy derived from averaging the equations of motion on sub-volumes of different sizes. In the context of 2D isotropic homogeneous turbulence, we first validate this approach on decaying turbulence by comparing the hydrodynamic recovery of an ensemble of LBM simulations against the one of an ensemble of Pseudo-Spectral (PS) simulations. We then conduct a benchmark of LBM simulations of forced turbulence with increasing Reynolds number by varying the input relaxation times of LBM. This approach can be extended to the study of implicit subgrid-scale (SGS) models, thus offering a promising route to quantify the implicit SGS models implied by existing stabilization techniques within the LBM framework.

Fluid-structure interaction using lattice Boltzmann method: Moving boundary treatment and discussion of compressible effect

We investigate fluid-structure interaction using lattice Boltzmann method (LBM), where we introduce a new simple treatment for moving boundary. Sub-grids are defined to separate structures from main-grid, thus structures can be created and calculated independently. Mapping and interpolation are used to connect main-grid and sub-grids. Our proposed simulation approach demonstrates high reliability and stability when compared to the direct bounce back method available in the literature. We validate the proposed approach by simulations of a single vibration cylinder in still water and in flowing water. The results show good agreement with theory and reference experiments. We find a delay of fluid force in the simulation of compact cylinder array, and conclude that Mach number (Ma) and boundary force term have a great influence on the accuracy of calculation results. Ma should be carefully chosen for a reliable result. Compressible effect in LBM and its influence on calculation of fluid-structure interaction, which has not been studied in detail, are also discussed in this paper. It is hard to avoid time delay effect under the framework of LBM according to the analysis, and this may lead to inaccurate results in fluid-structure interaction calculation using LBM under certain conditions, which deserve more attention. This paper investigates the vibration of structure in fluid using LBM, which will support the research for fluid induced vibration.

Lattice Boltzmann simulations of gravity currents

This paper is aimed at assessing the ability of the Lattice-Boltzmann Method (LBM) in reproducing the fundamental features of lock-exchange gravity currents. Both two- and three-dimensional numerical simulations are presented at different Reynolds numbers (1000≤Re≤30,000). Turbulence has been accounted for by implementing an equivalent Large Eddy Simulation (LES) model in the LBM framework. The advancement of the front position and the front velocity obtained by LBM numerical simulations are compared with laboratory experiments appositely performed with similar initial and boundary conditions and with previous results from literature, revealing that the dynamics of the gravity current as a whole is correctly reproduced. Lobes and clefts instabilities arising in three-dimensional simulations and the entrainment parameter are also analysed and comparisons with previous studies are presented.

A novel Lattice Boltzmann method for the dynamics of rigid particles suspended in a viscoelastic medium

We suggest a novel numerical algorithm based on the lattice Boltzmann method (LBM) to investigate particulate systems in which solid particles are suspended in a viscoelastic medium. In this model, polymer solution is described by the viscoelastic fluid based on the advection-diffusion LBM model, and it is coupled with the smoothed profile method (SPM) which describes the motion of rigid particles. To validate the present algorithm, we test three benchmark problems (two-dimensional simulation); viscoelastic flow past a cylinder, a single particle migration in a viscoelastic Couette flow, and dynamics of two particles in a viscoelastic Couette flow. Simulation results are carefully analyzed, and they are compared with previous simulation results implemented by finite element method (FEM) and finite volume method (FVM). In all test results, hydrodynamic properties and the motion of the particles induced by viscoelasticity are correctly captured, and they qualitatively as well as quantitatively correspond to previous reports. We conclude that both viscoelasticity and multi-body hydrodynamic interactions can be well incorporated in this new LBM algorithm. The present study has its significance as a first report, which strictly solves the flow behavior of solid particles immersed in a viscoelastic medium on the LBM framework.

Simulation of biomass particle evolution under pyrolysis conditions using lattice Boltzmann method

To accurately characterize biomass fast pyrolysis at the particle scale, intra-particle transport phenomena needs to be considered together with the gas flow surrounding the particle. In this study, a detailed numerical method was used to simulate the evolution of biomass particles under fast pyrolysis conditions. To conduct particle-scale simulations, the lattice Boltzmann method (LBM) was employed to solve the conservation equations, and pyrolysis kinetics were implemented to describe the chemical reactions. The present model was validated by comparing the numerical results with experimental data for a single biomass particle under pyrolysis conditions. The predicted temperature and conversion history agree with the experimental data. The temperature and density fields in the particle were found to be anisotropic due to the effect of the gas flow surrounding the particle, which was ignored by the 1D model. The non-uniform distributions of surface temperature indicate that using a constant temperature or heat flux as boundary conditions may cause numerical errors. Sensitivity analysis shows that density is the most influential parameter while porosity is the least. The heat of reaction converting the intermediate solid to char is more dominant than those of the three primary reactions. A parametric study was conducted to investigate the effect of particle shape on conversion time and final product yields. The simulation results show that the conversion time decreased when using the elliptic particle instead of the regular (circular) particle. The model also shows that more tar and syngas were produced, while less char was generated from an elliptic particle. The effect of particle shape on the center temperature of the biomass particle can be explained by comparing the heat transfer conditions at the front of the particle and the convective heat transfer at the top and bottom of the particle. The results demonstrated that the current LBM framework has the ability to reveal the detailed conversion process of biomass particles under various pyrolysis conditions, which can then be used to improve engineering models for reactor-scale simulation.

Lattice Boltzmann methods for the simulation of heat transfer in particle suspensions

This study examines the use of a lattice Boltzmann method framework to study heat transfer behaviours within particle suspensions. This has been done through the use of an adapted interface condition to attempt to resolve the required continuity of temperature and flux at the boundary between the solid and fluid phases. The proposed method is tested against analytical solutions for layered media in both a 1D bar and a radial layout. These tests showed that the model was able to generate results with first order convergence towards the analytical outcomes. The model was then used to examine the behaviour of two moving particles travelling along a channel to illustrate its potential for resolving complex suspension flows.

Numerical simulation of heat transfer in particulate flows using a thermal immersed boundary lattice Boltzmann method

In the current work the lattice Boltzmann method (LBM) is applied to investigate heat transfer phenomena in particulate flows. Different cases involving both two- and three-dimensional configurations are studied. For the fluid–particle interactions the direct-forcing and direct-heating immersed boundary (IB) method are applied to calculate the hydrodynamic force and energy exchange between the particle and the fluid, respectively. This Eulerian–Lagrangian approach captures the fluid flow around the particles with high accuracy. The Boussinesq approximation is applied to the coupling between flow and temperature fields. The energy equation is solved using a double-population model in the LBM framework. Numerical simulations reveal that this thermal IB-LBM can accurately predict the particle motion. A particularly interesting case involves particles with a variable temperature, where the competition between gravity and buoyancy induced by the temperature gradient can make particles sink or rise. It is observed that cold particles settle down faster than hot particles. Also, the thermal IB-LBM has been implemented for a collection of spherical particles. In this manner, the behavior of catalyst particles can be accurately predicted, as demonstrated in the last application, involving 60 particles interacting in an enclosure.