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1
Zhou, Jian Guo. "Macroscopic Lattice Boltzmann Method." Water 13, no. 1 (December 30, 2020): 61. http://dx.doi.org/10.3390/w13010061.
Анотація:
The lattice Boltzmann method (LBM) is a highly simplified model for fluid flows using a few limited fictitious particles. It has been developed into a very efficient and flexible alternative numerical method in computational physics, demonstrating its great power and potential for resolving more and more challenging physical problems in science and engineering covering a wide range of disciplines such as physics, chemistry, biology, material science and image analysis. The LBM is implemented through the two routine steps of streaming and collision using the three parameters of the lattice size, particle speed and collision operator. A fundamental question is if the two steps are integral to the method or if the three parameters can be reduced to one for a minimal lattice Boltzmann method. In this paper, it is shown that the collision step can be removed and the standard LBM can be reformulated into a simple macroscopic lattice Boltzmann method (MacLAB). This model relies on macroscopic physical variables only and is completely defined by one basic parameter of the lattice size δx, bringing the LBM into a precise “lattice” Boltzmann method. The viscous effect on flows is naturally embedded through the particle speed, making it an ideal automatic simulator for fluid flows. Three additional advantages compared to the existing LBMs are that: (i) physical variables can directly be retained as the boundary conditions; (ii) much less computational memory is required; and (iii) the model is unconditionally stable. The findings are demonstrated and confirmed with numerical tests including flows that are independent of and dependent on fluid viscosity, 2D and 3D cavity flows and an unsteady Taylor–Green vortex flow. This provides an efficient and powerful model for resolving physical problems in various disciplines of science and engineering.
2
Maier, Robert S., and Robert S. Bernard. "Accuracy of the Lattice-Boltzmann Method." International Journal of Modern Physics C 08, no. 04 (August 1997): 747–52. http://dx.doi.org/10.1142/s0129183197000631.
Анотація:
The accuracy of the lattice-Boltzmann method (LBM) is moderated by several factors, including Mach number, spatial resolution, boundary conditions, and the lattice mean free path. Results obtained with 3D lattices suggest that the accuracy of certain two-dimensional (2D) flows, such as Poiseuille and Couette flow, persist even when the mean free path between collisions is large, but that of the 3D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3D low-Reynolds-number flow. The influence of boundary representations on LBM accuracy is captured by the proposed index, when the accuracy of the prescribed boundary conditions is consistent with that of LBM.
3
Parise, G., A. Cianchi, A. Del Dotto, F. Guglietta, A. R. Rossi, and M. Sbragaglia. "Lattice Boltzmann simulations of plasma wakefield acceleration." Physics of Plasmas 29, no. 4 (April 2022): 043903. http://dx.doi.org/10.1063/5.0085192.
Анотація:
We explore a novel simulation route for Plasma Wakefield Acceleration (PWFA) by using the computational method known as the Lattice Boltzmann Method (LBM). LBM is based on a discretization of the continuum kinetic theory while assuring the convergence toward hydrodynamics for coarse-grained fields (i.e., density, velocity, etc.). LBM is an established numerical analysis tool in computational fluid dynamics, able to efficiently bridge between kinetic theory and hydrodynamics, but its application in the context of PWFA has never been investigated so far. This paper takes a step forward to fill this gap. Results of LBM simulations for PWFA are discussed and compared with those of a code (Architect) implementing a Cold Fluid (CF) model for the plasma. In the hydrodynamic framework, we discuss the importance of regularization effects related to diffusion properties intrinsic of the LBM, allowing to go beyond the CF approximations. Issues on computational efficiency are also addressed.
4
Parise, G., A. Cianchi, A. Del Dotto, F. Guglietta, A. R. Rossi, and M. Sbragaglia. "Lattice Boltzmann simulations of plasma wakefield acceleration." Physics of Plasmas 29, no. 4 (April 2022): 043903. http://dx.doi.org/10.1063/5.0085192.
Анотація:
We explore a novel simulation route for Plasma Wakefield Acceleration (PWFA) by using the computational method known as the Lattice Boltzmann Method (LBM). LBM is based on a discretization of the continuum kinetic theory while assuring the convergence toward hydrodynamics for coarse-grained fields (i.e., density, velocity, etc.). LBM is an established numerical analysis tool in computational fluid dynamics, able to efficiently bridge between kinetic theory and hydrodynamics, but its application in the context of PWFA has never been investigated so far. This paper takes a step forward to fill this gap. Results of LBM simulations for PWFA are discussed and compared with those of a code (Architect) implementing a Cold Fluid (CF) model for the plasma. In the hydrodynamic framework, we discuss the importance of regularization effects related to diffusion properties intrinsic of the LBM, allowing to go beyond the CF approximations. Issues on computational efficiency are also addressed.
5
Li, Yanbing, and Xiaowen Shan. "Lattice Boltzmann method for adiabatic acoustics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1944 (June 13, 2011): 2371–80. http://dx.doi.org/10.1098/rsta.2011.0109.
Анотація:
The lattice Boltzmann method (LBM) has been proved to be a useful tool in many areas of computational fluid dynamics, including computational aero-acoustics (CAA). However, for historical reasons, its applications in CAA have been largely restricted to simulations of isothermal (Newtonian) sound waves. As the recent kinetic theory-based reformulation establishes a theoretical framework in which LBM can be extended to recover the full Navier–Stokes–Fourier (NS) equations and beyond, in this paper, we show that, at least at the low-frequency limit (sound frequency much less than molecular collision frequency), adiabatic sound waves can be accurately simulated by the LBM provided that the lattice and the distribution function ensure adequate recovery of the full NS equations.
6
Mendl, Christian B. "Matrix-valued quantum lattice Boltzmann method." International Journal of Modern Physics C 26, no. 10 (June 24, 2015): 1550113. http://dx.doi.org/10.1142/s0129183115501132.
Анотація:
We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum Boltzmann equation, with the classical Maxwell distribution replaced by Fermi–Dirac functions. To accommodate the spin density matrix, the distribution functions become 2 × 2 matrix-valued. From an analytic perspective, the efficient, commonly used BGK approximation of the collision operator is valid in the present setting. The numerical scheme could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.
7
Wen, Mengke, Weidong Li, and Zhangyan Zhao. "A hybrid scheme coupling lattice Boltzmann method and finite-volume lattice Boltzmann method for steady incompressible flows." Physics of Fluids 34, no. 3 (March 2022): 037114. http://dx.doi.org/10.1063/5.0085370.
Анотація:
We present a new hybrid method coupling the adaptive mesh refinement lattice Boltzmann method (AMRLBM) and the finite-volume lattice Boltzmann method (FVLBM) to improve both the simulation efficiency and adaptivity for steady incompressible flows with complex geometries. The present method makes use of the domain decomposition, in which the FVLBM sub-domain is applied to the region adjacent to the walls, and is coupled to the lattice Boltzmann method (LBM) sub-domain in the rest of the flow field to enhance the ability of the LBM to deal with irregular geometries without sacrificing the high efficiency and accuracy property of the LBM. In the LBM sub-domain, a cell-centered lattice structure-based AMRLBM is used and, in the FVLBM sub-domain, the gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme-based FVLBM is adopted to reduce the numerical dissipation and enhance the efficiency of FVLBM. Moreover, not like the conventional LBM and Navier–Stokes equation solver-based hybrid schemes, the present hybrid scheme combines two kinds of lattice Boltzmann equation solvers, that is, AMRLBM and FVLBM, which makes the present scheme much simpler and better consistency than the conventional hybrid schemes. To assess the accuracy and efficacy of the proposed method, various benchmark studies, including the Kovasznay flow, the lid-driven cavity flow with Reynolds number [Formula: see text], 400, and 1000, and the steady flow past a cylinder with [Formula: see text] and 40, are also conducted. The numerical results show that the present scheme can be an efficient and reliable method for steady incompressible flows.
8
Tubbs, Kevin R., and Frank T. C. Tsai. "MRT-Lattice Boltzmann Model for Multilayer Shallow Water Flow." Water 11, no. 8 (August 6, 2019): 1623. http://dx.doi.org/10.3390/w11081623.
Анотація:
The objectives of this study are to introduce a multiple-relaxation-time (MRT) lattice Boltzmann model (LBM) to simulate multilayer shallow water flows and to introduce graphics processing unit (GPU) computing to accelerate the lattice Boltzmann model. Using multiple relaxation times in the lattice Boltzmann model has an advantage of handling very low kinematic viscosity without causing a stability problem in the shallow water equations. This study develops a multilayer MRT-LBM to solve the multilayer Saint-Venant equations to obtain horizontal flow velocities in various depths. In the multilayer MRT-LBM, vertical kinematic viscosity forcing is the key term to couple adjacent layers. We implemented the multilayer MRT-LBM to a GPU-based high-performance computing (HPC) architecture. The multilayer MRT-LBM was verified by analytical solutions for cases of wind-driven, density-driven, and combined circulations with non-uniform bathymetry. The results show good speedup and scalability for large problems. Numerical solutions compared well to the analytical solutions. The multilayer MRT-LBM is promising for simulating lateral and vertical distributions of the horizontal velocities in shallow water flow.
9
Falcucci, Giacomo, Stefano Ubertini, Gino Bella, and Sauro Succi. "Lattice Boltzmann Simulation of Cavitating Flows." Communications in Computational Physics 13, no. 3 (March 2013): 685–95. http://dx.doi.org/10.4208/cicp.291011.270112s.
Анотація:
AbstractThe onset of cavitating conditions inside the nozzle of liquid injectors is known to play a major role on spray characteristics, especially on jet penetration and break-up. In this work, we present a Direct Numerical Simulation (DNS) based on the Lattice Boltzmann Method (LBM) to study the fluid dynamic field inside the nozzle of a cavitating injector. The formation of the cavitating region is determined via a multi-phase approach based on the Shan-Chen equation of state. The results obtained by the LBM simulation show satisfactory agreement with both numerical and experimental data. In addition, numerical evidence of bubble break-up, following upon flow-induced cavitation, is also reported.
10
SHET, ANIRUDDHA G., K. SIDDHARTH, SHAHAJHAN H. SORATHIYA, ANAND M. DESHPANDE, SUNIL D. SHERLEKAR, BHARAT KAUL, and SANTOSH ANSUMALI. "ON VECTORIZATION FOR LATTICE BASED SIMULATIONS." International Journal of Modern Physics C 24, no. 12 (November 13, 2013): 1340011. http://dx.doi.org/10.1142/s0129183113400111.
Анотація:
We present a vector-friendly blocked computing strategy for the lattice Boltzmann method (LBM). This strategy, along with a recently developed data structure, Structure of Arrays of Structures (SoAoS), is implemented for multi-relaxation type lattice Boltzmann (LB). The proposed methodology enables optimal memory bandwidth utilization in the advection step and high compute efficiency in the collision step of LB implementation. In a dense computing environment, current performance optimization framework for LBM is able to achieve high single-core efficiency.
11
TIAN, ZHI-WEI, SHENG CHEN, and CHU-GUANG ZHENG. "LATTICE BOLTZMANN SIMULATION OF GASEOUS FINITE-KNUDSEN MICROFLOWS." International Journal of Modern Physics C 21, no. 06 (June 2010): 769–83. http://dx.doi.org/10.1142/s0129183110015464.
Анотація:
In this study, microscale gaseous flows in the transitional regime have been investigated by lattice Boltzmann method (LBM). In the existing microflows LBM models, the Knudsen layer correction function has been introduced into the models. According to the kinetic theory rigorously, we choose a proper expression of correction function, and then determine its adjustable parameter. A substitute high-order boundary conditions treatment is adopted to capture the velocity slip, without any difficulties in computing the high-order velocity derivatives. The numerical results of two typical microflows show that: the present results agree with the analytical solutions better than the existing LBM simulations. Evident improvements can also be found, especially for finite Kn microflows.
12
KAM, E. W. S., R. C. K. LEUNG, R. M. C. SO, and X. M. LI. "A LATTICE BOLTZMANN METHOD FOR COMPUTATION OF AEROACOUSTIC INTERACTION." International Journal of Modern Physics C 18, no. 04 (April 2007): 463–72. http://dx.doi.org/10.1142/s0129183107010693.
Анотація:
This paper reports a study of the ability of an improved LBM in replicating acoustic interaction. With a BGK model with two relaxation times approximating the collison term, the improved LBM is shown not only able to recover the equation of state, but also replicates the specific heat ratio, the fluid viscosity and thermal conductivity correctly. With these improvements, the recovery of full set of unsteady compressible Navier-Stokes equations is possible. Two complex aeroacoustic interaction problems, namely the interaction of three fundamental aeroacoustic pulses and scattering of short wave by a zero circulation vortex, are calculated. The LBM solutions are compared with DNS results. In the first case it has been shown that the improved LBM is as effective as the DNS in simulating aeroacoustic interaction of three pulses. Both methods obtain essentially same results using same truncated domains. In the scattering problem, LBM is able to replicate the directivity of scattered acoustic wave from the vortex but it does not accurately reproduce the symmetry as calculated using DNS.
13
SZILÁGYI, BÉLA, ROMEO SUSAN-RESIGA, and VICTOR SOFONEA. "LATTICE BOLTZMANN APPROACH TO VISCOUS FLOWS BETWEEN PARALLEL PLATES." International Journal of Modern Physics C 06, no. 03 (June 1995): 345–58. http://dx.doi.org/10.1142/s0129183195000253.
Анотація:
Four different kinds of laminar flows between two parallel plates are investigated using the Lattice Boltzmann Method (LBM). The LBM accuracy is estimated in two cases using numerical fits of the parabolic velocity profiles and the kinetic energy decay curves, respectively. The error relative to the analytical kinematic viscosity values was found to be less than one percent in both cases. The LBM results for the unsteady development of the flow when one plate is brought suddenly at a constant velocity, are found in excellent agreement with the analytical solution. Because the classical Schlichting’s approximate solution for the entrance-region flow is not valid for small Reynolds numbers, a Finite Element Method solution was used in order to check the accuracy of the LBM results in this case.
14
Hayatdavoodi, M. "Laminar flow around sharp and curved objects: the lattice Boltzmann method." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 225, no. 4 (September 12, 2011): 361–74. http://dx.doi.org/10.1177/1475090211416424.
Анотація:
The lattice Boltzmann method (LBM) is a relatively new computational method to model fluid flows by tracking collision, advection, and propagation of mesoscopic fluid particles. LBM originated from the cellular automata combined with kinetic theory and the Boltzmann equation. The method is used to solve the explicit finite-difference scheme lattice Boltzmann equations which are second order in space and first order in time. LBM does not attempt to solve the Navier–Stokes equations directly; however, it obeys the equations. The two-dimensional flows around square and circular cylinders are simulated with uniform and nonuniform grid structures using the LBM. The boundary layer growth and wake region physics are captured with small-scale details, and the results are validated by comparison with laboratory experiments for the Reynolds numbers between 50 and 350. Compatibility of the method in simulating flow around hydrofoil geometries and a combination of objects is also provided.
15
Бикулов, Д. А. "An efficient implementation of the lattice Boltzmann method for hybrid supercomputers." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 2 (June 30, 2015): 205–14. http://dx.doi.org/10.26089/nummet.v16r221.
Анотація:
Рассмотрены особенности эффективной реализации метода решеточных уравнений Больцмана (Lattice Boltzmann method, LBM) для гибридных суперкомпьютерных систем с множеством видеокарт. Описаны основные стратегии по сокращению требуемой для работы LBM памяти на графическом ускорителе. Представлены результаты измерения зависимости производительности реализованного программного модуля от числа задействованных видеокарт, полученные на суперкомпьютере Ломоносов. A number of features of an efficient implementation of the lattice Boltzmann method (LBM) for hybrid supercomputers with many graphics processing units (GPU) are discussed. The main strategies for reducing the memory space required by LBM are described. The performance dependence of the implemented solver on the number of the GPUs in use is analyzed for the Lomonosov supercomputer installed at Moscow State University.
16
Xu, Cang Su, Yang Xie, Dong Hua Fang, and Yi Fan Xu. "Diesel Engine Spray Modeling with Lattice Boltzmann Method." Advanced Materials Research 779-780 (September 2013): 996–1006. http://dx.doi.org/10.4028/www.scientific.net/amr.779-780.996.
Анотація:
In this paper we propose a novel Lattice Boltzmann method (LBM) incorporated with Large Eddy Simulation (LES) to simulate diesel engine spray process. The proposed LB-LES method combines several advantages of LBM and LES including clear physical pictures, easy implementation and capacity to describe turbulence structures of high Renolds fluid, it also can settle the problem that LBM cant converge of high Renolds. Simulation result shows: (1) Strong vortex exist around the spray cone and head of the spray; (2) A high fuel density regime exits inside the head of spray, that verifies the experiment result of American APS laboratory with the application of avalanche photodiode (APD) X-ray imaging technology to spray field; (3) LB-LES method can simulate the surface undulation phenomenon of spray which is generated by the aerodynamic force in the case of high Renolds.
17
Wang, Yansen, Xiping Zeng, and Jonathan Decker. "A GPU-Accelerated Radiation Transfer Model Using the Lattice Boltzmann Method." Atmosphere 12, no. 10 (October 9, 2021): 1316. http://dx.doi.org/10.3390/atmos12101316.
Анотація:
A prototype of a three-dimensional (3-D) radiation model is developed using the lattice Boltzmann method (LBM) and implemented on a graphical processing unit (GPU) to accelerate the model’s computational speed. This radiative transfer-lattice Boltzmann model (RT-LBM) results from a discretization of the radiative transfer equation in time, space, and solid angle. The collision and streaming computation algorithm, widely used in LBM for fluid flow modeling, is applied to speed up the RT-LBM computation on the GPU platform. The isotropic scattering is assumed in this study. The accuracy is evaluated using Monte Carlo method (MCM) simulations, showing RT-LBM is quite accurate when typical atmospheric coefficients of scattering and absorption are used. RT-LBM runs about 10 times faster than the MCM in a same CPU. When implemented on a NVidia Tesla V100 GPU in simulation with a large number of computation grid points, for example, RT-LBM runs ~120 times faster than running on a single CPU. The test results indicate RT-LBM is an accurate and fast model and is viable for simulating radiative transfer in the atmosphere with ranges for the isotropic atmosphere radiative parameters of albedo scattering (0.1~0.9) and optical depth (0.1~12).
18
Budinski, Ljubomir, Julius Fabian, and Matija Stipic. "Modeling groundwater flow by lattice Boltzmann method in curvilinear coordinates." International Journal of Modern Physics C 26, no. 02 (February 2015): 1550013. http://dx.doi.org/10.1142/s0129183115500138.
Анотація:
In order to promote the use of the lattice Boltzmann method (LBM) for the simulation of isotropic groundwater flow in a confined aquifer with arbitrary geometry, Poisson's equation was transformed into a curvilinear coordinate system. With the metric function between the physical and the computational domain established, Poisson's equation written in Cartesian coordinates was transformed in curvilinear coordinates. Following, the appropriate equilibrium function for the D2Q9 square lattice has been defined. The resulting curvilinear formulation of the LBM for groundwater flow is capable of modeling flow in domains of complex geometry with the opportunity of local refining/coarsening of the computational mesh corresponding to the complexity of the flow pattern and the required accuracy. Since the proposed form of the LBM uses the transformed equation of flow implemented in the equilibrium function, finding a solution does not require supplementary procedures along the curvilinear boundaries, nor in the zones requiring mesh density adjustments. Thus, the basic concept of the LBM is completely maintained. The improvement of the proposed LBM over the previously published classical methods is completely verified by three examples with analytical solutions. The results demonstrate the advantages of the proposed curvilinear LBM in modeling groundwater flow in complex flow domains.
19
Jo, Eunchan, Byungmoon Kim, and Oh-Young Song. "Lattice-Boltzmann and Eulerian Hybrid for Solid Burning Simulation." Symmetry 11, no. 11 (November 14, 2019): 1405. http://dx.doi.org/10.3390/sym11111405.
Анотація:
We propose a new hybrid simulation method to model burning solid interactions. Unlike gas fuel, fire and smoke interactions that have been relatively well studied in the past, simulations of solid fuel combustion processes remain largely unaddressed. These include pyrolysis/smoldering, interactions with oxygen and flow inside porous solid. To advance this simulation problem, we designed a new hybrid of the Lattice-Boltzmann method (LBM) and a Eulerian grid based Navier-Stokes equation (NSE). It uses the LBM, which has symmetrical directions of particle velocities in a cell, for inside the solid fuel and the NSE, which has a representative velocity in a cell, for outside the solid. At the interface where the two methods join, we develop a novel method to exchange physical quantities and show a natural transition between the two methods. Since LBM allows us to directly manage the quantity of exchanges from the microscopic perspective, that is, between lattice points, we can easily simulate the burning speed and the shape change of burning an inhomogeneous solid. Also, we derive an LBM version of the previously proposed porous Navier-Stokes equation to simulate gas flow inside the porous solid. In addition, we use the NS solver outside the solid where macroscopic behavior is much more dominant and, hence, LBM is less efficient than NS solver. Our results show us the physical stability and accuracy and visual realism.
20
QU, KUN, CHANG SHU, and JINSHENG CAI. "DEVELOPING LBM-BASED FLUX SOLVER AND ITS APPLICATIONS IN MULTI-DIMENSION SIMULATIONS." International Journal of Modern Physics: Conference Series 19 (January 2012): 90–99. http://dx.doi.org/10.1142/s2010194512008628.
Анотація:
In this paper, a new flux solver was developed based on a lattice Boltzmann model. Different from solving discrete velocity Boltzmann equation and lattice Boltzmann equation, Euler/Navier-Stokes (NS) equations were solved in this approach, and the flux at the interface was evaluated with a compressible lattice Boltzmann model. This method combined lattice Boltzmann method with finite volume method to solve Euler/NS equations. The proposed approach was validated by some simulations of one-dimensional and multi-dimensional problems.
21
Liu, Xin Hua, Hao Liu, and Yong Zhi Liu. "Theory and Application of Lattice Boltzmann Method." Applied Mechanics and Materials 79 (July 2011): 270–75. http://dx.doi.org/10.4028/www.scientific.net/amm.79.270.
Анотація:
The research progress and results of Lattice Boltzmann method (LBM) for the engineering technology fields are reviewed. Firstly, the basic ideas and principles of Lattice Boltzmann method are briefly introduced. Secondly, the boundary conditions of Lattice Boltzmann method are proposed. Thirdly, the applications in several fields such as single-phase flows, multiphase flows, porous media flows, compressible flows and mathematics are summarized. Finally, the direction of future development for Lattice Boltzmann method was discussed.
22
Delavar, Mojtaba Aghajani, and Junye Wang. "Lattice Boltzmann Method in Modeling Biofilm Formation, Growth and Detachment." Sustainability 13, no. 14 (July 16, 2021): 7968. http://dx.doi.org/10.3390/su13147968.
Анотація:
Biofilms are a complex and heterogeneous aggregation of multiple populations of microorganisms linked together by their excretion of extracellular polymer substances (EPS). Biofilms can cause many serious problems, such as chronic infections, food contamination and equipment corrosion, although they can be useful for constructive purposes, such as in wastewater treatment, heavy metal removal from hazardous waste sites, biofuel production, power generation through microbial fuel cells and microbially enhanced oil recovery; however, biofilm formation and growth are complex due to interactions among physicochemical and biological processes under operational and environmental conditions. Advanced numerical modeling techniques using the lattice Boltzmann method (LBM) are enabling the prediction of biofilm formation and growth and microbial community structures. This study is the first attempt to perform a general review on major contributions to LBM-based biofilm models, ranging from pioneering efforts to more recent progress. We present our understanding of the modeling of biofilm formation, growth and detachment using LBM-based models and present the fundamental aspects of various LBM-based biofilm models. We describe how the LBM couples with cellular automata (CA) and individual-based model (IbM) approaches and discuss their applications in assessing the spatiotemporal distribution of biofilms and their associated parameters and evaluating bioconversion efficiency. Finally, we discuss the main features and drawbacks of LBM-based biofilm models from ecological and biotechnological perspectives and identify current knowledge gaps and future research priorities.
23
Si, Hai Qing, Bing Wang, Yan Shi, and Xiao Jun Wu. "Aero-Acoustics Computations of Square Cylinder Using the Lattice Boltzmann Method." Applied Mechanics and Materials 444-445 (October 2013): 400–405. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.400.
Анотація:
In this paper the ability of the Lattice Boltzmann Method (LBM) is investigated for simulating acoustic problems, especially for the propagation of acoustic waves in a wall bounded region. To treat the wall boundary conditions, a non-equilibrium extrapolation scheme for the LBM is adopted. LBM is next applied to simulate the complex aerodynamic noise generated from a square cylinder. In order to efficiently suppress the disturbances at the computational boundaries, the improved absorbing boundary condition (IABC) is developed in this paper. To validate the flow and acoustic solution of a square cylinder, comparisons between the present LBM and the previous studies are carried out. It is demonstrated that the LBM can efficiently simulate the noise generated from a square cylinder.
24
Che Sidik, Nor Azwadi, and Aman Ali Khan. "Simulation of Flow over a Cavity Using Multi-Relaxation Time Thermal Lattice Boltzmann Method." Applied Mechanics and Materials 554 (June 2014): 296–300. http://dx.doi.org/10.4028/www.scientific.net/amm.554.296.
Анотація:
This article provides numerically study of the multi-relaxation time thermal lattice Boltzmann method (LBM) for compute the flow and isotherm characteristics in the bottom heated cavity located o n a floor of horizontal channel . A double-distribution function (DFF) was coupled with MRT thermal LBM to study the effects of various grashof number (Gr), Reynolds number (Re) and Aspect Ratio (AR) on the flow and isotherm characteristic. The results we re compared with the conventional single-relaxation time lattice Boltzmann scheme and benchmark solution for such flow configuration. The results of the numer ical simulation indicate that multi-relaxation time thermal lattice Boltzmann scheme demonstrated good agreement, which supports its validity in computing fluid flow problem.
25
Cao, Wen Jiong, Shou Bin Dong, Xin Wei Lu, and Zhao Yao Zhou. "Numerical Simulation of Filling Process in HPDC by Lattice Boltzmann Method." Advanced Materials Research 717 (July 2013): 354–58. http://dx.doi.org/10.4028/www.scientific.net/amr.717.354.
Анотація:
A general lattice Boltzmann Method (LBM) to simulate filling process of high pressure die casting (HPDC) is investigated. Boundary conditions are studied and the free surface model is established by combine the LBM with VOF method. The final model was substantiated by simulating filling process in HPDC in three dimensions. The simulated results from LBM and finite difference method (FDM) were compared with the experiments. The results show the former is in a better agreement with experiments. It demonstrates the efficiency and precision of this LBM model in describing flow pattern in filling process.
26
Maquart, Tristan, Romain Noël, Guy Courbebaisse, and Laurent Navarro. "Toward a Lattice Boltzmann Method for Solids—Application to Static Equilibrium of Isotropic Materials." Applied Sciences 12, no. 9 (May 4, 2022): 4627. http://dx.doi.org/10.3390/app12094627.
Анотація:
This work presents a novel method for simulating the behavior of solid objects with the Lattice Boltzmann Method (LBM). To introduce and validate our proposed framework, comparative studies are performed for computing the static equilibrium of isotropic materials. Remembering that the LBM has strong theoretical foundations in the Boltzmann equation; this latter is firstly adjusted to solid motions, through its Boltzmann-Vlasov special case. This is indeed the case when combined with a suitable mean-field external force term to set a reliable solid framework. Secondly, a library is built and plugged on the top of the well-known Parallel Lattice Boltzmann Solver (PaLaBoS) library. Numerical implementations based on the previous equation of motion for solids are led in a non-intrusive manner so as to present results with an easy and flawless reproducibility. A newly designed Lattice Boltzmann Method for Solids (LBMS) is exhibited through a few key algorithms, showing the overall operation plus the major improvements. Efficiency, robustness and accuracy of the proposed approach are illustrated and contrasted with a commercial Finite Element Analysis (FEA) software. The obtained results reveal considerable potential concerning static and further dynamic simulations involving solid constitutive laws within the LBM formalism.
27
HAYASHI, HIDEMITSU, SATORU YAMAMOTO, and SHI-AKI HYODO. "LATTICE-BOLTZMANN SIMULATIONS OF FLOW THROUGH NAFION POLYMER MEMBRANES." International Journal of Modern Physics B 17, no. 01n02 (January 20, 2003): 135–38. http://dx.doi.org/10.1142/s0217979203017217.
Анотація:
Simulations of flow through three-dimensional porous structures of NAFION polymer membranes are performed with a Lattice-Boltzmann method (LBM) for incompressible fluid. Geometry data of NAFION are constructed from a result of a dissipative particle dynamics simulation for three values of the water content, 10%, 20%, and 30%, and are used as the geometry input for the LBM. Permeability of the porous structure is extracted from results of the LBM simulation using Darcy's low. The permeability K is shown to be expressed as K = L2 × Ktpl with a characteristic length L and the dimensionless permeability Ktpl depending only on the topological structure of the porous media. Dependence of Ktpl is examined on the pressure gradient, the fluid viscosity, and the resolution of the computational grid.
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Guan, Dong, Jiu Hui Wu, Li Jing, and Kuan Lu. "Lattice Boltzmann simulation of acoustic resistance in microchannels." International Journal of Modern Physics B 29, no. 16 (June 23, 2015): 1550104. http://dx.doi.org/10.1142/s0217979215501040.
Анотація:
Lattice Boltzmann method (LBM) is utilized to model the acoustic resistance in microchannels at mesoscopic scale in this paper. Sound pressure distribution at different positions are studied. A number of physical parameters, such as the wavelength, channel number, channel width and length are investigated to find their effects on pressure variation. Simulation results are compared with those obtained by traditional methods and demonstrate that the LBM is a helpful approach to study sound attenuation in microchannels at mesoscopic scale. These results have potential application for designing the high-efficiency sound absorbers.
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WU, CHUI-JIE, and HUI GUAN. "LATTICE BOLTZMANN DYNAMICS AND DYNAMICAL SYSTEM SUB-GRID MODELS." Modern Physics Letters B 23, no. 03 (January 30, 2009): 349–52. http://dx.doi.org/10.1142/s0217984909018370.
Анотація:
The dynamics sub-grid scale (SGS) models and the dynamical system SGS model are introduced into the lattice Boltzmann method (LBM), and applied to numerical simulation of turbulent cavity flows. The results are compared with those of direct numerical simulation of turbulence and Smagorinsky SGS model. A new average method of eliminating the inherent unphysical oscillation of LBM is also given.
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Yang, L. M., C. Shu, and J. Wu. "Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows." Advances in Applied Mathematics and Mechanics 4, no. 04 (August 2012): 454–72. http://dx.doi.org/10.4208/aamm.10-m11146.
Анотація:
AbstractThis paper at first shows the details of finite volume-based lattice Boltzmann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conservation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parameter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV-LBM simulation of hypersonic flows.
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SRIVASTAVA, SUDHIR, THEO DRIESSEN, ROGER JEURISSEN, HERMAN WIJSHOFF, and FEDERICO TOSCHI. "LATTICE BOLTZMANN METHOD TO STUDY THE CONTRACTION OF A VISCOUS LIGAMENT." International Journal of Modern Physics C 24, no. 12 (November 13, 2013): 1340010. http://dx.doi.org/10.1142/s012918311340010x.
Анотація:
We employ a recently formulated axisymmetric version of the multiphase Shan–Chen (SC) lattice Boltzmann method (LBM) [S. Srivastava et al., Phys. Rev. E88, 013309 (2013)] to simulate the contraction of a liquid ligament. We compare the axisymmetric LBM simulation against the slender jet (SJ) approximation model [T. Driessen and R. Jeurissen, Int. J. Comput. Fluid Dyn.25, 333 (2011)]. We compare the retraction dynamics of the tail-end of the liquid ligament from the LBM simulation, the SJ model, Flow3D simulations and a simple model based on the force balance (FB). We find good agreement between the theoretical prediction FB, the SJ model and the LBM simulations.
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GEERDINK, JOOST B. W., and ALFONS G. HOEKSTRA. "COMPARING ENTROPIC AND MULTIPLE RELAXATION TIMES LATTICE BOLTZMANN METHODS FOR BLOOD FLOW SIMULATIONS." International Journal of Modern Physics C 20, no. 05 (May 2009): 721–33. http://dx.doi.org/10.1142/s0129183109013947.
Анотація:
We compare the Lattice BGK, the Multiple Relaxation Times and the Entropic Lattice Boltzmann Methods for time harmonic flows. We measure the stability, speed and accuracy of the three models for Reynolds and Womersley numbers that are representative for human arteries. The Lattice BGK shows predictable stability and is the fastest method in terms of lattice node updates per second. The Multiple Relaxation Times LBM shows erratic stability which depends strongly on the relaxation times set chosen and is slightly slower. The Entropic LBM gives the best stability at the price of fewer lattice node updates per second. A parameter constraint optimization technique is used to determine which is the fastest model given a certain preset accuracy. It is found that the Lattice BGK performs best at most arterial flows, except for the high Reynolds number flow in the aorta, where the Entropic LBM is the fastest method due to its better stability. However we also conclude that the Entropic LBM with velocity/pressure inlet/outlet conditions shows much worse performance.
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TIAN, ZHIWEI, YUNLIANG TAN, and SHENG CHEN. "A NUMERICAL STUDY ON PREMIXED MICROCOMBUSTION BY LATTICE BOLTZMANN METHOD." International Journal of Modern Physics C 23, no. 05 (May 2012): 1250037. http://dx.doi.org/10.1142/s0129183112500374.
Анотація:
Lattice Boltzmann method (LBM) has made great progress in the last decade, and its application became wider and wider. In this paper, based on our former combustion LBM model on the macroscale, we attempt to extend it into premixed microcombustion simulation. Considering the external heat losses in microcombustion, the second-order implicit scheme for boundary condition treatment was adopted in our LBM model. Numerical tests have proved that its accuracy and stability were suitable. Furthermore, planar microcombustion with backward-facing step was also studied in order to show its different performances and improvement, which are compared with microcombustor without back step.
34
Li, Jun, and Donald Brown. "Upscaled Lattice Boltzmann Method for Simulations of Flows in Heterogeneous Porous Media." Geofluids 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/1740693.
Анотація:
An upscaled Lattice Boltzmann Method (LBM) for flow simulations in heterogeneous porous media at the Darcy scale is proposed in this paper. In the Darcy-scale simulations, the Shan-Chen force model is used to simplify the algorithm. The proposed upscaled LBM uses coarser grids to represent the average effects of the fine-grid simulations. In the upscaled LBM, each coarse grid represents a subdomain of the fine-grid discretization and the effective permeability with the reduced-order models is proposed as we coarsen the grid. The effective permeability is computed using solutions of local problems (e.g., by performing local LBM simulations on the fine grids using the original permeability distribution) and used on the coarse grids in the upscaled simulations. The upscaled LBM that can reduce the computational cost of existing LBM and transfer the information between different scales is implemented. The results of coarse-grid, reduced-order, simulations agree very well with averaged results obtained using a fine grid.
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Tatulcenkovs, Andrejs, Andris Jakovics, Egbert Baake, and Bernard Nacke. "Lattice Boltzmann modelling for multiphase bubble flow in electroconducting liquids." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 2 (March 6, 2017): 401–7. http://dx.doi.org/10.1108/compel-05-2016-0224.
Анотація:
Purpose The purpose of this paper is to the study the multiphase bubbles flow motion in a vertical channel with an electroconducting liquid without and under the influence of a magnetic field. Design/methodology/approach For numerical calculations, the lattice Boltzmann method (LBM) is used, which is based on the kinetic theory for solving fluid mechanics and other physical problems. The phase-field lattice Boltzmann model is developed to simulate the behaviour of multiphase bubble–bubble interaction while rising in the fluid with high density ratios. Findings The behaviour of the rising bubble flow in a rectangular column of two phases is investigated with the two-dimensional LBM. Originality/value The multiphase flow in electroconducting liquids with high ratio of density is studied using the LBM.
36
Liu, Qiang, Wei Xie, Liao Yuan Qiu, and Xue Shen Xie. "Lattice Boltzmann Method for the Simulation of High Reynolds Number Flows." Applied Mechanics and Materials 444-445 (October 2013): 352–56. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.352.
Анотація:
The lattice Boltzmann method (LBM) is considered as an alternative scheme to the standard Navier-Stokes approach. To simulate the high Reynolds number turbulence, several approaches based on LBM have been proposed. Among them, 5 approaches including the direct numerical simulation, dynamic subgrid scale model, inertial range consistent subgrid model, very large eddy simulation and entropic lattice Boltzmann method are discussed in detail. Features including improvements and shortcomings of each approach are presented. Whats more, application prospects of these approaches in high Reynolds number turbulence simulations are pointed out.
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Song, Chao Shuai, Jun Yue, and Hong Xiu Gao. "Study of InSAS Interferogram Filtering Based on Lattice Boltzmann Method." Applied Mechanics and Materials 423-426 (September 2013): 2581–86. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.2581.
Анотація:
On the issue of interferogram filter in Interferomatric Synthetic Aperture Sonar(InSAS), P - M model based on partial differential equation (PDE) can not only remove noise effectively, but also better keep the interferogram details and edge information. But its computation efficiency is relatively low and it can not be parallelized to real-time processing. Aiming to overcome these shortcomings, a de-noising method based on lattice Boltzmann method(LBM) is introduced. Processing results of the simulation and real experimental data show that the interferogram filtering method based on LBM can de-noise more effectively, and its calculation efficiency is better. In view of it, LBM can be used for real-time processing.
38
Habib, Riffat, Tahir Saeed Khan, Zubair Ahmad, Muhammad Saad Khan, and Ebenezer Bonyah. "Two-dimensional stable lattice Boltzmann simulation of turbulent flow in wavy walled channel." AIP Advances 13, no. 1 (January 1, 2023): 015114. http://dx.doi.org/10.1063/5.0123033.
Анотація:
In recent years, the lattice Boltzmann equation has developed into a promising technique for computational fluid dynamics (CFD). The lattice Boltzmann model (LBM) approach is derived from the Boltzmann equation and kinetic theory, as opposed to the standard CFD methods that are based on direct discretization of the Navier–Stokes equations. In this paper, Newtonian flow passing through a wavy walled channel has been examined for laminar to turbulent transition by using the LBM. The simple LBM for this problem becomes unstable as the Reynolds number increases and the laminar to turbulent transition begins. When Ehrenfest’s limiters are introduced in the LBM, the simulation becomes stable for higher Reynolds numbers. Two types of channel geometries are studied here, the channel walls of relatively small amplitude and channel walls of large amplitude. Our findings are that for large amplitude channel walls, flow becomes unsteady for lower Reynolds numbers as compared to that for small amplitude channel walls. For large amplitude walls, the vortices formed exhibit periodic shedding inside the channel furrows and remain there. For small amplitude walls, the vortex shedding starts downstream of the channel. The present LBM variant is able to simulate small amplitude channel flow for a Reynolds number Re = 800 and large amplitude channel flow for a Reynolds number R = 570.
39
Tong, Ying, and Jian Xia. "The hydrodynamic FORCE of fluid–structure interaction interface in lattice Boltzmann simulations." International Journal of Modern Physics B 34, no. 14n16 (May 30, 2020): 2040085. http://dx.doi.org/10.1142/s0217979220400858.
Анотація:
The hydrodynamic force (HF) evaluation plays a critical role in the numerical simulation of fluid–structure interaction (FSI). By directly using the distribution functions of lattice Boltzmann equation (LBE) to evaluate the HF, the momentum exchange algorithm (MEA) has excellent features. Particularly, it is independent of boundary geometry and avoids integration on the complex boundary. In this work, the HF of lattice Boltzmann simulation (LBS) is evaluated by using the MEA. We conduct a comparative study to evaluate two lattice Boltzmann models for constructing the flow solvers, including the LBE with single-relaxation-time (SRT) and multiple-relaxation-time (MRT) collision operators. The second-order boundary condition schemes are used to address the curve boundary. The test case of flow past a cylinder asymmetrically placed in a channel is simulated. Comparing the numerical solutions of Lattice Boltzmann method (LBM) with those of Navier–Stokes equations in the literature, the influence of collision relaxation model, boundary conditions and lattice resolution is investigated. The results demonstrate that the MRT-LB improves the numerical stability of the LBM and the accuracy of HF.
40
Bawazeer, Saleh A., Saleh S. Baakeem, and Abdulmajeed A. Mohamad. "Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method." Mathematics 10, no. 3 (February 4, 2022): 501. http://dx.doi.org/10.3390/math10030501.
Анотація:
The lattice Boltzmann method (LBM) has two key steps: collision and streaming. In a conventional LBM, the streaming is exact, where each distribution function is perfectly shifted to the neighbor node on the uniform mesh arrangement. This advantage may curtail the applicability of the method to problems with complex geometries. To overcome this issue, a high-order meshless interpolation-based approach is proposed to handle the streaming step. Owing to its high accuracy, the radial basis function (RBF) is one of the popular methods used for interpolation. In general, RBF-based approaches suffer from some stability issues, where their stability strongly depends on the shape parameter of the RBF. In the current work, a stabilized RBF approach is used to handle the streaming. The stabilized RBF approach has a weak dependency on the shape parameter, which improves the stability of the method and reduces the dependency of the shape parameter. Both the stabilized RBF method and the streaming of the LBM are used for solving three benchmark problems. The results of the stabilized method and the perfect streaming LBM are compared with analytical solutions or published results. Excellent agreements are observed, with a little advantage for the stabilized approach. Additionally, the computational cost is compared, where a marginal difference is observed in the favor of the streaming of the LBM. In conclusion, one could report that the stabilized method is a viable alternative to the streaming of the LBM in handling both simple and complex geometries.
41
Tran, Nhat-Phuong, Myungho Lee, and Sugwon Hong. "Performance Optimization of 3D Lattice Boltzmann Flow Solver on a GPU." Scientific Programming 2017 (2017): 1–16. http://dx.doi.org/10.1155/2017/1205892.
Анотація:
Lattice Boltzmann Method (LBM) is a powerful numerical simulation method of the fluid flow. With its data parallel nature, it is a promising candidate for a parallel implementation on a GPU. The LBM, however, is heavily data intensive and memory bound. In particular, moving the data to the adjacent cells in the streaming computation phase incurs a lot of uncoalesced accesses on the GPU which affects the overall performance. Furthermore, the main computation kernels of the LBM use a large number of registers per thread which limits the thread parallelism available at the run time due to the fixed number of registers on the GPU. In this paper, we develop high performance parallelization of the LBM on a GPU by minimizing the overheads associated with the uncoalesced memory accesses while improving the cache locality using the tiling optimization with the data layout change. Furthermore, we aggressively reduce the register uses for the LBM kernels in order to increase the run-time thread parallelism. Experimental results on the Nvidia Tesla K20 GPU show that our approach delivers impressive throughput performance: 1210.63 Million Lattice Updates Per Second (MLUPS).
42
Gehrke, Martin, and Thomas Rung. "Scrutinizing Dynamic Cumulant Lattice Boltzmann Large Eddy Simulations for Turbulent Channel Flows." Computation 10, no. 10 (September 25, 2022): 171. http://dx.doi.org/10.3390/computation10100171.
Анотація:
This technical paper outlines the predictive performance of a recently published dynamic cumulant lattice Boltzmann method (C-LBM) to model turbulent shear flows at all resolutions. Emphasis is given to a simple strategy that avoids a frequently observed velocity overshoot phenomenon near rigid walls when combining the C-LBM with an all-resolution (universal) wall function. The examples included are confined to turbulent channel flow results for a variety of friction Reynolds numbers within 180 and 50,000, obtained on a sequence of isotropic, homogeneous grids that feature non-dimensional lattice spacings using inner coordinates from 4 to 2200. The results indicate that adjusting the near-wall distance of the first fluid node, i.e., the intersection of the wall with the first lattice edge, to the resolution provides a reasonably simple, robust, and accurate supplement to the all-resolution C-LBM approach. The investigated wall function/C-LBM combination displays a remarkable predictive performance for all investigated resolutions.
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CHEN, Y., and Q. D. CAI. "THE LATTICE BOLTZMANN METHOD BASED ON QUADTREE MESH." Modern Physics Letters B 23, no. 03 (January 30, 2009): 289–92. http://dx.doi.org/10.1142/s0217984909018229.
Анотація:
A lattice Boltzmann method (LBM) based on nonuniform quadtree mesh is proposed. For the two steps in LBM, the collision step is a local procedure and can be implemented in the same way for both uniform and nonuniform mesh grids, while the streaming step is equivalent to solving several linear advection equations. On quadtree mesh (and some other nonuniform meshes), it is usually trivial to construct a first order interpolation scheme for the streaming step. Then the back and forth error compensation and correction (BFECC) method is employed to improve the accuracy order, such that a second order scheme is obtained in streaming step. Several numerical test cases are carried out to prove the accuracy and efficiency of our method.
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Xue, Xiao, Hua-Dong Yao, and Lars Davidson. "Synthetic turbulence generator for lattice Boltzmann method at the interface between RANS and LES." Physics of Fluids 34, no. 5 (May 2022): 055118. http://dx.doi.org/10.1063/5.0090641.
Анотація:
The paper presents a synthetic turbulence generator (STG) for the lattice Boltzmann method (LBM) at the interface of the Reynolds averaged Navier–Stokes (RANS) equations and the LBM large eddy simulation (LES). We first obtain the RANS velocity field from a finite volume solver at the interface. Then, we apply a numerical interpolation from the RANS velocity field to the LBM velocity field due to the different grid types of RANS and LBM. The STG method generates the velocity fluctuations, and the regularized LBM reconstructs the particle distribution functions at the interface. We perform a turbulent channel flow simulation at [Formula: see text] with the STG at the inlet and the pressure-free boundary condition at the outlet. The velocity field is quantitatively compared with the periodic lattice Boltzmann based LES (LES-LBM) channel flow and the direct numerical simulation (DNS) channel flow. Both the adaptation length and time for the STG method are evaluated. Also, we compare the STG-LBM channel flow results with the existing LBM synthetic eddy method (SEM-LBM) results. Our numerical investigations show good agreement with the DNS and periodic LES-LBM channel flow within a short adaptation length. The adaptation time for the turbulent channel flow is quantitatively analyzed and matches the DNS around 1.5–3 domain flow-through time. Finally, we check the auto-correlation for the velocity components at different cross sections of the streamwise direction. The proposed STG-LBM is observed to be both fast and robust. The findings show good potential for the hybrid RANS/LES-LBM based solver on the aerodynamics simulations and a broad spectrum of engineering applications.
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Zhang, Bin, Jieke Yao, Min Zhang, and Xiao Hu. "An adaptive lattice boltzmann method based on nodal linked-list data structure." Journal of Physics: Conference Series 2551, no. 1 (July 1, 2023): 012020. http://dx.doi.org/10.1088/1742-6596/2551/1/012020.
Анотація:
Abstract An adaptive mesh refinement (AMR) technique based on nodal linked-list data structure for lattice Boltzmann method (LBM) is proposed in this paper. It makes connections between nodal linked-list data structure which is hierarchical and LBM calculation to retain the simplicity of LBM. Based on uniform meshes, the adaptive algorithm refines the meshes by constructing the linked-list of nodes and levels for mesh levels refined. In the nodal linked-list data structure, the relationships for nodal neighbors and upper and lower level indexes of nodes are appointed to help implement the LBM process in the different mesh levels. To guarantee precise transmission of flow field information and numerical stability in the different mesh levels, the average interpolation for temporal and spatial space is used, which chimes in with the accuracy of LBM itself. To verify the present method, flows over square cylinder at Re=30 and circle cylinder at Re=200 are carried out.
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Wang, Yan, Chang Shu, Chiang Juay Teo, Jie Wu, and Liming Yang. "Three-Dimensional Lattice Boltzmann Flux Solver and Its Applications to Incompressible Isothermal and Thermal Flows." Communications in Computational Physics 18, no. 3 (September 2015): 593–620. http://dx.doi.org/10.4208/cicp.300514.160115a.
Анотація:
AbstractA three-dimensional (3D) lattice Boltzmann flux solver (LBFS) is presented in this paper for the simulation of both isothermal and thermal flows. The present solver combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. It applies the finite volume method (FVM) to solve the N-S equations. Different from the conventional N-S solvers, its viscous and inviscid fluxes at the cell interface are evaluated simultaneously by local reconstruction of LBE solution. As compared to the conventional LBE solvers, which apply the lattice Boltzmann method (LBM) globally in the whole computational domain, it only applies LBM locally at each cell interface, and flow variables at cell centers are given from the solution of N-S equations. Since LBM is only applied locally in the 3D LBFS, the drawbacks of the conventional LBM, such as limitation to uniform mesh, tie-up of mesh spacing and time step, tedious implementation of boundary conditions, are completely removed. The accuracy, efficiency and stability of the proposed solver are examined in detail by simulating plane Poiseuille flow, lid-driven cavity flow and natural convection. Numerical results show that the LBFS has a second order of accuracy in space. The efficiency of the LBFS is lower than LBM on the same grids. However, the LBFS needs very less non-uniform grids to get grid-independence results and its efficiency can be greatly improved and even much higher than LBM. In addition, the LBFS is more stable and robust.
47
WANG, P., and S. Q. ZHANG. "A SIMPLE METHOD TO CONSTRUCT LOCAL EQUILIBRIUM FUNCTION FOR LATTICE BOLTZMANN METHOD." International Journal of Modern Physics C 24, no. 06 (May 2013): 1350038. http://dx.doi.org/10.1142/s0129183113500381.
Анотація:
We have developed a simple method to construct local equilibrium function for lattice Boltzmann method (LBM). This new method can make LBM model satisfy compressible flow with a flexible specific-heat ratio. Test cases, including the one-dimensional Sod flow, one-dimensional Lax flow and thermal Couette flow are presented. Good results obtained using proposed new method, indicate that the proposed method is potentially capable of constructing of the local equilibrium function for LBM.
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PATIL, D. V., K. N. PREMNATH, D. DESAI, and SANJOY BANERJEE. "ELECTRODEPOSITION MODELING USING COUPLED PHASE-FIELD AND LATTICE BOLTZMANN APPROACH." International Journal of Modern Physics C 25, no. 01 (December 2, 2013): 1340018. http://dx.doi.org/10.1142/s0129183113400184.
Анотація:
In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg–Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO 4 solution.
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AMATI, G., F. MASSAIOLI, G. GONNELLA, AIGUO XU, and A. LAMURA. "THREE-DIMENSIONAL LATTICE BOLTZMANN MODEL RESULTS FOR COMPLEX FLUIDS ORDERING." International Journal of Modern Physics C 16, no. 12 (December 2005): 1819–30. http://dx.doi.org/10.1142/s0129183105008345.
Анотація:
The kinetics of domain growth of fluid mixtures quenched from a disordered to a lamellar phase has been studied in three dimensions. We use a numerical approach based on the lattice Boltzmann method (LBM). A novel implementation for LBM which "fuses" the collision and streaming steps is used in order to reduce memory and bandwidth requirements. We find that extended defects between stacks of lamellae with different orientation dominate the late time dynamics.
50
Sun, Yifang, Sen Zou, Guang Zhao, and Bei Yang. "THE IMPROVEMENT AND REALIZATION OF FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD." Aerospace technic and technology, no. 1 (February 26, 2021): 4–13. http://dx.doi.org/10.32620/aktt.2021.1.01.
Анотація:
The Lattice Boltzmann Method (LBM) is a numerical method developed in recent decades. It has the characteristics of high parallel efficiency and simple boundary processing. The basic idea is to construct a simplified dynamic model so that the macroscopic behavior of the model is the same as the macroscopic equation. From the perspective of micro-dynamics, LBM treats macro-physical quantities as micro-quantities to obtain results by statistical averaging. The Finite-difference LBM (FDLBM) is a new numerical method developed based on LBM. The first finite-difference LBE (FDLBE) was perhaps due to Tamura and Akinori and was examined by Cao et al. in more detail. Finite-difference LBM was further extended to curvilinear coordinates with nonuniform grids by Mei and Shyy. By improving the FDLBE proposed by Mei and Shyy, a new finite difference LBM is obtained in the paper. In the model, the collision term is treated implicitly, just as done in the Mei-Shyy model. However, by introducing another distribution function based on the earlier distribution function， the implicitness of the discrete scheme is eliminated, and a simple explicit scheme is finally obtained, such as the standard LBE. Furthermore, this trick for the FDLBE can also be easily used to develop more efficient FVLBE and FELBE schemes. To verify the correctness and feasibility of this improved FDLBM model, which is used to calculate the square cavity model, and the calculated results are compared with the data of the classic square cavity model. The comparison result includes two items: the velocity on the centerline of the square cavity and the position of the vortex center in the square cavity. The simulation results of FDLBM are very consistent with the data in the literature. When Re=400, the velocity profiles of u and v on the centerline of the square cavity are consistent with the data results in Ghia's paper, and the vortex center position in the square cavity is also almost the same as the data results in Ghia's paper. Therefore, the verification of FDLBM is successful and FDLBM is feasible. This improved method can also serve as a reference for subsequent research.