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Journal articles on the topic 'Lattice Boltzmann scheme'

Author: Grafiati

Published: 16 September 2023

Last updated: 31 July 2025

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1

Dubois, François, and Pierre Lallemand. "On Triangular Lattice Boltzmann Schemes for Scalar Problems." Communications in Computational Physics 13, no. 3 (2013): 649–70. http://dx.doi.org/10.4208/cicp.381011.270112s.

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AbstractWe propose to extend the d’Humieres version of the lattice Boltzmann scheme to triangular meshes. We use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed to be constant. On such meshes, it is possible to define the lattice Boltzmann scheme as a discrete particle method, without need of finite volume formulation or Delaunay-Voronoi hypothesis for the lattice. We test this idea for the heat equation and perform an asymptotic analysis with the Taylor expansion method for two schemes named D2T4 and D2T7. The results show a conv

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2

Xu, Kun, and Li-Shi Luo. "Connection Between Lattice-Boltzmann Equation and Beam Scheme." International Journal of Modern Physics C 09, no. 08 (1998): 1177–87. http://dx.doi.org/10.1142/s0129183198001072.

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In this paper we analyze and compare the lattice-Boltzmann equation with the beam scheme in detail. We notice the similarity and differences between the lattice Boltzmann equation and the beam scheme. We show that the accuracy of the lattice-Boltzmann equation is indeed second order in space. We discuss the advantages and limitations of the lattice-Boltzmann equation and the beam scheme. Based on our analysis, we propose an improved multi-dimensional beam scheme.

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Venturi, Sara, Silvia Di Francesco, Martin Geier, and Piergiorgio Manciola. "Forcing for a Cascaded Lattice Boltzmann Shallow Water Model." Water 12, no. 2 (2020): 439. http://dx.doi.org/10.3390/w12020439.

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This work compares three forcing schemes for a recently introduced cascaded lattice Boltzmann shallow water model: a basic scheme, a second-order scheme, and a centred scheme. Although the force is applied in the streaming step of the lattice Boltzmann model, the acceleration is also considered in the transformation to central moments. The model performance is tested for one and two dimensional benchmarks.

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4

Gao, Shangwen, Chengbin Zhang, Yingjuan Zhang, Qiang Chen, Bo Li, and Suchen Wu. "Revisiting a class of modified pseudopotential lattice Boltzmann models for single-component multiphase flows." Physics of Fluids 34, no. 5 (2022): 057103. http://dx.doi.org/10.1063/5.0088246.

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Since its emergence, the pseudopotential lattice Boltzmann (LB) method has been regarded as a straightforward and practical approach for simulating single-component multiphase flows. However, its original form always results in a thermodynamic inconsistency, which, thus, impedes its further application. Several strategies for modifying the force term have been proposed to eliminate this limitation. In this study, four typical and widely used improved schemes—Li's single-relaxation-time (SRT) scheme [Li et al., “Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows,” Ph

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Qiu, Ruofan, Rongqian Chen, and Yancheng You. "An implicit-explicit finite-difference lattice Boltzmann subgrid method on nonuniform meshes." International Journal of Modern Physics C 28, no. 04 (2017): 1750045. http://dx.doi.org/10.1142/s0129183117500450.

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In this paper, an implicit-explicit finite-difference lattice Boltzmann method with subgrid model on nonuniform meshes is proposed. The implicit-explicit Runge–Kutta scheme, which has good convergence rate, is used for the time discretization and a mixed difference scheme, which combines the upwind scheme with the central scheme, is adopted for the space discretization. Meanwhile, the standard Smagorinsky subgrid model is incorporated into the finite-difference lattice Boltzmann scheme. The effects of implicit-explicit Runge–Kutta scheme and nonuniform meshes of present lattice Boltzmann metho

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van der Sman, R. G. M., and M. H. Ernst. "Convection-Diffusion Lattice Boltzmann Scheme for Irregular Lattices." Journal of Computational Physics 160, no. 2 (2000): 766–82. http://dx.doi.org/10.1006/jcph.2000.6491.

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7

LALLEMAND, PIERRE, and LI-SHI LUO. "HYBRID FINITE-DIFFERENCE THERMAL LATTICE BOLTZMANN EQUATION." International Journal of Modern Physics B 17, no. 01n02 (2003): 41–47. http://dx.doi.org/10.1142/s0217979203017060.

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We analyze the acoustic and thermal properties of athermal and thermal lattice Boltzmann equation (LBE) in 2D and show that the numerical instability in the thermal lattice Boltzmann equation (TLBE) is related to the algebraic coupling among different modes of the linearized evolution operator. We propose a hybrid finite-difference (FD) thermal lattice Boltzmann equation (TLBE). The hybrid FD-TLBE scheme is far superior over the existing thermal LBE schemes in terms of numerical stability. We point out that the lattice BGK equation is incompatible with the multiple relaxation time model.

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8

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 (2022): 037114. http://dx.doi.org/10.1063/5.0085370.

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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 e

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9

Van Der Sman, R. G. M. "Lattice-Boltzmann Scheme for Natural Convection in Porous Media." International Journal of Modern Physics C 08, no. 04 (1997): 879–88. http://dx.doi.org/10.1142/s0129183197000758.

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A lattice-Boltzmann scheme for natural convection in porous media is developed and applied to the heat transfer problem of a 1000 kg potato packaging. The scheme has features new to the field of LB schemes. It is mapped on a orthorhombic lattice instead of the traditional cubic lattice. Furthermore the boundary conditions are formulated with a single paradigm based upon the particle fluxes. Our scheme is well able to reproduce (1) the analytical solutions of simple model problems and (2) the results from cooling down experiments with potato packagings.

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10

Wang, Liang, Zhaoli Guo, Baochang Shi, and Chuguang Zheng. "Evaluation of Three Lattice Boltzmann Models for Particulate Flows." Communications in Computational Physics 13, no. 4 (2013): 1151–72. http://dx.doi.org/10.4208/cicp.160911.200412a.

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AbstractA comparative study is conducted to evaluate three types of lattice Boltzmann equation (LBE) models for fluid flows with finite-sized particles, including the lattice Bhatnagar-Gross-Krook (BGK) model, the model proposed by Ladd [Ladd AJC, J. Fluid Mech., 271, 285-310 (1994); Ladd AJC, J. Fluid Mech., 271, 311-339 (1994)], and the multiple-relaxation-time (MRT) model. The sedimentation of a circular particle in a two-dimensional infinite channel under gravity is used as the first test problem. The numerical results of the three LBE schemes are compared with the theoretical results and

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11

SOFONEA, VICTOR, and ROBERT F. SEKERKA. "DIFFUSIVITY OF TWO-COMPONENT ISOTHERMAL FINITE DIFFERENCE LATTICE BOLTZMANN MODELS." International Journal of Modern Physics C 16, no. 07 (2005): 1075–90. http://dx.doi.org/10.1142/s0129183105007741.

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Diffusion equations are derived for an isothermal lattice Boltzmann model with two components. The first-order upwind finite difference scheme is used to solve the evolution equations for the distribution functions. When using this scheme, the numerical diffusivity, which is a spurious diffusivity in addition to the physical diffusivity, is proportional to the lattice spacing and significantly exceeds the physical value of the diffusivity if the number of lattice nodes per unit length is too small. Flux limiter schemes are introduced to overcome this problem. Empirical analysis of the results

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12

MILLER, W. "CRYSTAL GROWTH KINETICS AND FLUID FLOW." International Journal of Modern Physics B 17, no. 01n02 (2003): 227–30. http://dx.doi.org/10.1142/s0217979203017394.

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A new type of a lattice phase-field model is developed and coupled with the lattice Boltzmann method to compute the soldification influenced by convection. Two methods of treating the solid-fluid interaction within the lattice Boltzmann scheme are tested.

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13

WANG, Y., Y. L. HE, T. S. ZHAO, G. H. TANG, and W. Q. TAO. "IMPLICIT-EXPLICIT FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD FOR COMPRESSIBLE FLOWS." International Journal of Modern Physics C 18, no. 12 (2007): 1961–83. http://dx.doi.org/10.1142/s0129183107011868.

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We propose an implicit-explicit finite-difference lattice Boltzmann method for compressible flows in this work. The implicit-explicit Runge–Kutta scheme, which solves the relaxation term of the discrete velocity Boltzmann equation implicitly and other terms explicitly, is adopted for the time discretization. Owing to the characteristic of the collision invariants in the lattice Boltzmann method, the implicitness can be completely eliminated, and thus no iteration is needed in practice. In this fashion, problems (no matter stiff or not) can be integrated quickly with large Courant–Friedriche–Le

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14

Wang, Boyu. "A splitting lattice Boltzmann scheme for (2+1)-dimensional soliton solutions of the Kadomtsev-Petviashvili equation." AIMS Mathematics 8, no. 11 (2023): 28071–89. http://dx.doi.org/10.3934/math.20231436.

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<abstract> <p>Recently, considerable attention has been given to (2+1)-dimensional Kadomtsev-Petviashvili equations due to their extensive applications in solitons that widely exist in nonlinear science. Therefore, developing a reliable numerical algorithm for the Kadomtsev-Petviashvili equations is crucial. The lattice Boltzmann method, which has been an efficient simulation method in the last three decades, is a promising technique for solving Kadomtsev-Petviashvili equations. However, the traditional higher-order moment lattice Boltzmann model for the Kadomtsev-Petviashvili equa

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15

Ma, Huifang, Bin Wu, Ying Wang, et al. "A Novel Lattice Boltzmann Scheme with Single Extended Force Term for Electromagnetic Wave Propagating in One-Dimensional Plasma Medium." Electronics 11, no. 6 (2022): 882. http://dx.doi.org/10.3390/electronics11060882.

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A one-dimensional plasma medium is playing a crucial role in modern sensing device design, which can benefit significantly from numerical electromagnetic wave simulation. In this study, we introduce a novel lattice Boltzmann scheme with a single extended force term for electromagnetic wave propagation in a one-dimensional plasma medium. This method is developed by reconstructing the solution to the macroscopic Maxwell’s equations recovered from the lattice Boltzmann equation. The final formulation of the lattice Boltzmann scheme involves only the equilibrium and one non-equilibrium force term.

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16

TAKADA, NAOKI, AKIO TOMIYAMA, and SHIGEO HOSOKAWA. "LATTICE BOLTZMANN SIMULATION OF INTERFACIAL DEFORMATION." International Journal of Modern Physics B 17, no. 01n02 (2003): 179–82. http://dx.doi.org/10.1142/s0217979203017308.

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This study describes the numerical simulations of two-phase interfacial deformations using the binary fluid (BF) model in the lattice Boltzmann method (LBM), where a macroscopic fluid involves mesoscopic particles repeating collisions and propagations and an interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. Schemes for the BF model are proposed to simulate motions of immiscible two phases with different mass densities. For higher Reynolds number, the finite difference-based lattice Boltzmann scheme is applied to the kinetic equation

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17

ZHOU, JIAN GUO. "LATTICE BOLTZMANN SIMULATIONS OF DISCONTINUOUS FLOWS." International Journal of Modern Physics C 18, no. 01 (2007): 1–14. http://dx.doi.org/10.1142/s0129183107010280.

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The lattice Boltzmann model for the shallow water equations (LABSWE) is applied to the simulation of certain discontinuous flows. Curved boundaries are treated efficiently, using either the elastic-collision scheme for slip and semi-slip boundary conditions or the bounce-back scheme for no-slip conditions. The force term is accurately determined by means of the centred scheme. Simulations are presented of a small pulse-like perturbation of the still water surface, a dam break, and a surge wave interaction with a circular cylinder. The results agree well with predictions from alternative high-r

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18

Krivovichev, Gerasim Vladimirovich. "On the stability of lattice boltzmann equations for one-dimensional diffusion equation." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 01 (2017): 1750013. http://dx.doi.org/10.1142/s1793962317500131.

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Stability analysis of lattice Boltzmann equations (LBEs) on initial conditions for one-dimensional diffusion is performed. Stability of the solution of the Cauchy problem for the system of linear Bhatnaghar–Gross–Krook kinetic equations is demonstrated for the cases of D1Q2 and D1Q3 lattices. Stability of the scheme for D1Q2 lattice is analytically analyzed by the method of differential approximation. Stability of parametrical scheme is numerically investigated by von Neumann method in parameter space. As a result of numerical analysis, the correction of the hypothesis on transfer of stability

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19

Succi, S., and P. Vergari. "A Lattice Boltzmann Scheme for Semiconductor Dynamics." VLSI Design 6, no. 1-4 (1998): 137–40. http://dx.doi.org/10.1155/1998/54940.

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20

Xu, Hailin, Yuxin Wang, and Longzhou Jian. "Mitigating spurious currents at the three phase interfaces in pseudo-potential lattice boltzmann simulations of contact angles via equations of state and forcing schemes." Journal of Physics: Conference Series 3021, no. 1 (2025): 012086. https://doi.org/10.1088/1742-6596/3021/1/012086.

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Abstract Thermodynamic inconsistency, manifesting as large spurious currents near three-phase interfaces, remains a significant challenge in pseudopotential lattice Boltzmann simulations of contact angles. Previous solutions have primarily involved equations of state (EOSs) and forcing schemes. This work examines the incorporation of diverse EOSs and forcing schemes into a single-component multiphase lattice Boltzmann model. A thorough evaluation of phase separation in these nonideal single-component systems is provided through a comparison of numerical simulation outcomes of spurious currents

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21

NOR AZWADI, C. S., and T. TANAHASHI. "SIMPLIFIED THERMAL LATTICE BOLTZMANN IN INCOMPRESSIBLE LIMIT." International Journal of Modern Physics B 20, no. 17 (2006): 2437–49. http://dx.doi.org/10.1142/s0217979206034789.

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In this paper, an incompressible thermohydrodynamics for the lattice Boltzmann scheme is developed. The basic idea is to solve the velocity field and the temperature field using two different distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation is discussed in detail. By using the same procedure as in the derivation of the discretised density distribution function, we found that a new lattice of four-velocity model for internal energy density distribution function can be developed where the viscous and compressive heating effects are negli

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22

SUGA, SHINSUKE. "STABILITY AND ACCURACY OF LATTICE BOLTZMANN SCHEMES FOR ANISOTROPIC ADVECTION-DIFFUSION EQUATIONS." International Journal of Modern Physics C 20, no. 04 (2009): 633–50. http://dx.doi.org/10.1142/s0129183109013856.

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The stability of the numerical schemes for anisotropic advection-diffusion equations derived from the lattice Boltzmann equation with the D2Q4 particle velocity model is analyzed through eigenvalue analysis of the amplification matrices of the scheme. Accuracy of the schemes is investigated by solving benchmark problems, and the LBM scheme is compared with traditional implicit schemes. Numerical experiments demonstrate that the LBM scheme produces stable numerical solutions close to the analytical solutions when the values of the relaxation parameters in x and y directions are greater than 1.9

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23

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.

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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

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24

Delouei, A. Amiri, M. Nazari, M. H. Kayhani, and S. Succi. "Immersed Boundary – Thermal Lattice Boltzmann Methods for Non-Newtonian Flows Over a Heated Cylinder: A Comparative Study." Communications in Computational Physics 18, no. 2 (2015): 489–515. http://dx.doi.org/10.4208/cicp.060414.220115a.

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AbstractIn this study, we compare different diffuse and sharp interface schemes of direct-forcing immersed boundary — thermal lattice Boltzmann method (IB-TLBM) for non-Newtonian flow over a heated circular cylinder. Both effects of the discrete lattice and the body force on the momentum and energy equations are considered, by applying the split-forcing Lattice Boltzmann equations. A new technique based on predetermined parameters of direct forcing IB-TLBM is presented for computing the Nusselt number. The study covers both steady and unsteady regimes (20<Re<80) in the power-law index ra

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25

Li, Qiaojie, Zhoushun Zheng, Shuang Wang, and Jiankang Liu. "A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/925920.

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An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. TheL2, L∞and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.

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26

Ilyin, Oleg. "Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising." Mathematics 11, no. 22 (2023): 4601. http://dx.doi.org/10.3390/math11224601.

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In the present paper, a novel approach for image denoising based on the numerical solution to the nonlinear diffusion equation is proposed. The Perona–Malik-type equation is solved by employing a hybrid lattice Boltzmann model with five discrete velocities. In this method, the regions with large values of the diffusion coefficient are modeled with the lattice Boltzmann scheme for which hyper-viscous defects are reduced, while other regions are modeled with the conventional lattice Boltzmann model. The new method allows us to solve Perona–Malik-type equations with relatively large time steps an

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27

XUAN, Yimin. "Application of lattice Boltzmann scheme to nanofluids." Science in China Series E 47, no. 2 (2004): 129. http://dx.doi.org/10.1360/03ye0163.

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28

Dubois, François, Pierre Lallemand, and Mahdi Tekitek. "On a superconvergent lattice Boltzmann boundary scheme." Computers & Mathematics with Applications 59, no. 7 (2010): 2141–49. http://dx.doi.org/10.1016/j.camwa.2009.08.055.

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29

Succi, S., M. Vergassola, and R. Benzi. "Lattice Boltzmann scheme for two-dimensional magnetohydrodynamics." Physical Review A 43, no. 8 (1991): 4521–24. http://dx.doi.org/10.1103/physreva.43.4521.

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30

ZHENG, H. W., and C. SHU. "EVALUATION OF THE PERFORMANCE OF THE HYBRID LATTICE BOLTZMANN BASED NUMERICAL FLUX." International Journal of Modern Physics: Conference Series 42 (January 2016): 1660152. http://dx.doi.org/10.1142/s2010194516601526.

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It is well known that the numerical scheme is a key factor to the stability and accuracy of a Navier-Stokes solver. Recently, a new hybrid lattice Boltzmann numerical flux (HLBFS) is developed by Shu's group. It combines two different LBFS schemes by a switch function. It solves the Boltzmann equation instead of the Euler equation. In this article, the main object is to evaluate the ability of this HLBFS scheme by our in-house cell centered hybrid mesh based Navier-Stokes code. Its performance is examined by several widely-used bench-mark test cases. The comparisons on results between calculat

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31

Haussmann, Marc, Stephan Simonis, Hermann Nirschl, and Mathias J. Krause. "Direct numerical simulation of decaying homogeneous isotropic turbulence — numerical experiments on stability, consistency and accuracy of distinct lattice Boltzmann methods." International Journal of Modern Physics C 30, no. 09 (2019): 1950074. http://dx.doi.org/10.1142/s0129183119500748.

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Stability, consistency and accuracy of various lattice Boltzmann schemes are investigated by means of numerical experiments on decaying homogeneous isotropic turbulence (DHIT). Therefore, the Bhatnagar–Gross–Krook (BGK), the entropic lattice Boltzmann (ELB), the two-relaxation-time (TRT), the regularized lattice Boltzann (RLB) and the multiple-relaxation-time (MRT) collision schemes are applied to the three-dimensional Taylor–Green vortex, which represents a benchmark case for DHIT. The obtained turbulent kinetic energy, the energy dissipation rate and the energy spectrum are compared to refer

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ZHOU, J. G. "AN ELASTIC-COLLISION SCHEME FOR LATTICE BOLTZMANN METHODS." International Journal of Modern Physics C 12, no. 03 (2001): 387–401. http://dx.doi.org/10.1142/s0129183101001833.

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An elastic-collision scheme is developed to achieve slip and semi-slip boundary conditions for lattice Boltzmann methods. Like the bounce-back scheme, the proposed scheme is efficient, robust and generally suitable for flows in arbitrary complex geometries. It involves an equivalent level of computation effort to the bounce-back scheme. The new scheme is verified by predicting wind-driven circulating flows in a dish-shaped basin and a flow in a strongly bent channel, showing good agreement with analytical solutions and experimental data. The capability of the scheme for simulating flows throug

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Zhang, Raoyang, Chenghai Sun, Yanbing Li, et al. "Lattice Boltzmann Approach for Local Reference Frames." Communications in Computational Physics 9, no. 5 (2011): 1193–205. http://dx.doi.org/10.4208/cicp.021109.111110s.

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AbstractIn this paper we present a generalized lattice Boltzmann based approach for sliding-mesh local reference frame. This scheme exactly conserves hydrodynamic fluxes across local reference frame interface. The accuracy and robustness of our scheme are demonstrated by benchmark validations.

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PAN, X. F., AIGUO XU, GUANGCAI ZHANG, and SONG JIANG. "LATTICE BOLTZMANN APPROACH TO HIGH-SPEED COMPRESSIBLE FLOWS." International Journal of Modern Physics C 18, no. 11 (2007): 1747–64. http://dx.doi.org/10.1142/s0129183107011716.

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We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara15 and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number u

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BERNASCHI, MASSIMO, and SAURO SUCCI. "ACCELERATED LATTICE BOLTZMANN SCHEME FOR STEADY-STATE FLOWS." International Journal of Modern Physics B 17, no. 01n02 (2003): 1–7. http://dx.doi.org/10.1142/s021797920301700x.

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Yahia, Eman, William Schupbach, and Kannan N. Premnath. "Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows." Fluids 6, no. 9 (2021): 326. http://dx.doi.org/10.3390/fluids6090326.

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Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these paramet

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37

Liu, Ning Ning. "The Numerical Solution of Richards Equation Using the Lattice Boltzmann Method." Applied Mechanics and Materials 188 (June 2012): 90–95. http://dx.doi.org/10.4028/www.scientific.net/amm.188.90.

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The Richards equation is applied to describe the unsaturated soil moisture movement. The Lattice Boltzmann method is developed to solve this partial differential equation. The accuracy and efficiency of the Lattice Boltzmann method in modeling unsaturated soil moisture movement are compared to the Philip series method as well as Crank-Nicolson finite difference scheme. The results reveal that all three methods provide solutions of comparable accuracy. The computation efficiency, accuracy and simplicity of the Lattice Boltzmann method indicate that it has the capacity to model unsaturated soil

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JI, C. Z., C. SHU, and N. ZHAO. "A LATTICE BOLTZMANN METHOD-BASED FLUX SOLVER AND ITS APPLICATION TO SOLVE SHOCK TUBE PROBLEM." Modern Physics Letters B 23, no. 03 (2009): 313–16. http://dx.doi.org/10.1142/s021798490901828x.

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This paper presents an approach, which combines the conventional finite volume method (FVM) with the lattice Boltzmann Method (LBM), to simulate compressible flows. Similar to the Godunov scheme, in the present approach, LBM is used to evaluate the flux at the interface for local Riemann problem when solving Euler/Navier-Stokes (N-S) equations by FVM. Two kinds of popular compressible Lattice Boltzmann models are applied in the new scheme, and some numerical experiments are performed to validate the proposed approach. From the sharper shock profile and higher computational efficiency, numerica

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CHEN, Q., and X. B. ZHANG. "A NOVEL LESS DISSIPATION FINITE-DIFFERENCE LATTICE BOLTZMANN SCHEME FOR COMPRESSIBLE FLOWS." International Journal of Modern Physics C 23, no. 11 (2012): 1250074. http://dx.doi.org/10.1142/s012918311250074x.

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In this paper, a new smoothness indicator is proposed to improve the finite-difference lattice Boltzmann method (FDLBM). The necessary and sufficient conditions for convergence are derived. A detailed analysis reveals that the convergence order is higher than that of the previous finite-difference scheme. The coupled double distribution function (DDF) model is used to describe discontinuity flows and verify the improvement. Numerical simulations of compressible flows with shock wave show that the improved finite-difference lattice Boltzmann scheme is accurate and has less dissipation. The nume

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ZHOU, JIAN GUO. "MRT RECTANGULAR LATTICE BOLTZMANN METHOD." International Journal of Modern Physics C 23, no. 05 (2012): 1250040. http://dx.doi.org/10.1142/s0129183112500404.

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A multiple-relaxation-time (MRT) collision operator is introduced into the author's rectangular lattice Boltzmann method for simulating fluid flows. The model retains both the advantages and the standard procedure of using a constant transformation matrix in the conventional MRT scheme on a square lattice, leading to easy implementation in the algorithm. This allows flow problems characterized by dominant feature in one direction to be solved more efficiently. Two numerical tests have been carried out and shown that the proposed model is able to capture complex flow characteristics and generat

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Zarghami, A., M. J. Maghrebi, J. Ghasemi, and S. Ubertini. "Lattice Boltzmann Finite Volume Formulation with Improved Stability." Communications in Computational Physics 12, no. 1 (2012): 42–64. http://dx.doi.org/10.4208/cicp.151210.140711a.

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AbstractThe most severe limitation of the standard Lattice Boltzmann Method is the use of uniform Cartesian grids especially when there is a need for high resolutions near the body or the walls. Among the recent advances in lattice Boltzmann research to handle complex geometries, a particularly remarkable option is represented by changing the solution procedure from the original “stream and collide” to a finite volume technique. However, most of the presented schemes have stability problems. This paper presents a stable and accurate finite-volume lattice Boltzmann formulation based on a cell-c

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Dubois, François. "Third order equivalent equation of lattice Boltzmann scheme." Discrete and Continuous Dynamical Systems 23, no. 1/2 (2008): 221–48. http://dx.doi.org/10.3934/dcds.2009.23.221.

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Krivovichev, G. V. "On the finite-element-based lattice Boltzmann scheme." Applied Mathematical Sciences 8 (2014): 1605–20. http://dx.doi.org/10.12988/ams.2014.4138.

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Halliday, I., L. A. Hammond, and C. M. Care. "Enhanced closure scheme for lattice Boltzmann equation hydrodynamics." Journal of Physics A: Mathematical and General 35, no. 12 (2002): L157—L166. http://dx.doi.org/10.1088/0305-4470/35/12/102.

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SETA, Takeshi, Koji KONO, Daniel MARTINEZ, and Shiyi CHEN. "Lattice Boltzmann Scheme for Simulating Two-Phase Flows." JSME International Journal Series B 43, no. 2 (2000): 305–13. http://dx.doi.org/10.1299/jsmeb.43.305.

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Ho, Jeng-Rong, Chun-Pao Kuo, Wen-Shu Jiaung, and Cherng-Jyh Twu. "LATTICE BOLTZMANN SCHEME FOR HYPERBOLIC HEAT CONDUCTION EQUATION." Numerical Heat Transfer, Part B: Fundamentals 41, no. 6 (2002): 591–607. http://dx.doi.org/10.1080/10407790190053798.

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SETA, Takeshi, Koji KONO, Daniel MARTINEZ, and Shiyi CHEN. "Lattice Boltzmann Scheme for Simulating Two-Phase Flows." Transactions of the Japan Society of Mechanical Engineers Series B 65, no. 634 (1999): 1955–63. http://dx.doi.org/10.1299/kikaib.65.1955.

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Tian, Zhi-Wei, Chun Zou, Hong-Juan Liu, Zhao-Li Guo, Zhao-Hui Liu, and Chu-Guang Zheng. "Lattice Boltzmann scheme for simulating thermal micro-flow." Physica A: Statistical Mechanics and its Applications 385, no. 1 (2007): 59–68. http://dx.doi.org/10.1016/j.physa.2007.01.021.

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Alvarez-Ramírez, José, Francisco J. Valdés-Parada, and J. Alberto Ochoa-Tapia. "A lattice-Boltzmann scheme for Cattaneo’s diffusion equation." Physica A: Statistical Mechanics and its Applications 387, no. 7 (2008): 1475–84. http://dx.doi.org/10.1016/j.physa.2007.10.051.

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Chen, Sheng, Zhaohui Liu, Zhiwei Tian, Baochang Shi, and Chuguang Zheng. "A simple lattice Boltzmann scheme for combustion simulation." Computers & Mathematics with Applications 55, no. 7 (2008): 1424–32. http://dx.doi.org/10.1016/j.camwa.2007.08.020.

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