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Journal ArticleDOI

Comparison of analysis techniques for the lattice Boltzmann method

01 Sep 2009-Computers & Mathematics With Applications (Pergamon Press, Inc.)-Vol. 58, Iss: 5, pp 883-897
TL;DR: It is shown that the Chapman-Enskog expansion can be viewed as a special instance of a general expansion procedure which also encompasses other methods like the regular error expansion and multi-scale techniques and that any two expansions which properly describe the lattice Boltzmann solution necessarily coincide up to higher order terms.
Abstract: We show that the Chapman-Enskog expansion can be viewed as a special instance of a general expansion procedure which also encompasses other methods like the regular error expansion and multi-scale techniques and that any two expansions which properly describe the lattice Boltzmann solution necessarily coincide up to higher order terms. For a model problem, both the regular error expansion and the Chapman-Enskog expansion are carried out. It turns out that the classical Chapman-Enskog method leads to an unstable equation at super-Burnett order in a parameter regime for which the underlying lattice Boltzmann algorithm is stable. However, our approach naturally allows us to consider variants of the super-Burnett equation which do not suffer from instabilities. The article concludes with a detailed comparison of the Chapman-Enskog and the regular error expansion.
Citations
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Journal ArticleDOI
Hiroaki Yoshida1, Makoto Nagaoka1
TL;DR: An asymptotic analysis of the model equation with boundary rules for the Dirichlet and Neumann-type (specified flux) conditions is carried out to show that the model is first- and second-order accurate in time and space, respectively.

283 citations


Cites background or methods from "Comparison of analysis techniques f..."

  • ...The classical Chapman–Enskog (CE) analysis is closely related to the asymptotic analysis [51]....

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  • ...Although the former is a powerful tool to show that the LBE reproduces certain partial differential equations, the dependence of the numerical solution on the expansion parameter is not immediately clear [51]....

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Journal ArticleDOI
TL;DR: In this article, a brief review of the application of lattice Boltzmann method on the prediction of nanofluid is provided, and opportunities for future research are identified.
Abstract: In recent years, the lattice Boltzmann method (LBM) has become an alternative and attractive approach to simulate numerous fluid flow problems. A colloidal mixture of nano-sized particles in a base liquid called nanofluid, which is the new generation of heat transfer fluid for various heat transfer applications, has recently been demonstrated to have great potential for improving the heat transfer properties of liquids. This paper intends to provide a brief review of researches on application of lattice Boltzmann method on the prediction of nanofluid and identifies opportunities for future research.

44 citations

Journal ArticleDOI
17 Dec 2015-Entropy
TL;DR: Some representative applications show the wide applicability of the momentum exchange method, such as movements of rigid particles, interactions of deformation particles, particle suspensions in turbulent flow and multiphase flow, etc.
Abstract: As a native scheme to evaluate hydrodynamic force in the lattice Boltzmann method, the momentum exchange method has some excellent features, such as simplicity, accuracy, high efficiency and easy parallelization. Especially, it is independent of boundary geometry, preventing from solving the Navier–Stokes equations on complex boundary geometries in the boundary-integral methods. We review the origination and main developments of the momentum exchange method in lattice Boltzmann simulations. Then several practical techniques to fill newborn fluid nodes are discussed for the simulations of fluid-structure interactions. Finally, some representative applications show the wide applicability of the momentum exchange method, such as movements of rigid particles, interactions of deformation particles, particle suspensions in turbulent flow and multiphase flow, etc.

21 citations

Journal ArticleDOI
TL;DR: Patil et al. as mentioned in this paper derived a modified partial differential equation from a numerical approximation of the discrete Boltzmann equation, and then the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms.
Abstract: The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

20 citations


Cites methods from "Comparison of analysis techniques f..."

  • ...The CE expansion has been extensively applied to recover the conservation equations from various formulations of LBE [12–25]....

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Journal ArticleDOI
TL;DR: In this article, the authors considered the permeable bounce-back scheme in the lattice Boltzmann (LB) method for incompressible flows, in which a fraction of the distribution function is bounced back and the remainder travels to the neighboring lattice points.
Abstract: We consider the permeable bounce-back scheme in the lattice Boltzmann (LB) method for incompressible flows, in which a fraction of the distribution function is bounced back and the remainder travels to the neighboring lattice points. An asymptotic analysis of the scheme is carried out in order to show that the fractional coefficient, referred to as the transmission–reflection coefficient, relates the pressure drop to the flow velocity. The derived relation, which clarifies the role played by the transmission–reflection coefficient in the macroscopic description, is helpful in using the scheme to simulate flows involving a pressure drop or gradient. The scheme is compared with the existing methods in which the transmission–reflection coefficient is employed, and the difference is clarified. As an application of the permeable bounce-back scheme, we perform an LB simulation for flows through porous media described by the Brinkman model.

18 citations


Cites methods from "Comparison of analysis techniques f..."

  • ...The asymptotic analysis is similar to the Chapman–Enskog analysis [6,7], which is the most widely used method for the analysis of the LB equation, but is essentially different in that the analysis proceeds order by order in the expansion in terms of the powers of the small parameter representing the grid interval [5]....

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References
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Journal ArticleDOI
TL;DR: An overview of the lattice Boltzmann method, a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities, is presented.
Abstract: We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

6,565 citations

Book
01 Jan 1969
TL;DR: In this paper, the authors present a simulation of a free jet expansion of a high-energy scattering of molecular beams in the presence of high-temperature Viscosity cross sections.
Abstract: Collisional Processes.- Analytical Formulae for Cross Sections and Rate Constants of Elementary Processes in Gases.- Relaxation of Velocity Distribution of Electrons Cooled (Heated) By Rotational Excitation (De-Excitation) Of N2.- Effects of the Initial Molecular States in a High-Energy Scattering of Molecular Beams.- Differential Cross Sections for Ion-Pair Formation with Selection of the Exit Channel.- Low-temperature Viscosity Cross Sections Measured in a Supersonic Argon Beam II.- Excited Oxygen Iodine Kinetic Studies.- Determination of Antisymmetric Mode Energy of CO2 Injected into a Supersonic Nitrogen Flow.- Molecular Beams.- Where are we going with molecular beams?.- Cesium Vapor Jettarget Produced With a Supersonic Nozzle.- Basic Features of the Generation and Diagnostics of Atomic Hydrogen Beams in the Ground and Metastable 22S1/2-States to Determine the Fundamental Physical Constants.- Optical Pumping Of Metastable Neon Atoms in A Weak Magnetic Field.- CO2-Laser Excitation of a Molecular Beam Monitored By Spontaneous Raman Effect.- Time-of-Flight and Electron Beam Fluorescence Diagnostics: Optimal Experimental Designs.- Molecular Beam Time-of-Flight Measurements in A Nearly Freejet Expansion of High Temperature Gas Produced By a Shock Tube.- Electron Beam Diagnostics.- Electron-Beam Diagnostics of High Temperature Rarefied Gas Flows.- Excitation Models Used in the Electron Beam Fluorescence Technique.- Electron - Beam Diagnostics in Nitrogen Multiquantum Rotational Transitions.- Free Jets, Nonequilibrium Expansions.- Free Jet as an Object of Nonequilibrium Processes Investigation.- State Dependent Angular Distributions of Na2 Molecules in a Na/Na2 Free Jet Expansion.- Molecular Beam Time-of-Flight Measurements and Moment Method Calculations of Translational Relaxation in Highly Heated Free Jets of Monatomic Gas Mixtures.- Rovibrational State Population Distributions of CO (v ? 4, J ? 10) In Highly Heated Supersonic Free Jets of CO-N2 Mixtures.- Free Jet Expansion with A Strong Condensation Effect.- Measured Densities in UF6 Free Jets.- Rotational Relaxation of NO in Seeded, Pulsed Nozzle Beams.- The Free-Jet Expansion from a Capillary Source.- Rotational Relaxation in High Temperature Jets of Nitrogen.- Translational Nonequilibrium in a Free Jet Expansion of a Binary Gas Mixture.- Laser Induced Fluorescence Study of Free Jet Expansions.- Jet-Surface Interactions.- Experimental Study of Plume Impingement and Heating Effect on Ariane's Payload.- The Interaction of a Jet Exhausting from a Body with a Supersonic Free Flow of a Rarefied Gas.- Modelling Control Thruster Plume Flow and Impingement.- Impingement of a Supersonic, Underexpanded Rarefied Jet upon a Flat Plate.- Some Peculiarities of Power and Heat Interaction of a Low Density Highly Underexpanded Jet with a Flat Plate.- Condensation in Flows.- Nonequilibrium Condensation in Free Jets.- Condensation and Vapour-Liquid Interaction in a Reflected Shock Region.- Homogeneous and Heterogeneous Condensation of Nitrogen in Transonic Flow.- Investigation of Nonequilibrium Homogeneous Gas Condensation.- The Peculiarities of Condensation Process in Conical Nozzle and in Free Jet Behind it.- Investigation of Nonequilibrium Argon Condensation In Supersonic Jet By Mass-Spectrometry, Electron Diffraction and VUV Emission Spectroscopy.- Clusters and Nucleation Kinetics.- The Microscopic Theory of Clustering and Nucleation.- Kinetics of Cluster Formation and Growth in the Process of Isothermal Condensation.- Relaxation Processes in a Molecular Dynamic Model of Cluster from the Lennard-Jones Particles.- Quantum-Chemical Study Of Processes With Cluster Isomerism.- The Homogeneous Nucleation at the Continuously Changing Temperature and Vapour Concentration.- Molecular Clusters as Heterogeneous Condensation Nuclei.- Experiments with Clusters.- The Photochemistry of Small van der Waals Molecules as Studied by Laser Spectroscopy in Supersonic Free Jets.- Diagnostics of Clusters in Molecular Beams.- Experimental Studies of Water-Aerosol Explosive Vaporization.- Laser Probing of Cluster Formation and Dissociation in Molecular Beams.- Free Molecule Drag on Helium Clusters.- Vibrational Relaxation Kinetics in a Two-Phase Gas-Cluster System.- Gas-Particle Flows.- Long-Range Attraction in the Collisions of Free-Molecular and Transition Regime Aerosol Particles.- Nonequilibrium Statistical Theory of Dispersed Systems.- The Mechanism of Strong Electric Field Effect on the Dispersed Media in the Rarefied Gas.- Generation of High-Speed Aerosol Beams By Laval Nozzles.- Kinetic Model of a Gas Suspension.- Gas Mixtures.- Kinetic Phenomena in the Rarefied Gas Mixtures Flowing Through Channels.- On the Discrete Boltzmann Equation for Binary Gas Mixtures.- Peculiarities and Applicability Conditions of Macroscopic Description of Disparate Molecular Masses Mixture Motion.- Numerical Solution of the Boltzmann Kinetic Equation for the Binary Gas Mixture.- Species Isotope Separation.- Gas or Isotope Separation by Injection into Light Gas Flow.- Molecular Diffusion Through a Fine-Pored Filter Versus Resonante IR-Radiation Intensity.- On Limiting Situations of Gas Dynamic Separation.- A Study of Reverse Leaks.- Investigation of Nonequilibrium Effects in Separation Nozzles by Monte-Carlo Simulation.- Separation of Binary Gas Mixtures at their Effusion through a Capillary and a Nuclear Filler into Vacuum.- Ionized Gases.- Effects of Nonideality in Quantum Kinetic Theory.- Molecular Mass and Heat Transfer of Chemical Equilibrium Multicomponent Partially Ionized Gases in Electromagnetic Field.- Spectroscopic Study of a Plasma Flow along the Stagnation Streamline of a Blunt Body.- On Model Kinetic Operators and Corresponding Langevin Sources for a Non-Equilibrium Plasma.- Related Fields.- Rarefied Gas Dynamics as Related to Controlled Thermonuclear Fusion.- Vacuum Ejectors with Appreciably Uneven Flows in Channels at Low Reynolds Numbers.- Simulation of the Process of the Cosmic Body Formation.

2,747 citations

Journal ArticleDOI
TL;DR: Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented and are found to be in excellent agreement with theory.
Abstract: In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of o(M 2), where M is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure p instead of the mass density ρ is the independent dynamic variable. The incompressible Navier–Stokes equations are derived from the incompressible LB model via Chapman–Enskog procedure. Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.

1,115 citations