A lattice Boltzmann model for multiphase flows with large density ratio

Zheng, Hongwei; Chen, Shu; Chew, Y. T.

doi:10.1016/j.jcp.2006.02.015

Cited by 446 publications

(326 citation statements)

References 33 publications

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“…The lattice Boltzmann method (LBM), as a kinetic-based numerical method, has made a great progress in the study of fluid flows for its advantage in dealing with complex boundaries [5][6][7][8][9], and has also been extended to solve the CDE [10][11][12][13][14][15][16][17][18][19][20][21][22]. Dawson et al [10] first applied the LBM to the study of solvent flow where an LB model was used to solve the N-S equations for fluid flow, while another was adopted to solve the CDE for the concentration field; the method has also been extended to investigate thermal flows [11].…”

Section: Introductionmentioning

confidence: 99%

“…However, the collision process of the model with the space-derivative term cannot be implemented locally (here the word "local" means that the computation of a physical variable at one point only depends on the information of this point) since a finite-difference scheme is needed to compute the space-derivative term, which not only affects the computational efficiency of the lattice Boltzmann method, but also gives rise to some difficulties in adopting a local scheme to treat the boundary condition of the CDE. The other is to construct an LB model with a modified evolution equation (without adding a source term in the evolution equation) to ensure that the unwanted terms in the previous models can be eliminated completely [21,22]. However, the collision process cannot yet be performed locally, and thus the problems mentioned above still remain.…”

Section: Introductionmentioning

confidence: 99%

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Lattice Boltzmann model for the convection-diffusion equation

2013

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We propose a lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) and show that the CDE can be recovered correctly from the model by the Chapman-Enskog analysis. The most striking feature of the present LB model is that it enables the collision process to be implemented locally, making it possible to retain the advantage of the lattice Boltzmann method in the study of the heat and mass transfer in complex geometries. A local scheme for computing the heat and mass fluxes is then proposed to replace conventional nonlocal finite-difference schemes. We further validate the present model and the local scheme for computing the flux against analytical solutions to several classical problems, and we show that both the model for the CDE and the computational scheme for the flux have a second-order convergence rate in space. It is also demonstrated the present model is more accurate than existing LB models for the CDE.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann model for the convection-diffusion equation

2013

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“…Several kinds of lattice Boltzmann model for simulating multiphase fluid have been established and applied to the simulations of gas bubbles under gravitysuccessfully. These models include potential method proposed by Shan et al [7], color method proposed by Rothman et al [8], and free energy method proposed by Swift et al [9]and improved byZheng et al [10]. The free energy method [10] was proved to be a good tool for the study of two-phase flows with high viscosity ratios and high density ratio.As shown by Gupta et al [11] and Yu et al [12], in comparison with the case of single bubble, the motion of multiple bubbles under gravity could be much more complex due to hydrodynamic interactions between bubbles.…”

Section: Introductionmentioning

confidence: 99%

“…However,a detailed numerical study of the influence of bubble collision and coalescence on the rising velocity has not been undertaken. It is important to focus on the fundamental understanding of the bubble collision and coalescence when multiple bubbles are rising under gravity.To fulfil this task the LBM proposed by Zheng et al [10] is adopted in this work to study the rise behavior of multiple bubbles which are initially placed in in-line arrangement.This study will evaluate the coalescence patternand rising velocity of the bubbleswhich not only depend on the computational parameters but also depend on the initial arrangements. In addition, the terminal velocity is compared with the result of single bubble under the same conditions to illustrate the influence of multiple bubbles motion.…”

Section: Introductionmentioning

confidence: 99%

Bubble Motion under Gravity through Lattice Boltzmann Method

Nie¹,

Qiu²,

Zhang³

2015

Advances in Intelligent Systems Research

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Abstract-The motion of two bubbles under gravity is numerically studied through the lattice Boltzmann method for the Eotvos number ranging from 1 to 12. The effects of Eotvos number on the bubble coalescence and rising velocity are investigated. It has been found that the uppermost bubble deforms the most because of the maximum drag.In addition, the averaged rising velocity of the bubbles is also studied in this work.

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“…The LBM originated from lattice gas automata is based on microscopic models and mesoscopic kinetic equations [9]. It is a regular lattice-based scheme for fluid flow simulation, which has been proved to be accurate and applicable to various hydrodynamic problems for its simplicity, efficiency, and parallelism characteristics [10]- [15]. The IBM was initially…”

Section: Introductionmentioning

confidence: 99%

Interpolated Velocity Correction Immersed Boundary-Lattice Boltzmann Method for Fluid Flows with Flexible Boundary

Chen¹,

Wan²

2015

IJMMM

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Abstract-An interpolated velocity correction scheme for the simulation of the interaction between fluid and flexible boundary using an immersed boundary-lattice Boltzmann method (IB-LBM) is proposed. In the conventional IB-LBM, the velocity field on the immersed boundary is determined by interpolating from an Eluerian grid to a Lagrangian grid using a discrete Dirac delta function, which is not divergence-free. As a result, this method can generally suffer from poor volume conservation for the closed immersed boundary. The key idea of the proposed interpolated velocity correction scheme is correcting the interpolated velocity field to satisfy a discrete divergence-free constraint defined on the Lagrangian boundary in the fluid. The proposed scheme makes no modifications to solve Navier-Stokes (N-S) equations using the lattice Boltzmann method (LBM) on the Eulerian grid and also improves volume conservation for the closed immersed boundary. Two examples are presented to verify the efficiency and accuracy of the proposed scheme. proposed by Peskin [16] in 1970s for simulating cardiac mechanics and associated blood flow, which employs a fixed Eulerian grid for the flow field and a Lagrangian grid for an immersed boundary in the fluid, which is modeled by a singular force which is incorporated into the forcing term in the N-S equations. The interaction between the fluid and the immersed boundary is tackled using the IBM. A discrete Dirac delta function is used to spread the singular force from the Lagrangian grid to the Eluerian grid, and to interpolate the velocity from the Eluerian grid to the Lagrangian grid.It is well known that the IBM can suffer from poor volume conservation for the closed immersed boundary in the fluid [17]- [21]. One cause of this lack of volume conservation is that the interpolated velocity field that determines the motion of the Lagrangian structure is not generally divergence-free, even if the Eulerian velocity is divergence-free with respect to the discrete divergence operator used in the numerical solution of the incompressible N-S equations. This problem was solved by modifying their divergence operator relative to their chosen interpolation operator, which would remain discretely divergence free on the Lagrangian grid when interpolated with their specific interpolation operator [18]. The immersed interface method [19] modifies the finite difference stencils of the fluid solver near the immersed boundary instead of utilizing discrete delta functions to spread the force form the Lagrangian to Eulerian grid. The Blob projection method [20] finds an analytic expression that represents the projection of a regularized form of the forces along the boundary onto the space of divergence-free vector fields. However, all these methods are difficult to implement and are not readily extendable to three dimensions for general problems, they also need more computationally expensive interpolation and spreading. In our work, when the LBM is used for solving the N-S equations, the velocity field on th...

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A lattice Boltzmann model for multiphase flows with large density ratio

Cited by 446 publications

References 33 publications

Lattice Boltzmann model for the convection-diffusion equation

Lattice Boltzmann model for the convection-diffusion equation

Bubble Motion under Gravity through Lattice Boltzmann Method

Interpolated Velocity Correction Immersed Boundary-Lattice Boltzmann Method for Fluid Flows with Flexible Boundary

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