Lattice Boltzmann models for the convection-diffusion equation: D2Q5 vs D2Q9

Li, Like; Mei, Renwei; Klausner, James F.

doi:10.1016/j.ijheatmasstransfer.2016.11.092

Cited by 129 publications

(81 citation statements)

References 46 publications

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“…On the contrast, when the convection effect is very strong, the D2Q9 model has better numerical accuracy. Similar conclusions can be obtained in 3D [154].…”

Section: The Internal-energy-and Temperature-based Ddf Modelssupporting

confidence: 89%

“…However, whether the D2Q9 model is numerically better than the D2Q4 or D2Q5 model is still an open question. In a recent work by Li et al [154], they pointed out that the D2Q5 model is more robust and accurate than the D2Q9 model when the convection effect is not very strong and the boundary effect is significant. On the contrast, when the convection effect is very strong, the D2Q9 model has better numerical accuracy.…”

Section: The Internal-energy-and Temperature-based Ddf Modelsmentioning

confidence: 99%

“…In the past years, attempts have also been made to use the MRT method to solve the convection-diffusion equation [154][155][156][157]. In the MRT model, the number of tunable parameters is sufficient to cover the anisotropic diffusion coefficient.…”

Section: The Ddf-mrt Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review

Liu

et al. 2019

International Journal of Heat and Mass Transfer

204

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Since its introduction 30 years ago, the lattice Boltzmann (LB) method has achieved great success in simulating fluid flows and modeling physics in fluids. Owing to its kinetic nature, the LB method has the capability to incorporate the essential microscopic or mesoscopic physics, and it is particularly successful in modeling transport phenomena involving complex boundaries and interfacial dynamics.The LB method can be considered to be an efficient numerical tool for fluid flow and heat transfer in porous media. Moreover, since the LB method is inherently transient, it is especially useful for investigating transient solid-liquid phase-change processes wherein the interfacial behaviors are very important. In this article, a comprehensive review of the LB methods for single-phase and solid-liquid phase-change heat transfer in porous media at both the pore scale and representative elementary volume (REV) scale. The review first introduces the fundamentals of the LB method for fluid flow and heat transfer. Then the REV-scale LB method for fluid flow and single-phase heat transfer in porous media, and the LB method for solid-liquid phase-change heat transfer, are described. Some applications 2 of the LB methods for single-phase and solid-liquid phase-change heat transfer in porous media are provided. In addition, applications of the LB method to predict effective thermal conductivity of porous materials are also provided. Finally, further developments of the LB method in the related areas are discussed. Keyword: Lattice Boltzmann method; Single-phase heat transfer; Solid-liquid phase change; Porous media proposed the RLBE model with an enhanced collision operator, which was shown to be linearly stable. Based on the Bhatnagar-Gross-Krook (BGK) collision operator [104], the LB model using a single relaxation time, referred to as the BGK-LB model, has been independently proposed by Chen et al. [14], Koelman [15], and Qian et al. [16]. In the BGK-LB model, the equilibrium distribution function is chosen to recover the incompressible N-S equations in the incompressible limit. Due to its high efficiency and extreme simplicity, the BGK-LB model has become the most popular LB model, in spite of some well-known deficiencies (e.g., numerical instability, viscosity dependence of boundary 9 locations). Almost at the same time when the BGK-LB method was developed, d'Humières [17] proposed the multiple-relaxation-time (MRT) LB method. The MRT-LB equation (also referred to as generalized lattice Boltzmann equation (GLBE)) is an important extension of the RLBE proposed by Higuera et al. [12,13]. This work is significant because, in addition to it overcomes some deficiencies of the BGK-LB model, it facilitates the extension of the LB method, expanding the applications to a much wider range of phenomena and processes.In 1997, a direct connection between the LB equation and the continuous Boltzmann equation in kinetic theory was rigorously established by He and Luo [19,20]. In particular, it has been demonstrated that the LB equation c...

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“…On the contrast, when the convection effect is very strong, the D2Q9 model has better numerical accuracy. Similar conclusions can be obtained in 3D [154].…”

Section: The Internal-energy-and Temperature-based Ddf Modelssupporting

confidence: 89%

Section: The Internal-energy-and Temperature-based Ddf Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review

Liu

et al. 2019

International Journal of Heat and Mass Transfer

204

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“…Once the flow field was obtained, we simulated solute transport with a particle distribution function g , using the regularized LB algorithm (RLB) for numerical accuracy [42,43] and the D2Q5 lattice for numerical efficiency [44]: where c i are the lattice velocities ( c 0 = (0,0), c 1 = (1,0), c 2 = (0,1), c 3 = (−1,0), c 4 = (0,-1), c 5 = (1,1)) corresponding to the lattice weights ω i ( ω 0 = 1/3, ω 1-4 = 1/6), and is the tensor contraction between the two tensors and .…”

Section: Resultsmentioning

confidence: 99%

Mathematical investigation of microbial quorum sensing under various flow conditions

Jung¹,

Meile

2020

Preprint

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10Microorganisms efficiently coordinate phenotype expressions through a decision-making 11 process known as quorum sensing (QS). We investigated QS amongst heterogeneously 12 distributed microbial aggregates under various flow conditions using a process-driven numerical 13 model. Model simulations assess the conditions suitable for QS induction and quantify the 14 importance of advective transport of signaling molecules. In addition, advection dilutes signaling 15 molecules so that faster flow conditions require higher microbial densities, faster signal 16 production rates, or higher sensitivities to signaling molecules to induce QS. However, 17 autoinduction of signal production can substantially increase the transport distance of signaling 18 molecules in both upstream and downstream directions. We present approximate analytical 19 solutions of the advection-diffusion-reaction equation that describe the concentration profiles of 20 signaling molecules for a wide range of flow and reaction rates. These empirical relationships, 21 which predict the distribution of dissolved solutes following zero-order production kinetics along 22 pore channels, allow to quantitatively estimate the effective communication distances amongst 23 multiple microbial aggregates without further numerical simulations. 24 25 Author Summary 26Microbes can interact with their surrounding environments by producing and sensing small 27 signaling molecules. When the microbes experience a high enough concentration of the signaling 28 molecules, they express certain phenotypes which is often energetically expensive. This 29 microbial decision-making process known as quorum sensing (QS) has been understood to 30 confer evolutionary benefits. However, it is still not completely understood how transport of the 31 produced signaling molecules affects QS. Using a mathematical approach investigating QS 32 across a range of environmentally relevant flow conditions, we find that advective transport 33 promotes QS downstream yet also dilutes the concentration of signaling molecules. We quantify 34 the importance of microbial cell location with respect to both other microbes and flow direction. 35 By analyzing complex numerical simulation results, we provide analytical approximations to 36 assess the distribution of signaling molecules in pore channels across a range of flow and 37 reaction conditions. 38 39 Introduction 40Microorganisms preferentially reside on solid surfaces, which often leads to a closer 41 proximity of neighboring cells than when in a planktonic form [1]. At elevated cell densities, 42 microorganisms need to efficiently coordinate the expression of energetically expensive 43 phenotypes, such as biofilm development, exoenzyme production, and microbial dispersal. 44 Efficiency is achieved by producing and detecting relatively cheap signaling molecules which 45 regulate the phenotype expression only when a sufficient signal concentration has been reached 46 [2]. This microbial decision-making process called "quorum sensing (QS)" was orig...

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“…On the other hand, there are also some LB models for the diffusion equations or CDEs [24,32,[44][45][46][47][48][49][50][51][52][53][54][55][56]. Based on the recent works [24,[52][53][54][55], the LB equation of present model for Eq.…”

Section: Lattice Boltzmann Model For Two-phase Flow In Porous Mediamentioning

confidence: 99%

A Lattice Boltzmann Model for Two-Phase Flow in Porous Media

Chai¹,

Liang²,

Du³

et al. 2019

SIAM J. Sci. Comput.

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In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied for saturation evolution described by the convection-diffusion equation with a source term. We first performed a Chapman-Enskog analysis, and show that the macroscopic nonlinear equations for pressure and saturation can be recovered correctly from present LB model. Then in the framework of LB method, we develop a local scheme for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal secondorder finite-difference schemes. We also perform some numerical simulations, and the results show that the developed LB model and local scheme for ve- * locity are accurate and also have a second-order convergence rate in space.Finally, compared to the available pore-scale LB models for two-phase flow in porous media, the present LB model has more potential in the study of the large-scale problems.

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Lattice Boltzmann models for the convection-diffusion equation: D2Q5 vs D2Q9

Abstract: 2016-12-23T18:37:48

Cited by 129 publications

References 46 publications

Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review

Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review

Mathematical investigation of microbial quorum sensing under various flow conditions

A Lattice Boltzmann Model for Two-Phase Flow in Porous Media

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