Investigation of local and non-local lattice Boltzmann models for transient heat transfer between non-stationary, disparate media

McCullough, J. W. S.; Leonardi, Christopher; Jones, Bruce D.; Aminossadati, Saiied M.; Williams, John R.

doi:10.1016/j.camwa.2018.01.018

Cited by 5 publications

(3 citation statements)

References 41 publications

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“…It is appropriately accurate and significantly improves the convergence of solution process (Bhatnagar et al, 1954;Buick, 1997;. LBM has been used by many studies to investigate flows in different geometries and boundary conditions; in addition, its ability to simulate particle suspensions suggests its capability in modeling nanofluids (Aghakhani et al, 2018;McCullough et al, 2018;McCullough et al, 2016;Leonardi et al, 2016;Jones et al, 2015;Wang et al, 2018). Owing to low computational costs and acceptable results, LBM has been used in many studies for simulating free or mixed convection heat transfer (Chen et al, 2015;Rahmati et al, 2016;Abbassi et al, 2018;Vijaybabu et al, 2017;Mozaffari et al, 2019).…”

Section: R E T R a C T E Dmentioning

confidence: 99%

Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux

Mozaffari

D’Orazio

Karimipour

et al. 2019

HFF

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Purpose The purpose of this paper is to improve the lattice Boltzmann method’s ability to simulate a microflow under constant heat flux. Design/methodology/approach Develop the thermal lattice Boltzmann method based on double population of hydrodynamic and thermal distribution functions. Findings The buoyancy forces, caused by gravity, can change the hydrodynamic properties of the flow. As a result, the gravity term was included in the Boltzmann equation as an external force, and the equations were rewritten under new conditions. Originality/value To the best of the authors’ knowledge, the current study is the first attempt to investigate mixed-convection heat transfer in an inclined microchannel in a slip flow regime.

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Section: R E T R a C T E Dmentioning

confidence: 99%

Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux

Mozaffari

D’Orazio

Karimipour

et al. 2019

HFF

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“…A common choice of the speed of sound c s is 1/ √ 3, which reduces the error in higher moments. The moments of the equilibrium distribution are truncated by some authors on the second order terms [5,9,10,12,37,[55][56][57][58][59], by not including the terms u 2…”

Section: Moments Of the Distributionmentioning

confidence: 99%

“…Another technique to couple the fluid-solid interaction is through the partially saturated method [35], where a lattice node is categorised as a pure fluid, pure solid or mixed node. Recent applications can be found in the studies of heat transfer in particle suspensions [36,37].…”

Section: Introductionmentioning

confidence: 99%

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

Gruszczyński¹,

Dzikowski²,

Łaniewski-Wołłk³

2021

Preprint

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This study derives a method to consistently recover the second-order convergence of the lattice Boltzmann method (LBM), which is frequently degraded by the improper discretisation of required source terms. The work focuses on advection-diffusion models in which the source terms are dependent on the intensity of transported fields. Such terms can be observed in reaction-type equations used for example in heat and mass transfer problems or multiphase flows. The main findings are applicable to a wide range of formulations within the LBM framework. All considered source terms are interpreted as contributions to the zeroth-moment of the distribution function. These account for sources in a scalar field, such as density, concentration, temperature or a phase field. In addition to this, certain immersed boundary methods can be interpreted as a source term in their formulation, highlighting a further application for this work.This paper makes three primary contributions to the current state-of-the-art. Firstly, it identifies the differences observed between the ways source terms are included in the LBM schemes present in the literature. The algebraic manipulations are explicitly presented in this paper to clarify the differences observed, and identify their origin. Secondly, it derives in full detail, the implicit relation between the value of the transported macroscopic field, and the sum of the LBM densities. This relation is shown in the paper to be a crucial ingredient for preserving the second-order convergence in the case of complex source terms. Moreover, the derived relation is valid for any source term discretization scheme, and three equivalent forms of the second-order accurate collision operator are presented. Finally, closed form solutions of this implicit relation are shown for a variety of common models, including general linear and second order terms; population growth models, such as the Logistic or Gompertz model; and Allen-Cahn Equation.The second-order convergence of the proposed LBM schemes is verified on both linear and non-linear source terms. Commonly used diffusive and acoustic scalings are discussed, and their pitfalls are identified. Moreover, for a simplified case, the competing errors are shown visually with isolines of error in the space of spatial and temporal resolutions.

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Mesoscopic Methods in Engineering and Science

Janßen

Krafczyk

Luo

2020

Computers & Mathematics with Applications

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Investigation of local and non-local lattice Boltzmann models for transient heat transfer between non-stationary, disparate media

Cited by 5 publications

References 41 publications

Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux

Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

Mesoscopic Methods in Engineering and Science

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