Double MRT thermal lattice Boltzmann method for simulating convective flows

Mezrhab, Ahmed; Moussaoui, Mohammed Amine; Jami, Mohammed; Naji, Hassane; Bouzidi, M.

doi:10.1016/j.physleta.2010.06.059

Cited by 153 publications

(110 citation statements)

References 50 publications

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“…The use of the D2Q5 model instead of the D2Q9 was with the objective to reduce the computational effort generally excessive for the MRT scheme. The effectiveness of the D2Q5 model was confirmed in many previous works (Mezrhab et al, 2010;Guo et al, 2010). In the present work, a triple distribution function (TDF) is tested to simulate velocity, temperature and micro-rotation.…”

Section: D2q5 Model For Temperature and Microrotationsupporting

confidence: 64%

MRT-LBM Simulation of Natural Convection in a Rayleigh-Benard Cavity With Linearly Varying Temperatures on the Sides: Application to a Micropolar Fluid

Mansouri¹,

Hasnaoui²,

Amahmid³

et al. 2017

Frontiers in Heat and Mass Transfer

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A two-dimensional numerical simulation is conducted to study natural convection flow and heat transfer characteristics in a square cavity filled with a micropolar fluid. The lower and upper walls of the cavity are respectively subject to isothermal heating and cooling while the temperatures of both vertical sides decrease linearly in the upwards direction. The Lattice-Boltzmann Method (LBM), with the multi-relaxation time (MRT) scheme for the collision process, is used to solve the problem with the objective to assess the ability and efficiency of this numerical method to describe the micropolar fluid behavior under the effect of the imposed thermal boundary conditions. Computations are carried out for Rayleigh number, , and material parameter (vortex viscosity), , varying respectively in the ranges 10 3  10 6 and 0 2. Combined effects of these parameters on the multiplicity of solutions and critical values of from which transitions occur are investigated for Pr 7. An increase of the material parameter is shown to increase the critical Rayleigh numbers, which confirms the stabilizing effect of the micropolar fluid compared to the Newtonian case ( 0). The study covers both steady and unsteady aspects of the problem under consideration. Initial perturbations play an important role in the cooling process of the hot bottom wall in the present configuration. The bicellular ascending and descending flows are two solutions mirror images of each other but they lead to very different quantities of heat from the bottom wall.

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Section: D2q5 Model For Temperature and Microrotationsupporting

confidence: 64%

MRT-LBM Simulation of Natural Convection in a Rayleigh-Benard Cavity With Linearly Varying Temperatures on the Sides: Application to a Micropolar Fluid

Mansouri¹,

Hasnaoui²,

Amahmid³

et al. 2017

Frontiers in Heat and Mass Transfer

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“…There have been various LBE models [16,[18][19][20][21][22][23][24][25][26] proposed for solving Eq. (1).…”

Section: Lattice Boltzmann Models For the Convection-diffusion Equationmentioning

confidence: 99%

Lattice Boltzmann method for conjugate heat and mass transfer with interfacial jump conditions

Guo

Xiao

et al. 2015

International Journal of Heat and Mass Transfer

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“…The LBE method has become an alternative numerical method in fluid flow simulations including multiphase and multicomponent flows [8,9,[13][14][15][16][17][18][19][20], turbulent flows [13][14][15][20][21][22], microflows [4,5,15,20,23], and flows through porous media [2,8,9,11,12,14,24,25], Various TLBE models have also been developed [26][27][28][29][30][31][32][33][34][35] and some of them have been successfully applied in complex thermal simulations such as turbulent thermal flows [36,37] and thermal flows in porous media [38,39], The LBE method has its inherent advantages such as explicitness in formulation, convenience in implementation and parallelization. It is also well known for its capability to treat boundary conditions involving interfacial dynamics and complex geometries as the LBE method deals with the distribution functions, Eor fluid flow simulations, the most commonly used boundary treatment is the "bounce-back" method [40-^2]…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer Evaluation on Curved Boundaries in Thermal Lattice Boltzmann Equation Method

Li¹,

Mei²,

Klausner³

2013

Journal of Heat Transfer

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An efficient and accurate approaehfor heat transfer evaluation on curved boundaries is proposed in the thermal lattice Boltzmann equation (TLBE) method. The boundary heat fluxes in the discrete velocity direetions of the TLBE model are obtained using the given thermal boundary condition and the temperature distribution functions at the lattiee nodes close to the boundaiy. Integration of the diserete boundary heat fluxes with effective surface areas gives the heat flow rate across the boundary. For lattice models with square or cubic structures and uniform lattice spacing the effective surface area is constant for each discrete heat flux, thus the heat flux integration becomes a summation of all the discrete heat fluxes with constant effective surface area. The proposed heat transfer evaluation scheme does not require a determination of the normal heat flux component or a surface area approximation on the boundary; thus, it is very efficient in curvedboundaiy simulations. Several numerical tests are conducted to validate the applicability and accuracy of the proposed heat transfer evaluation scheme, including: (i) twodimensional (2D) steady-state thermal flow in a channel, (ii) one-dimensional (ID) transient heat conduction in an inclined semi-infinite solid, (Hi) 2D transient heat conduction inside a circle, (iv) three-dimensional (3D) steady-state thermal flow in a circular pipe, and (v) 2D steady-state natural convection in a square enclosure with a circular cylinder at the center. Comparison between numerical results and analytical solutions in tests (i)-(iv) shows that the heat transfer is second-order accurate for straight boundaries perpendicular to one of the discrete lattice velocity vectors, and first-order accurate for curx'ed boundaries due to the irregularly distributed lattice fractions intersected by the curved boundaiy. For test (v), the computed surface-averagedNusselt numbers agree well with published results. [DOI: 10,1115/1,4025046] Keywords: thermal lattice Boltzmann equation, heat flux, heat transfer, curved boundary while the heat transfer on the boundaries and fluid-solid interfaces, especially those with curved geometries, has not been Journal of Heat Transfer

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Double MRT thermal lattice Boltzmann method for simulating convective flows

Cited by 153 publications

References 50 publications

MRT-LBM Simulation of Natural Convection in a Rayleigh-Benard Cavity With Linearly Varying Temperatures on the Sides: Application to a Micropolar Fluid

MRT-LBM Simulation of Natural Convection in a Rayleigh-Benard Cavity With Linearly Varying Temperatures on the Sides: Application to a Micropolar Fluid

Lattice Boltzmann method for conjugate heat and mass transfer with interfacial jump conditions

Heat Transfer Evaluation on Curved Boundaries in Thermal Lattice Boltzmann Equation Method

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