Thermal boundary condition for the thermal lattice Boltzmann equation

Tang, G.H.; Tao, Wen‐Quan; He, Yingli

doi:10.1103/physreve.72.016703

Cited by 106 publications

(92 citation statements)

References 33 publications

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“…However, on one hand, these schemes rely on the specific lattice Boltzmann model; on the other hand, the extension to general boundaries is difficult. To this end, several extrapolation schemes have been proposed, such as the Chen scheme [77] and the non-equilibrium extrapolation scheme [16,78,79] .…”

Section: Boundary Schemesmentioning

confidence: 99%

“…In order to eliminate or reduce this error, many efforts have been made to construct incompressible lattice BGK models [6][7][8][9][10] . In recent years, LBM has also been extended to simulate incompressible thermal flows [11][12][13][14][15][16][17][18] , compressible flows [19][20][21][22][23][24][25][26][27][28][29][30] , microscale gaseous flows [31][32][33][34][35][36][37][38][39][40] , etc.…”

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confidence: 99%

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Lattice Boltzmann method and its applications in engineering thermophysics

Wang

et al. 2009

Chin. Sci. Bull.

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The lattice Boltzmann method (LBM), a mesoscopic method between the molecular dynamics method and the conventional numerical methods, has been developed into a very efficient numerical alternative in the past two decades. Unlike conventional numerical methods, the kinetic theory based LBM simulates fluid flows by tracking the evolution of the particle distribution function, and then accumulates the distribution to obtain macroscopic averaged properties. In this article we review some work on LBM applications in engineering thermophysics: (1) brief introduction to the development of the LBM; (2) fundamental theory of LBM including the Boltzmann equation, Maxwell distribution function, Boltzmann-BGK equation, and the lattice Boltzmann-BGK equation; (3) lattice Boltzmann models for compressible flows and non-equilibrium gas flows, bounce back-specular-reflection boundary scheme for microscale gaseous flows, the mass modified outlet boundary scheme for fully developed flows, and an implicit-explicit finite-difference-based LBM; and (4) applications of the LBM to oscillating flow, compressible flow, porous media flow, non-equilibrium flow, and gas resonant oscillating flow. lattice Boltzmann method, numerical simulation, engineering thermophysicsThe lattice Boltzmann method (LBM), a mesoscopic numerical method based on the kinetic theory, has attracted the attention of many scholars at home and abroad and has been developed rapidly in both theory and applications in the past years. At the macroscopic level, LBM can be considered as a discrete method, while at the microscopic level it can be treated as a continuum method. In comparison with conventional numerical methods, kinetic features of LBM enable it to be more effective for simulating complex flows, such as flow in porous media, suspension flow, multiphase flow, and multi-component flow. Its main advantages can be briefly summarized as follows: nearly ideal amenability to parallel computing, complex boundary conditions can be easily formulated in terms of elementary mechanics rules, and simple programming.LBM historically originated from the lattice gas automata method which has been plagued by several diseases: (1) violation of the Galilei invariance; (2) explicit dependence of equation of state on velocity; (3) noise due to Boolen variables; and (4) complicated collision operator.In order to get rid of the noise in the lattice gas automata method, McNamara and Zanetti [1] introduced the first lattice Boltzmann model in 1988, in which Boolen fields were replaced by continuous distributions over the lattices, and the Fermi-Dirac distribution was used as the equilibrium distribution function. In 1989, Higuera and Jimenez made an important simplification of the lattice Boltzmann method, in which they proposed to use a linearized collision operator by assuming that the distribution was close to its local equilibrium state [2,3] . Subsequently, the Bhatnagar-Gross-Krook (BGK) collision operator was independently introduced into LBM by

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Section: Boundary Schemesmentioning

confidence: 99%

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confidence: 99%

Lattice Boltzmann method and its applications in engineering thermophysics

Wang

et al. 2009

Chin. Sci. Bull.

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“…Therefore, Peng et al developed a simplified method regardless of the compression work exerted by the pressure and viscous heat dissipation terms [16]. Other studies also have been dedicated to the thermal boundary condition such as constant temperature and constant heat flux [17][18][19][20].…”

Section: Introductionmentioning

confidence: 97%

Solution of inverse heat conduction problem using the lattice Boltzmann method

Kameli

Kowsary

2012

International Communications in Heat and Mass Transfer

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“…The method retains a computational efficiency comparable to Navier-Stokes solvers but is potentially a more accurate model for gas flows, over a broad range of Knudsen numbers, because its origins lie in kinetic theory. Since Nie et al [15] and Lim et al [16] first applied the lattice Boltzmann method to simulate rarefied gas flows, many publications have emerged which demonstrate that velocity slip and temperature jump phenomena can be captured by the lattice Boltzmann equation (LBE) approach [17][18][19][20][21][22][23][24][25][26]. However, the foregoing work focused on developing new boundary conditions for the velocity slip and temperature jump rather than constructing new LBE models that conserve symmetry for the higher-order moments (an essential requirement to obtain quantitative results for high Knudsen number flows).…”

Section: Introductionmentioning

confidence: 99%

Capturing Knudsen layer phenomena using a lattice Boltzmann model

et al. 2006

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In recent years, lattice Boltzmann methods have been increasingly used to simulate rarefied gas flows in micro-and nano-scale devices. This is partly due to the fact that the method is computationally efficient, particularly when compared to solution techniques like the direct simulation Monte Carlo approach. However, lattice Boltzmann models developed for rarefied gas flows have difficulty in capturing the nonlinear relationship between the shear stress and strain rate within the Knudsen layer. As a consequence, these models are equivalent to slip-flow solutions of the Navier-Stokes equations.In this paper, we propose an effective mean free path to address the Knudsen layer effect, so that the capabilities of lattice Boltzmann methods can be extended beyond the slip-flow regime. The model has been applied to rarefied shear-driven and pressure-driven flows between parallel plates at Knudsen numbers between 0.01 and 1. Our results show that the proposed approach significantly improves the near-wall accuracy of the lattice Boltzmann method and provides a computationally economic solution technique over a wide range of Knudsen numbers.

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Thermal boundary condition for the thermal lattice Boltzmann equation

Cited by 106 publications

References 33 publications

Lattice Boltzmann method and its applications in engineering thermophysics

Lattice Boltzmann method and its applications in engineering thermophysics

Solution of inverse heat conduction problem using the lattice Boltzmann method

Capturing Knudsen layer phenomena using a lattice Boltzmann model

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