Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations

Li, Qing; He, Ya‐Ling; Wang, Yueshe; Tao, Wen‐Quan

doi:10.1103/physreve.76.056705

Cited by 119 publications

(78 citation statements)

References 36 publications

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“…Nevertheless, the Prandtl number, which plays a very important role in most applications in the field of engineering thermophysics, is fixed at unit. To breach this limit, we have presented a lattice Boltzmann model for the compressible Navier-Stokes equations [26] based on the double-distribution-function (DDF) LBM [15,17] . The following issues have been considered in constructing the model:…”

Section: Modelsmentioning

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: Modelsmentioning

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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“…In Equation (16), the unknowns are f  and ĝ  defined in Equation (13), which include both equilibrium and non-equilibrium density and temperature distribution functions Figure 1 shows an interface between two adjacent control cells for local reconstruction of fluxes [10], in which the D2Q9 and D2Q4 lattice velocity models respectively for DDF and TDF are embedded. The non-equilibrium parts for DDF and TDF are given by Equation (14).…”

Section: Finite Volume Discretizationmentioning

confidence: 99%

From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver

Wang

Yang

Chen

2015

Entropy

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Based on the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS), which combines the advantages of conventional Navier-Stokes solvers and lattice Boltzmann solvers, was proposed recently. Specifically, LBFS applies the finite volume method to solve the macroscopic governing equations which provide solutions for macroscopic flow variables at cell centers. In the meantime, numerical fluxes at each cell interface are evaluated by local reconstruction of LBM solution. In other words, in LBFS, LBM is only locally applied at the cell interface for one streaming step. This is quite different from the conventional LBM, which is globally applied in the whole flow domain. This paper shows three different versions of LBFS respectively for isothermal, thermal and compressible flows and their relationships with the standard LBM. In particular, the performance of isothermal LBFS in terms of accuracy, efficiency and stability is investigated by comparing it with the standard LBM. The thermal LBFS is simplified by using the D2Q4 lattice velocity model and its performance is examined by its application to simulate natural convection with high Rayleigh numbers. It is demonstrated that the compressible LBFS can be effectively used to simulate both inviscid and viscous flows by incorporating non-equilibrium effects into the process for inviscid flux reconstruction. Several numerical examples, including lid-driven cavity flow, natural convection in a square cavity at Rayleigh numbers of 10

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“…The traditional LBM methods can only handle low-speed incompressible fluid flow, can not be used for high-speed moving objects such as aircraft simulation, thereby limiting the application of the method. To calculate the high-speed compressible fluid flow, researchers have begun a new model of research, such as Alexander et al [7] approaches such as the use of controlled speed of sound; Yu and Zhao [8] introduce magnetism to reduce the speed of sound, thus alleviating the constraints of small Mach number impact, but these methods do not restore the energy equation, and apply to a limited extent. Palmer and Rector et al [9][10] made the thermal LBM model, but still do not reflect the high Mach number phenomenon; Qu et al [11] proposed to use a circle function instead of using the Maxwell distribution function; Li et al [12] proposed a pairs of distribution function method; Sun et al [13] made the locally adaptive LB model, the speed of his model can get a very wide speed unlimited size; Yan Guang-wu [14] proposed multi-level multi-speed compressible model.…”

Section: Introductionmentioning

confidence: 99%