Thermal lattice Boltzmann equation for low Mach number flows: Decoupling model

Guo, Zhaoli; Chen, Zheng; Shi, Baochang; Zhao, Tianshou

doi:10.1103/physreve.75.036704

Cited by 257 publications

(239 citation statements)

References 42 publications

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“…The discussion is made by comparing the analytical solutions to three physical problems and numerical results obtained with the present model and the nonequilibrium scheme. The problems under consideration include diffusion of the Gaussian hill [13,19,21], thermal Couette flow with heat dissipation [46][47][48][49][50], and planar thermal Poiseuille flow [50,51]. The relative error (E) is used to test the deviation between the analytical solutions and the numerical results and is defined as…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

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Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method

Chai

Zhao

2014

Phys. Rev. E

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In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

“…We now consider the planar thermal Poiseuille flow with heat dissipation [50,51]. The schematic of the problem is shown in Fig.…”

Section: Example Planar Thermal Poiseuille Flowmentioning

confidence: 99%

Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method

Chai

Zhao

2014

Phys. Rev. E

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“…3.1). The LB model turns out to be more flexible than LGCA, and there is now a rich literature that includes thermal [81][82][83][84][85][86] and multiphase flows, involving both liquid-gas coexistence and multicomponent mixtures [87][88][89][90][91][92][93][94][95][96]. In the present article, we will consider only singlephase flows of a single solvent species, such that we can describe the dynamics in terms of a single particle type.…”

Section: The Fluctuating Lattice-boltzmann Equationmentioning

confidence: 99%

Lattice Boltzmann Simulations of Soft Matter Systems

Dünweg¹,

Ladd²

2008

Advances in Polymer Science

201

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This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview of the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice-Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice-Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.

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“…The DDF approach [37,38,53] is based on the principle that the isothermal LBM can be directly derived by properly discretizing the continuous Boltzmann equation in temporal, spatial, and velocity spaces. Following the same procedure, an internal energy distribution function model is derived by discretizing the continuous evolution equation for the internal energy distribution, and then two independent distribution functions are obtained, one for the flow field and the other for the temperature field.…”

Section: Introductionmentioning

confidence: 99%

“…This model has attracted much attention since its emergence for its excellent numerical stability and adjustability of the Prandtl number and has found applications in a variety of fields [39][40][41]. However, the DDF method includes complicated gradient terms if viscous heat dissipation and compression work are taken into account which may introduce some additional errors and do harm to the numerical stability [38]. Since in the present paper, viscous heat dissipation and compression work are neglected, the DDF is applied as a stable approach for solving the energy equation.…”

Section: Introductionmentioning

confidence: 99%