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Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices

Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices
Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices
In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard two-dimensional nine-velocity (D2Q9) lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and general features of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature
1539-3755
016710-[16]
Li, Q.
54e51d2b-808c-42f2-95bb-62b4110df4dd
Luo, K.H.
1c9be6c6-e956-4b12-af13-32ea855c69f3
He, Y.L.
1df9b2fa-2860-4148-821a-150bf42c60b4
Gao, Y.J.
a0993a8d-0509-4a39-8a78-a6ed700b07f3
Tao, W.Q.
a66d70c2-d167-40a8-8a06-29347180f2fe
Li, Q.
54e51d2b-808c-42f2-95bb-62b4110df4dd
Luo, K.H.
1c9be6c6-e956-4b12-af13-32ea855c69f3
He, Y.L.
1df9b2fa-2860-4148-821a-150bf42c60b4
Gao, Y.J.
a0993a8d-0509-4a39-8a78-a6ed700b07f3
Tao, W.Q.
a66d70c2-d167-40a8-8a06-29347180f2fe

Li, Q., Luo, K.H., He, Y.L., Gao, Y.J. and Tao, W.Q. (2012) Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices. Physical Review E, 85, 016710-[16]. (doi:10.1103/PhysRevE.85.016710).

Record type: Article

Abstract

In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard two-dimensional nine-velocity (D2Q9) lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and general features of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature

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Published date: 20 January 2012
Organisations: Bioengineering Group

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Local EPrints ID: 334452
URI: https://eprints.soton.ac.uk/id/eprint/334452
ISSN: 1539-3755
PURE UUID: 6e41bc41-f644-4e0d-86f6-327e03310403

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Date deposited: 09 Mar 2012 11:37
Last modified: 16 Jul 2019 22:10

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