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Journal ArticleDOI

A coupled discrete unified gas-kinetic scheme for Boussinesq flows

05 Oct 2015-Computers & Fluids (Pergamon)-Vol. 120, pp 70-81
TL;DR: In this article, a thermal and coupled discrete unified gas-kinetic scheme is derived for the Boussinesq flows, where the velocity and temperature fields are described independently, and the boundary conditions for both velocities and temperatures are also proposed.
About: This article is published in Computers & Fluids.The article was published on 2015-10-05 and is currently open access. It has received 38 citations till now. The article focuses on the topics: Rayleigh number & Natural convection.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a numerical study of three-dimensional natural convection of air in a differentially heated cubical cavity with Rayleigh number (Ra) up to 10 10 is performed by using the recently developed coupled discrete unified gas-kinetic scheme.

79 citations


Cites background or methods from "A coupled discrete unified gas-kine..."

  • ...Generally, for flows without solid boundaries, for example the decaying turbulent flow, the accuracy of standard LBM is slightly higher than the DUGKS [32], while for flows involving solid boundaries, the DUGKS is even more accurate than the standard LBM [28,33]....

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  • ...In fact, several comparative studies of the standard LBM and DUGKS have been preformed systematically for laminar flows [28,31], turbulent flows [32,33], and natural convection flows [29] in previous work....

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  • ...Many kinetic methods have been recently utilized to simulate NCF problem, such as the lattice Boltzmann methods (LBM) [15–23] and the gas-kinetic scheme [24]....

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  • ...Some FV based LBM have been also developed in the past decades, but it has been demonstrated that the DUGKS is obviously superior to the current best FV-LBM [35] in terms of accuracy and numerical stability [31]....

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  • ...But benefiting from the FV nature, non-uniform meshes can be easily employed without loss of accuracy and additional efforts in DUGKS, and its efficiency can be significantly improved by employing a non-uniform mesh according to the local accuracy requirement [28,29,32]....

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Journal ArticleDOI
TL;DR: In this article, the performance of the discrete velocity method (DVM) and discrete unified gas-kinetic scheme (DUGKS) in finding steady-state solutions of low-speed force-driven Poiseuille and lid-driven cavity flows is investigated.

76 citations

Journal ArticleDOI
TL;DR: In this article, a parallel implementation of the discrete unified gas-kinetic scheme (DUGKS) for 3D Taylor-green vortex flow is presented. And the results are compared to short-time analytical solution as well as to those from LBM and pseudo-spectral method.

53 citations

Journal ArticleDOI
TL;DR: The proposed DUGKS is an effective and reliable method for binary gas mixtures in all flow regimes based on the Andries-Aoki-Perthame kinetic model and is compared with those from other reliable numerical methods.
Abstract: Recently a discrete unified gas kinetic scheme (DUGKS) in a finite-volume formulation based on the Boltzmann model equation has been developed for gas flows in all flow regimes. The original DUGKS is designed for flows of single-species gases. In this work, we extend the DUGKS to flows of binary gas mixtures of Maxwell molecules based on the Andries-Aoki-Perthame kinetic model [P. Andries et al., J. Stat. Phys. 106, 993 (2002)JSTPBS0022-471510.1023/A:1014033703134. A particular feature of the method is that the flux at each cell interface is evaluated based on the characteristic solution of the kinetic equation itself; thus the numerical dissipation is low in comparison with that using direct reconstruction. Furthermore, the implicit treatment of the collision term enables the time step to be free from the restriction of the relaxation time. Unlike the DUGKS for single-species flows, a nonlinear system must be solved to determine the interaction parameters appearing in the equilibrium distribution function, which can be obtained analytically for Maxwell molecules. Several tests are performed to validate the scheme, including the shock structure problem under different Mach numbers and molar concentrations, the channel flow driven by a small gradient of pressure, temperature, or concentration, the plane Couette flow, and the shear driven cavity flow under different mass ratios and molar concentrations. The results are compared with those from other reliable numerical methods. The results show that the proposed scheme is an effective and reliable method for binary gas mixtures in all flow regimes.

50 citations

Journal ArticleDOI
TL;DR: The proposed IB-DUGKS is a promising tool for simulating particulate flows and preserves the respective advantages of the IB and DUGKS, i.e., the flexibility and efficiency for treating complex flows, and the robustness and low numerical-dissipation.

45 citations

References
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Journal ArticleDOI

6,206 citations


"A coupled discrete unified gas-kine..." refers methods in this paper

  • ...Up to date, a variety of kinetic methods have been proposed, such as the lattice gas cellular automata (LGCA) [1], the lattice Boltzmann equation (LBE) [2, 3], the gas-kinetic scheme (GKS) [4, 5, 6, 7], and the smoothed particle hydrodynamics(SPH) [8], among which the GKS and LBE are specifically designed for CFD....

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Journal ArticleDOI
TL;DR: In this paper, the authors used mesh refnement and extrapolation to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls.
Abstract: Details are given of the computational method used to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls. Second-order, central difference approximations were used. Mesh refnement and extrapolation led to solutions for 103⩽Ra⩽10 6 which are believed to be accurate to better than 1 per cent at the highest Rayleigh number and down to one-tenth of that at the lowest value.

2,529 citations

Journal ArticleDOI
TL;DR: In this paper, Chen et al. used the half-way wall bounceback boundary condition for the 2-D Poiseuille flow with forcing to obtain second-order accuracy for the 3-D square duct flow.
Abstract: Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions are proposed. These conditions are constructed in consistency of the wall boundary condition based on an idea of bounceback of non-equilibrium distribution. When these conditions are used together with the improved incompressible LBGK model by Zou et al., the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy. Since the half-way wall bounceback boundary condition is very easy to implement and was shown theoretically to give second-order accuracy for the 2-D Poiseuille flow with forcing, it is used with pressure (density) inlet/outlet conditions proposed in this paper and in Chen et al. to study the 2-D Poiseuille flow and the 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback is comparable with that using some other published boundary conditions. Besides, the bounceback condition has a much better stability behavior than that of other boundary conditions.

2,001 citations

Journal ArticleDOI
TL;DR: The half-way wall bounceback boundary condition is also used with the pressure ~density! inlet/outlet conditions proposed in this article to study 2-D Poiseuille flow and 3-D square duct flow.
Abstract: Pressure ~density! and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models ~LBGK! and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model @J. Stat. Phys. 81 ,3 5 ~1995!# the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure ~density! difference. The half-way wall bounceback boundary condition is also used with the pressure ~density! inlet/outlet conditions proposed in this paper and in Phys. Fluids 8, 2527 ~1996! to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior. © 1997 American Institute of Physics. @S1070-6631~97!03406-5#

1,854 citations

Journal ArticleDOI
TL;DR: A novel lattice Boltzmann thermal model is proposed for studying thermohydrodynamics in incompressible limit that can incorporate viscous heat dissipation and compression work done by the pressure, in contrast to the passive-scalar-based thermal latticeboltzmann models.

1,243 citations


"A coupled discrete unified gas-kine..." refers background or methods in this paper

  • ...Such strategy has been adopted in both GKS and LBE methods [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]....

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  • ...Later both schemes are extended to low speed thermal flows [11, 12, 13, 14, 15, 16]....

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  • ...The simulation results by the theoretical analysis [27], the original GKS [12], and the LBE method [16] are also included ....

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  • ...Also included are the results given by theoretical analysis [27], the original GKS [12], and the LBE [16]....

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