Lattice Boltzmann simulations of axisymmetric natural convection with anisotropic thermal diffusion

Zuo, Wei; Zhang, Wenfan; Zhang, Jiazhong

doi:10.1016/j.ijheatmasstransfer.2016.05.002

Cited by 15 publications

(8 citation statements)

References 32 publications

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“…Figure 10 shows the computed contours of the azimuthal velocity, temperature field, vorticity and streamlines for the above three values of σ. When σ = 0, there is no buoyancy force and the flow and the temperature fields are influenced by the centrifugal force and the forced in the positive azimuthal direction θ is seen to be enhanced, while that negative θ direction appear to be diminished and these observations are consistent with the benchmarks results [58,59] and recent numerical simulations [29]. In order to quantify the heat transfer rate in the presence of mixed convection, a mean equivalent thermal conductivity at the inner cylinder can be defined as [61,62,22,30]).…”

Section: Mixed Convection In a Slender Vertical Annulus Between Two Csupporting

confidence: 90%

“…Cascaded LB scheme for temperature field: operator splitting for source term As in the previous section, we consider a D2Q5 lattice, and use the orthogonal basis vectors L β and the transformation matrix L given in Eqs. (29) and (30), respectively, to design a cascaded LB scheme for the solution of the temperature field φ = T . Its evolution is presented by the advection-diffusion equation with a source term given in Eqs.…”

Section: Post-collision Mass Sourcementioning

confidence: 99%

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Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects

Hajabdollahi

Premnath

Welch

2019

International Journal of Heat and Mass Transfer

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Section: Mixed Convection In a Slender Vertical Annulus Between Two Csupporting

confidence: 90%

Section: Post-collision Mass Sourcementioning

confidence: 99%

Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects

Hajabdollahi

Premnath

Welch

2019

International Journal of Heat and Mass Transfer

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“…Since the first axisymmetric lattice Boltzmann (LB) model proposed by Halliday et al, successive models were then developed to truly recover the desired macroscopic equations Furthermore, different attempts were devoted to simplifying the treatments of source terms by either reducing the number of the source terms or avoiding the computations of spatial gradients therein . Moreover, the applicability of the axisymmetric LBM has also been well verified by practical axisymmetric flow tests …”

Section: Introductionmentioning

confidence: 99%

“…5,6,[12][13][14][15][16] Moreover, the applicability of the axisymmetric LBM has also been well verified by practical axisymmetric flow tests. 15,[17][18][19][20][21][22][23] Despite its widespread applications, LBM suffers from some drawbacks, such as its limitation to simple geometry and uniform mesh, constraint to viscous flows, and the intrinsic tie-up between the time interval and the mesh spacing. 24,25 Morover, the implementation of boundary constraints of the second or the third types (ie, the Neumann condition and Robin conditions) for the LB method is still challenging, especially for curved boundaries.…”

mentioning

confidence: 99%

An improved axisymmetric lattice Boltzmann flux solver for axisymmetric isothermal/thermal flows

Zhang

Жен

Yang

et al. 2019

Numerical Methods in Fluids

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Summary In this work, an improved axisymmetric lattice Boltzmann flux solver (LBFS) is proposed for simulation of axisymmetric isothermal and thermal flows. This solver globally resolves the axisymmetric Navier‐Stokes (N‐S) equations through the finite volume strategy and locally reconstructs numerical fluxes with solutions to the lattice Boltzmann equation. Compared with previous axisymmetric LBFS, some novel strategies are adopted in this work to simplify the formulations and improve the accuracy. First, the macroscopic equations are reformulated to reduce the number of source terms and remove spatial derivatives involved in the source terms. Second, the local reconstruction of numerical fluxes utilizes relationships given by the Chapman‐Enskog analysis and combines the radial coordinate (r) with the local solution to the standard LB equation. By adopting these two modifications, the present axisymmetric LBFS avoids the fractional‐step formulation and the finite‐difference approximation adopted in the previous solver, which reduces the complexity of implementation. Moreover, an alternative way of predicting intermediate pressure is proposed, which could effectively fix the inaccurate resolution of the pressure field in previous axisymmetric LBFS. Further extensions are made to enrich the applicability of the present solver in thermal axisymmetric flows. Validations on various benchmark tests are carried out for comprehensive evaluation of the robustness and flexibility of the proposed solver.

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“…Subsequently, the temperature distribution function or concentration distribution function was directly defined for recovering the macroscopic CDE [21][22][23][24]26,28], and additional modifications were then implemented to remove the deviation term in the recovered macroscopic equation [21,22]. Furthermore, CDE LB models were also proposed for nonlinear CDE [23,26] and anisotropic diffusion [21,24,32,33] processes, and thus the applications of the LB method in heat and mass transfer systems are significantly extended.…”

Section: Introductionmentioning

confidence: 99%

Consistent second-order boundary implementations for convection-diffusion lattice Boltzmann method

et al. 2018

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In this study, an alternative second-order boundary scheme is proposed under the framework of the convection-diffusion lattice Boltzmann (LB) method for both straight and curved geometries. With the proposed scheme, boundary implementations are developed for the Dirichlet, Neumann and linear Robin conditions in a consistent way. The Chapman-Enskog analysis and the Hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second-order accuracy. Then, the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming [see the paragraph after Eq. (29) for the discussions of the "streaming step" in LB method]. After that, the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes. For straight boundaries, boundary nodes are directly placed at the physical boundary surface, and the present scheme is applied directly. When extending the present scheme to curved geometries, a local curvilinear coordinate system and first-order Taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface. In essence, the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface. Therefore, the advantages of the present boundary implementations are (i) the locality, i.e., no information from neighboring fluid nodes is required; (ii) the consistency, i.e., the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes, thus the three kinds of conditions are realized in a consistent way. It should be noted that the present focus is on two-dimensional cases, and theoretical derivations as well as the numerical validations are performed in the framework of the two-dimensional five-velocity lattice model.

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Lattice Boltzmann simulations of axisymmetric natural convection with anisotropic thermal diffusion

Cited by 15 publications

References 32 publications

Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects

Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects

An improved axisymmetric lattice Boltzmann flux solver for axisymmetric isothermal/thermal flows

Consistent second-order boundary implementations for convection-diffusion lattice Boltzmann method

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