Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

Zheng, Lin; Guo, Zhaoli; Shi, Baochang; Chen, Zheng

doi:10.1016/j.jcp.2010.04.026

Cited by 24 publications

(16 citation statements)

References 25 publications

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“…(5) Implement the flux calculations by Equations (21a) to (21d) and by Equations (22a) to (22e). (6) Apply the pressure modifications given in Equations (23) to (26), and then replace the momentum flux from Equation (5b) with the modified flux ′ . (7) Solve the ordinary differential equation in Equation (20) by Euler explicit scheme for steady flows or four-stage Runge-Kutta scheme for time-dependent flows.…”

Section: Computational Sequencementioning

confidence: 99%

“…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%

See 2 more Smart Citations

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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Section: Computational Sequencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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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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“…11-14, we used a recently developed lattice-Boltzmann model (Guo et al 2009;Zheng et al 2010). The evolution equations for the velocity and concentration can be written as …”

Section: Appendixmentioning

confidence: 99%

Dynamic solute release from marine aggregates

Liu

Kindler

Khalili

2012

Limn Fluids and Environments

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Rapidly sinking marine snow aggregates play an important role in the vertical transport of carbon in the ocean. During their descent, particulate organic carbon is gradually turned over by microbial respiration and solubilization, while solutes are constantly released into the water. This steady-state scenario is interrupted when the aggregate passes through density discontinuities (pycnoclines), resulting in a retention period before resuming their decent. The accumulated excess solutes mediated by the absence of advection will then release dynamically into ambient water. In an attempt to quantify this dynamic process, we present numerical simulations of the flow adjacent to and solute release from porous spheres in a hydrodynamic regime representative of marine snow. We focus on the interdependence of internal diffusion-dominated transport and advective flow around an aggregate. The aggregate has been assumed to have a constant size, excess density, and permeability. We propose a new relationship for the dynamic release of solutes from sinking, porous aggregates in terms of the average Sherwood number, Sh ¼ 1 + 8Pe ), as a function of the Peclét number, Pe, where Pe ¼ aw s D -1 , a is the radius of the sphere, w s is the settling velocity, and D is the diffusion coefficient. An additional degradation rate constant, which was considered, did not change this finding significantly. From this relationship, release times and export depths-that is, the distances within which 99% of the excess solute is released into the ambient water-can be readily obtained as a function of aggregate size and excess density.

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“…The obtained formulation is referred to the lattice Boltzmann BGK model, which is the widely used version. The method has been developed in recent years when Zheng et al 14,15 proposed a simple LBE model for axisymmetric thermal flow. The formulation of the standard lattice Boltzmann (LB) model is based on the cartesian coordinate system (x, y).…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical study of Couette‐Taylor flow with an axial flow using lattice Boltzmann method

Mehrez

Gheith

Aloui

et al. 2019

Numerical Methods in Fluids

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Summary In this study, the numerical models for swirling flows developed by Li et al and Zhou for lattice Boltzmann method (LBM) are chosen. These models were firstly validated using the Couette‐Taylor flow between two concentric cylinders simulations. Numerical results showed the efficiency of the Zhou's model. Numerical simulation results using LBM are in good agreement for the steady and unsteady regimes compared to the literature review. In a second step, the Zhou model was then adopted to our study to determine the Couette‐Taylor instabilities with an axial flow. Two protocols are tested. The first one (direct protocol) starts with an azimuthal flow without any axial flow (Re = 0). Once the regime is established, an axial flow is then superposed to the Couette‐Taylor flow (with a sudden or a progressive manner). The second protocol (inverse protocol) starts with an axial flow at a given Reynolds number (Poiseuille flow). Once the regime is established, an azimuthal flow is the executed (with a sudden or a progressive manner). The effect of various parameters controlling the physical situation is also discussed. The increase of the azimuthal velocity mainly led to the emergence and development of Taylor vortices. Its influence decreases when the axial Reynolds number increases. The relevant result for this study is the change of the critical axial Reynolds number Rec (total disappearance of instabilities) with both protocols and both manners.

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Kinetic theory based lattice Boltzmann equation with viscous dissipation and pressure work for axisymmetric thermal flows

Cited by 24 publications

References 25 publications

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

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

Dynamic solute release from marine aggregates

Theoretical and numerical study of Couette‐Taylor flow with an axial flow using lattice Boltzmann method

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