Lattice BGK Model for Incompressible Navier–Stokes Equation

Guo, Zhaoli; Shi, Bowen; Wang, Nengchao

doi:10.1006/jcph.2000.6616

Cited by 428 publications

(239 citation statements)

References 20 publications

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“…The result of LBM is indicated by the filled circle, while the analytical solution, Eq. (20), is shown by the solid line. For reference, moreover, the numerical solution of the NS equation is shown in Fig.…”

Section: Accuracy Of Lbm-coupled Model For Steady State Flowmentioning

confidence: 99%

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Acceleration of Macrosegregation Simulation Based on Lattice Boltzmann Method

Ohno

Sato

2018

ISIJ Int.

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Lattice Boltzmann Method (LBM), newly developing technique of computational fluid dynamics, is coupled with solute and energy conservation equations to develop a macrosegregation simulation model (LBM-coupled model) with high computational efficiency. LBM does not require time-consuming calculations for correction of velocity and pressure of fluid in contrast to methods directly solving Navier-Stokes (NS) equation and, therefore, LBM is computationally efficient. In this study, the accuracy of the LBMcoupled model is investigated by calculating the steady state flows and by comparing the results with those of analytical solutions and a conventional model based on the NS equation. The results between them are almost identical with each other and it indicates that the accuracy of the LBM-coupled model is sufficiently high. Moreover, a macrosegregation simulation is carried out for a simple case where the macrosegregation emerges only by natural convection, by means of the LBM-coupled and conventional models. The LBM-coupled model yields almost the same result with the one of NS-based model. Importantly, however, the simulation of LBM-coupled model is about five times faster than the one of NS-based model.

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Section: Accuracy Of Lbm-coupled Model For Steady State Flowmentioning

confidence: 99%

“…[14][15][16][17][18][19][20] It is a newly developing technique of computational fluid dynamics. LBM describes the time evolution of particle distribution function, from which one can calculate the macroscopic quantities such as the density, velocity and pressure of fluid.…”

Section: Introductionmentioning

confidence: 99%

Acceleration of Macrosegregation Simulation Based on Lattice Boltzmann Method

Ohno

Sato

2018

ISIJ Int.

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“…In the present study, a two-dimensional nine-velocity (D2Q9) model and the Bhatnagar-Gross-Krook (BGK) collision model used in the standard Boltzmann equation are adopted [19].…”

Section: Incompressible Lattice Bhatnagar-gross-krook (Ilbgk) Modelmentioning

confidence: 99%

“…The incompressible Navier-Stokes equations can be recovered from this incompressible LBGK model [19,20].…”

Section: Incompressible Lattice Bhatnagar-gross-krook (Ilbgk) Modelmentioning

confidence: 99%

Numerical simulation of flow past rectangular cylinders with different aspect ratios using the incompressible lattice Boltzmann method

et al. 2012

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This paper presents a numerical study of a uniform flow past a rectangular cylinder using the incompressible lattice Boltzmann method (ILBM). Firstly, we use the ILBM to simulate the flow past a square cylinder symmetrically placed in a two-dimensional channel and results are validated against the well-resolved results obtained using finite-difference method and finite-volume method. Secondly, the effects of the aspect ratio defined as R = width/height on the fluid forces, vortex shedding frequency and the flow structures in the wake are investigated. Aspect ratios ranging from 0.15 to 4.00 and four Reynolds numbers Re = 100, 150, 200 and 250 are selected for the investigation. The results show that the effects of aspect ratio on physical quantities such as drag and lift coefficients, Strouhal number and the vortex shedding mechanism are very notable in the range between 0 and 2. In general, the drag coefficient decreases with the aspect ratio and the decreasing rate is more distinct in the range of 0.15 ≤ R ≤ 2.0. There is no local maximum found at around R = 0.6 in the drag coefficient as reported for higher Reynolds numbers in the literature. However the root-mean-square value of the lift coefficient shows a maximum value at R ≈ 0.5 for all Reynolds numbers selected. The variation of Strouhal number with R appears to be different for four selected Reynolds numbers. Especially for Re = 250, a discontinuity in St, as has been observed for higher Reynolds numbers, is observed at around R = 1.45 where multiple peaks are found in the result of Fourier spectrum analysis of the lift force and irregular vortex shedding behavior with no fixed shedding frequency is observed from the instantaneous vorticity contours. Such discontinuity is not observed for Re = 100, 150 and 200. The present results using the LBM are compared with some existing experimental data and numerical studies. The comparison shows that the LBM can capture the characteristics of the bluff body flow well and is a useful tool for bluff body flow studies.

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“…The velocity vectors are illustrated in Figure 2. The velocity directions of the D2Q9 Lattice Boltzmann BGK model are defined as (Guo et al, 2000).…”

Section: D Lattice Boltzmann Bgk Modelmentioning

confidence: 99%

Lattice Boltzmann Simulation of Fluid Flow in Synthetic Fractures

Eker

Akın

2006

Transp Porous Med

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Fractures play an important role in geothermal reservoir engineering as they dominate the fluid flow in the reservoir. Because of this reason determination of fracture permeability is very important to predict the performance of the geothermal reservoir. A fracture is usually assumed as a set of smooth parallel plates separated by a constant width. The absolute permeability of a smooth-walled fracture is related to the fracture aperture using the cubic law. However, the flow characteristics of an actual fracture surface would be quite different, affected by tortuousity and surface roughness. Though several researchers have discussed the effect of friction on flow, a unified methodology for studying flow on a rough fracture surface has not emerged. As experimental methods are expensive and time consuming most of the time numerical methods are used. In this work, we present results of the numerical computations for single phase flow simulations through two-dimensional synthetically created fracture apertures. These synthetic rock fractures are created using different fractal dimensions, anisotropy factors, and mismatch lengths that are obtained from the producing geothermal reservoirs in South Western Turkey. Lattice Boltzmann Method, which is a new computational approach suitable to simulate fluid flow especially in complex geometries, was then used to determine the permeability for different fractures. Regions of high velocity and low velocity flow were identified. The resulting permeability values were less than the ones obtained with the cubic law estimates. It has been found that as the mean aperture-fractal dimension ratio increased permeability increased. Moreover as the anisotropy factor increased permeability decreased with a second order polynomial relationship.

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Lattice BGK Model for Incompressible Navier–Stokes Equation

Cited by 428 publications

References 20 publications

Acceleration of Macrosegregation Simulation Based on Lattice Boltzmann Method

Acceleration of Macrosegregation Simulation Based on Lattice Boltzmann Method

Numerical simulation of flow past rectangular cylinders with different aspect ratios using the incompressible lattice Boltzmann method

Lattice Boltzmann Simulation of Fluid Flow in Synthetic Fractures

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