Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model

Leclaire, Sébastien; Reggio, Marcelo; Trépanier, Jean‐Yves

doi:10.1016/j.apm.2011.08.027

Cited by 115 publications

(86 citation statements)

References 42 publications

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“…25 Also in 2D°ows, it has been shown that the interface can be maintained even with a zero interfacial tension. 26 2.3. Three-dimensional rising bubble°ow…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

“…Liu et al 24 extend this procedure to the D3Q19 lattice. Leclaire et al [25][26][27] introduced the recoloring operator, the isotropic gradient discretization and a scaling mechanism into the CGM, in order to signi¯cantly reduce the spurious currents at the interface. Approach to increase the Galilean invariance of the CGM has also been proposed.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

Leclaire

Parmigiani

Chopard

et al. 2017

Int. J. Mod. Phys. C

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In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear°ow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scienti¯c results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and su®ers fewer limitations.

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“…25 Also in 2D°ows, it has been shown that the interface can be maintained even with a zero interfacial tension. 26 2.3. Three-dimensional rising bubble°ow…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

Leclaire

Parmigiani

Chopard

et al. 2017

Int. J. Mod. Phys. C

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“…This CGM has been showed to be compatible with many solutions of hydrodynamic fluid-fluid interaction problems, namely planar interface [76]; Laplace law [53]; two-phase Couette flow [39]; two-phase spinodal decomposition growth law [42]; oscillating plate [42]; Zalesak disk [42]; 2D capillary wave [42]; 2D oscillating bubble [42]; two-phase Poiseuille flow [41]; two-phase hydrostatic pressure [41]; 2D bubble subject to Archimedes force [41]; 2D capillary-gravity wave [41]; and 2D static contact angles on a curved geometry [44], among others which may use a variant of the CGM.…”

Section: Numerical Simulationmentioning

confidence: 89%

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

et al. 2017

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This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

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“…Latva-Kokko and Rothman 17 improved the recoloring step in the RÀK model, which is able to reduce the lattice pinning e®ect and decrease the spurious currents. 2,18 Now the recoloring step is widely used in applications of the RÀK model. 2,13,19 Recently, Reis and Phillips developed a twodimensional nine-velocity RÀK model.…”

Section: Introductionmentioning

confidence: 99%

“…2,20,23,25 In the literature, it is more often that cases with identical densities were simulated using the RÀK model, such as droplet deformation and breakup in simple shear°o w, 2 two-phase°ow in porous media, 4 high-viscosity ratio two-phase parallel°ow in a channel. 18,25 Note in the latter two°ows, only two°uids with identical densities but di®erent kinematic viscosities are simulated.…”

Section: Introductionmentioning

confidence: 99%

On Simulations of High-Density Ratio Flows Using Color-Gradient Multiphase Lattice Boltzmann Models

Huang

et al. 2013

Int. J. Mod. Phys. C

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Originally, the color-gradient model proposed by Rothman and Keller (RÀK) was unable to simulate immiscible two-phase°ows with di®erent densities. Later, a revised version of the RÀK model was proposed by Grunau et al. [D. Grunau, S. Chen and K. Eggert, Phys. Fluids A: Fluid Dyn. 5, 2557 (1993).] and claimed it was able to simulate two-phase°ows with high-density contrast. Some studies investigate high-density contrast two-phase°ows using this revised RÀK model but they are mainly focused on the stationary spherical droplet and bubble cases. Through theoretical analysis of the model, we found that in the recovered NavierÀStokes (NÀS) equations which are derived from the RÀK model, there are unwanted extra terms. These terms disappear for simulations of two-phase°ows with identical densities, so the correct NÀS equations are fully recovered. Hence, the RÀK model is able to give accurate results for°ows with identical densities. However, the unwanted terms may a®ect the accuracy of simulations signi¯cantly when the densities of the two°uids are di®erent. For the simulations of spherical bubbles and droplets immersed in another°uid (where the densities of the two°uids are di®erent), the extra terms may not be important and hence, in terms of surface tension, accurate results can be obtained. However, generally speaking, the unwanted term may be signi¯cant in many°ows and the RÀK model is unable to obtain the correct results due to the e®ect of the extra terms. Through numerical simulations of parallel two-phase°ows in a channel, we con¯rm that the RÀK model is not appropriate for general two-phase°ows with di®erent densities. A scheme to eliminate the unwanted terms is also proposed and the scheme works well for cases of density ratios less than 10.

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Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model

Cited by 115 publications

References 42 publications

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

On Simulations of High-Density Ratio Flows Using Color-Gradient Multiphase Lattice Boltzmann Models

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