Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios

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

doi:10.1016/j.jcp.2013.03.039

Cited by 110 publications

(107 citation statements)

References 36 publications

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“…Note that other viscosity interpolation schemes are possible [62]. Then, the effective relaxation parameter is…”

Section: A Single-phase Collision Operatormentioning

confidence: 99%

“…Again, the limited density ratio between the fluid components seems to be the main limitation of their approach. Indeed, the literature suggests that the Tölke et al model fails to model variable density ratios in simple benchmark cases like Couette flows [62].…”

Section: Introductionmentioning

confidence: 99%

“…The CGM can therefore be considered a mature tool for both industry and academia for the characterization of porous media. However, all the CGM methods described above still suffer from some deficiencies, as they may lack Galilean invariance to a certain extent and therefore may be inaccurate for simulating flow with density ratio in many practical situations [37,39,41,49,62]. Consequently, they can only simulate multicomponent flow through porous media with a more limited ratio of dynamic viscosity.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Note that other viscosity interpolation schemes are possible [62]. Then, the effective relaxation parameter is…”

Section: A Single-phase Collision Operatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…eff at the interface. Various interpolation methods at the interface are possible [35]. If k is the kinematic viscosity of the fluid k, we use the harmonic density weighted average to define the viscosity at the interface between the fluids:…”

Section: Single-phase Collision Operatormentioning

confidence: 99%

Modeling of static contact angles with curved boundaries using a multiphase lattice Boltzmann method with variable density and viscosity ratios

Leclaire

Abahri

Belarbi

et al. 2016

Numerical Methods in Fluids

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SUMMARYNumerical modeling of multiphase flow generally requires a special procedure at the solid wall in order to be consistent with Young's law for static contact angles. The standard approach in the lattice Boltzmann method, which consists of imposing fictive densities at the solid lattice sites, is shown to be deficient for this task. Indeed, fictive mass transfer along the boundary could happen and potentially spoil the numerical results. In particular, when the contact angle is less than 90 degrees, the deficiencies of the standard model are major. Various videos that demonstrate this behavior are provided (Supporting Information). A new approach is proposed and consists of directly imposing the contact angle at the boundaries in much the same way as Dirichlet boundary conditions are generally imposed. The proposed method is able to retrieve analytical solutions for static contact angles in the case of straight and curved boundaries even when variable density and viscosity ratios between the phases are considered. Although the proposed wetting boundary condition is shown to significantly improve the numerical results for one particular class of lattice Boltzmann model, it is believed that other lattice Boltzmann multiphase schemes could also benefit from the underlying ideas of the proposed method. The proposed algorithm is two-dimensional, and the D2Q9 lattice is used. Copyright

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“…As a particular type of LBM, the two-phase lattice Boltzmann model (TP-LBM) can be used to describe interface dynamics between gas and liquid, which is generally classified into four categories in computational physics: pseudopotential model [29], [30], color model [31], [32], meanfield model [13], [33], and phase-field model [14], [34]. In the literature of computer graphics, there are works [35], [36], [37] that are based on the phase-field model and a specific type of two-fluid model [38].…”

Section: Two-phase Lattice Boltzmann Modelmentioning

confidence: 99%

A Unified Detail-Preserving Liquid Simulation by Two-Phase Lattice Boltzmann Modeling

Guo

Liu

2017

IEEE Trans. Visual. Comput. Graphics

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Traditional methods in graphics to simulate liquid-air dynamics under different scenarios usually employ separate approaches with sophisticated interface tracking/reconstruction techniques. In this paper, we propose a novel unified approach which is easy and effective to produce a variety of liquid-air interface phenomena. These phenomena, such as complex surface splashes, bubble interactions, as well as surface tension effects, can co-exist in one single simulation, and are created within the same computational framework. Such a framework is unique in that it is free from any complicated interface tracking/reconstruction procedures. Our approach is developed from the two-phase lattice Boltzmann method with the mean field model, which provides a unified framework for interface dynamics but is numerically unstable under turbulent conditions. Considering the drawbacks of the existing approaches, we propose techniques to suppress oscillations for significant stability enhancement, as well as derive a new subgrid-scale model to further improve stability, faithfully preserving liquid-air interface details without excessive diffusion by taking into account the density variation. The whole framework is highly parallel, enabling very efficient implementation. Comparisons with the related approaches show superiority on stable simulations with detail preservation and multiphase phenomena simultaneously involved. A set of animation results demonstrate the effectiveness of our method.

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Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios

Cited by 110 publications

References 36 publications

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

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

Modeling of static contact angles with curved boundaries using a multiphase lattice Boltzmann method with variable density and viscosity ratios

A Unified Detail-Preserving Liquid Simulation by Two-Phase Lattice Boltzmann Modeling

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