A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows

Suga, Kazuhiko; Kuwata, Yusuke; Takashima, Koji; Chikasue, Ryu

doi:10.1016/j.camwa.2015.01.010

Cited by 166 publications

(99 citation statements)

References 36 publications

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“…These matrices are derived similarly as in Refs. [73][74][75]; the only difference here concerns the ordering indexes i of the velocity space which is different from these studies. It has been judged pertinent to reproduce them in the present article so that all the matrices and indexes are presented here with the same ordering of the lattice connectivity vectors.…”

Section: A Single-phase Collision Operatormentioning

confidence: 76%

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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Section: A Single-phase Collision Operatormentioning

confidence: 76%

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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“…Furthermore, it is found that the nonorthogonal MRT-LBM requires approximately 25% less computational time than the orthogonal MRT model in Ref. [48]. …”

Section: Appendix C: Nonorthogonal Mrt-lbm For 3d Lid-driven Cavity Flowmentioning

confidence: 99%

“…Therefore, compared with the D3Q27 MRT-LBM in Ref. [48], an MRT-LBM based on the present raw moment set can simplify the implementation and reduce the computational cost. As shown in Appendix C, the simulation results for 3D Lid-driven cavity flow by the nonorthogonal MRT-LBM are in good agreement with the benchmark solutions by Ku et al [49], which implies that the nonorthogonal MRT-LBM can retain the numerical accuracy when simplifying the implementation.…”

Section: B Central Moment Set Equilibria and Forcing Termsmentioning

confidence: 99%

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Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

Fei

Luo

2018

Phys. Rev. E

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The cascaded or central-moment-based lattice Boltzmann method (CLBM) proposed in [Phys. Rev. E 73, 066705 (2006)] possesses very good numerical stability. However, two constraints exist in three-dimensional (3D) CLBM simulations. First, the conventional implementation for 3D CLBM involves cumbersome operations and requires much higher computational cost compared to the single-relaxation-time (SRT) LBM. Second, it is a challenge to accurately incorporate a general force field into the 3D CLBM. In this paper, we present an improved method to implement CLBM in 3D. The main strategy is to adopt a simplified central moment set and carry out the central-moment-based collision operator based on a general multi-relaxation-time (GMRT) framework. Next, the recently proposed consistent forcing scheme for CLBM [Fei and Luo, Phys. Rev. E 96, 053307 (2017)] is extended to incorporate a general force field into 3D CLBM. Compared with the recently developed nonorthogonal CLBM [Rosis, Phys. Rev. E 95, 013310 (2017)], our implementation is proved to reduce the computational cost significantly. The inconsistency of adopting the discrete equilibrium distribution functions in the nonorthogonal CLBM is analyzed and validated. The 3D CLBM developed here in conjunction with the consistent forcing scheme is verified through numerical simulations of several canonical force-driven flows, highlighting very good properties in terms of accuracy, convergence, and consistency with the nonslip rule. Finally, the techniques developed here for 3D CLBM can be applied to make the implementation and execution of 3D MRT-LBM more efficient.

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“…The porous wall consists of staggered cube arrays in which solid cubes are interconnected and the porosity of the porous wall is set to 0.71. To directly treat the porous structure, the D3Q27 multiple relaxation time (MRT) lattice Boltzmann method (LBM) of Suga et al (2015) with the imbalance correction local grid refinement method of Kuwata and Suga (2016) is employed for the turbulent flow simulation.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann direct numerical simulation of interface turbulence over porous and rough walls

Kuwata

Suga

2016

International Journal of Heat and Fluid Flow

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A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows

Cited by 166 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

Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

Lattice Boltzmann direct numerical simulation of interface turbulence over porous and rough walls

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