Color-gradient lattice Boltzmann model with nonorthogonal central moments: Hydrodynamic melt-jet breakup simulations

Saito, Shigemi; Rosis, Alessandro De; Festuccia, Alessio; Kaneko, Akiko; Abe, Yutaka; Koyama, Kazuya

doi:10.1103/physreve.98.013305

Cited by 34 publications

(29 citation statements)

References 93 publications

(191 reference statements)

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“…This is totally consistent with the BGK counterpart, where equilibrium populations just account for an extra magnetic field-dependent term [40]. Moreover, a third-order velocity term has been added to the equilibrium to simulate jet breakup [41] and, again, it is found that it does not affect the algorithmic procedure. In principle, it is possible to derive a central-momentsbased procedure for whatever arbitrary truncation order of the equilibrium populations.…”

Section: Introductionsupporting

confidence: 76%

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

Rosis

Luo

2019

Phys. Rev. E

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The cascaded lattice Boltzmann method decomposes the collision stage on a basis of central moments on which the equilibrium state is assumed equal to that of the continuous Maxwellian distribution. Such a relaxation process is usually considered as an assumption, which is then justified a posteriori by showing the enhanced Galilean invariance of the resultant algorithm. An alternative method is to relax central moments to the equilibrium state of the discrete second-order truncated distribution. In this paper, we demonstrate that relaxation to the continuous Maxwellian distribution is equivalent to the discrete counterpart if higher-order (up to sixth) Hermite polynomials are used to construct the equilibrium when the D3Q27 lattice velocity space is considered. Therefore, a theoretical a priori justification of the choice of the continuous distribution is formally provided for the first time.

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Section: Introductionsupporting

confidence: 76%

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

Rosis

Luo

2019

Phys. Rev. E

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“…While the original formulation of LBM using explicit time stepping with local spatial interactions (thus, devoid of global solves) had been recognized in graphics as highly parallelizable [18]- [21], it quickly fell into disuse due to its substandard visual results and its limited stability and/or accuracy with respect to density ratios and Reynolds numbers. Yet, LBM has experienced a series of developments in recent years [22]- [24], especially with the development of central-moment relaxation models and coupling with Shan-Chen, free energy, or phase-field models [25]. As a result, modern Fig.…”

Section: Introductionmentioning

confidence: 99%

Kinetic-Based Multiphase Flow Simulation

Liu

Desbrun

et al. 2021

IEEE Trans. Visual. Comput. Graphics

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Multiphase flows exhibit a large realm of complex behaviors such as bubbling, glugging, wetting, and splashing which emerge from air-water and water-solid interactions. Current fluid solvers in graphics have demonstrated remarkable success in reproducing each of these visual effects, but none have offered a model general enough to capture all of them concurrently. In contrast, computational fluid dynamics have developed very general approaches to multiphase flows, typically based on kinetic models. Yet, in both communities, there is dearth of methods that can simulate density ratios and Reynolds numbers required for the type of challenging real-life simulations that movie productions strive to digitally create, such as air-water flows. In this paper, we propose a kinetic model of the coupling of the Navier-Stokes equations with a conservative phase-field equation, and provide a series of numerical improvements over an existing kinetic-based solver to offer a general multiphase flow solver. The resulting algorithm is embarrassingly parallel, conservative, far more stable than current solvers even for real-life conditions, and general enough to capture the typical multiphase flow behaviors. Various simulation results are presented, including comparisons to both previous work and real footage, to highlight the advantages of our new method.

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“…During the last three decades, the mesoscopic lattice Boltzmann method (LBM), based on the kinetic theory, has become an increasingly important method for numerical simulations of multiphase flows, mainly on account of its meso-scale features, easy implementation, and computational efficiency. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] Generally, the existing multiphase LB models can be classified into four categories: the color-gradient model, 20,21 the pseudopotential model, 3,22 the free-energy model, 23,24 and the mean-field model. 25 Among them, the pseudopotential model is considered in the present work due to its simplicity and computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

“…35,36 In addition, the cascaded lattice Boltzmann method (CLBM), which employs moments in a co-moving frame in contrast to the stationary moments in MRT, has also been shown to improve numerical stability significantly compared with the classical SRT-LBM. 7,12,16,[37][38][39] The present work focuses on the MRT-LBM, in which the collision step is carried out in a (raw) moment space via a transformation matrix M, where different moments can be relaxed independently. The post-collision moments are then transformed back via M −1 , and the streaming step is implemented in the discrete velocity space as usual.…”

Section: Introductionmentioning

confidence: 99%

“…In parallel, the CLBM, 37 which can be viewed as a non-orthogonal MRT-LBM in the comoving frame, has been shown to possess very good numerical stability for high Rayleigh number thermal flows, 39 as well as high Reynolds and Weber number multiphase flows. 7,12,16 Recently, an improved three-dimensional (3D) CLBM has been proposed by Fei et al, 44 where an improved set of non-orthogonal basis vectors were employed and a generalized multiple-relaxationtime (GMRT) scheme 39,45 was adopted to cast MRT-LBM and CLBM into a unified framework. Within the GMRT framework, the CLBM can reduce to a non-orthogonal MRT-LBM when the shift matrix is a unit matrix, where the shift matrix is defined to shift (raw) moments of the DFs to the corresponding central moments.…”

Section: Introductionmentioning

confidence: 99%

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Modeling realistic multiphase flows using a non-orthogonal multiple-relaxation-time lattice Boltzmann method

Fei

Luo

et al. 2019

Physics of Fluids

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In this paper, we develop a three-dimensional multiple-relaxation-time lattice Boltzmann method (MRT-LBM) based on a set of nonorthogonal basis vectors. Compared with the classical MRT-LBM based on a set of orthogonal basis vectors, the present non-orthogonal MRT-LBM simplifies the transformation between the discrete velocity space and the moment space and exhibits better portability across different lattices. The proposed method is then extended to multiphase flows at large density ratio with tunable surface tension, and its numerical stability and accuracy are well demonstrated by some benchmark cases. Using the proposed method, a practical case of a fuel droplet impacting on a dry surface at high Reynolds and Weber numbers is simulated and the evolution of the spreading film diameter agrees well with the experimental data. Furthermore, another realistic case of a droplet impacting on a super-hydrophobic wall with a cylindrical obstacle is reproduced, which confirms the experimental finding of Liu et al. ["Symmetry breaking in drop bouncing on curved surfaces," Nat. Commun. 6, 10034 (2015)] that the contact time is minimized when the cylinder radius is comparable with the droplet radius.

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Color-gradient lattice Boltzmann model with nonorthogonal central moments: Hydrodynamic melt-jet breakup simulations

Cited by 34 publications

References 93 publications

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

Kinetic-Based Multiphase Flow Simulation

Modeling realistic multiphase flows using a non-orthogonal multiple-relaxation-time lattice Boltzmann method

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