A novel two-dimensional coupled lattice Boltzmann model for incompressible flow in application of turbulence Rayleigh–Taylor instability

Wei, Yikun; Yue, Qian; Wang, Zhengdao

doi:10.1016/j.compfluid.2017.07.003

Cited by 35 publications

(21 citation statements)

References 24 publications

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“…ω i and c i depend on the choice of the discrete-velocity lattice model. For plane flows, the popular D2Q9 lattice model [17,18,50,52] is adopted here, and ω i can be then given by ω 0 = 4/9, ω 1−4 = 1/9, ω 5−8 = 1/36, and c i is defined as…”

Section: Axisymmetric Lb Model For the Allen-cahn Equationmentioning

confidence: 99%

Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio

Liang

Yang

Chen

et al. 2019

International Journal of Heat and Mass Transfer

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In this paper, a novel lattice Boltzmann (LB) model based on the Allen-Cahn phase-field theory is proposed for simulating axisymmetric multiphase flows. The most striking feature of the model is that it enables to handle multiphase flows with large density ratio, which are unavailable in all previous axisymmetric LB models. The present model utilizes two LB evolution equations, one of which is used to solve fluid interface, and another is adopted to solve hydrodynamic properties. To simulate axisymmetric multiphase flows effectively, the appropriate source term and equilibrium distribution function are introduced into the LB equation for interface tracking, and simultaneously, a simple and efficient forcing distribution function is also delicately designed in the LB equation for hydrodynamic properties. Unlike many existing LB models, the source and forcing terms of the model arising from the axisymmetric effect include no additional gradients, and consequently, the present model contains only one non-local phase field variable, which in * Corresponding author. this regard is much simpler. In addition, to enhance the model's numerical stability, an advanced multiple-relaxation-time (MRT) model is also applied for the collision operator. We further conducted the Chapman-Enskog analysis to demonstrate the consistencies of our present MRT-LB model with the axisymmetric Allen-Cahn equation and hydrodynamic equations. A series of numerical examples, including static droplet, oscillation of a viscous droplet, breakup of a liquid thread, and bubble rising in a continuous phase, are used to test the performance of the proposed model. It is found that the present model can generate relatively small spurious velocities and can capture interfacial dynamics with higher accuracy than the previously improved axisymmetric LB model. Besides, it is also found that our present numerical results show excellent agreement with analytical solutions or available experimental data for a wide range of density ratios, which highlights the strengths of the proposed model.

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Section: Axisymmetric Lb Model For the Allen-cahn Equationmentioning

confidence: 99%

Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio

Liang

Yang

Chen

et al. 2019

International Journal of Heat and Mass Transfer

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“…From a computational resource perspective, the remarkable merits are brevity of programming, numerical potency, inherent parallelism, and ease treatment of intricate boundary conditions. This kind of method has comprehensive capacities in quite several fields, from phonon transport [13] to approximate incompressible flows [14][15][16][17][18][19][20][21][22][23][24][25], full compressible flows [26][27][28][29][30][31][32][33][34][35][36][37], dendrite growth [38,39] and thermal multiphase flows [40]. Recently, the mesoscopic kinetics method is also becoming increasingly popular in computational mathematics and engineering science for solving certain NPDEs, including Burgers' equations [41,42], Korteweg-de Vries equation [43], Gross-Pitaevskii equation [44], convection-diffusion equation [45][46][47][48][49][50][51], Kuramoto-Sivashinsky equation [52], wave equation [53,54], Dirac equation [55], Poisson equation…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model

Lai

Shi

2019

Entropy

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In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon.

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“…However, it was found that these lattices are completely Galilean invariant and more accurate than conventional lattices [28,29]. Despite these instability concerns, the D2Q13 lattice has recently been used in work related to incompressible ow of the Rayleigh-Taylor instability using a modied equilibrium distribution [30]. Considering the above, we view these lattices suitable for the work presented here if we relax the entropy requirement and limit our work to within this viscosity range.…”

Section: Numerical Stabilitymentioning

confidence: 99%

Introducing a variable speed of sound in single-component lattice Boltzmann simulations of isothermal fluid flows

et al. 2018

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To simulate the hydrodynamics and mixing characteristics of chemical reactors by means of a lattice Boltzmann method (LBM), it is essential to consider components with varying molecular weights (and therefore speeds of sound). This option requires modication of the standard equilibrium distribution function and the use of an extended velocity set. In this paper, we show that, for isothermal incompressible single-component non-reactive ows, tuning the speed of sound with a modied equilibrium distribution and an extended velocity set allows for reproducing the proper ow characteristics with strongly reduced errors compared to LBM simulations on standard lattices. This is done for two isothermal benchmarks, viz. a damped standing pressure wave and a decaying viscous Taylor-Green vortex. The convergence as a function of the number of lattice nodes used improves substantially for varying values of the speed of sound.

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A novel two-dimensional coupled lattice Boltzmann model for incompressible flow in application of turbulence Rayleigh–Taylor instability

Cited by 35 publications

References 24 publications

Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio

Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio

Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model

Introducing a variable speed of sound in single-component lattice Boltzmann simulations of isothermal fluid flows

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