Discrete Boltzmann equation model for nonideal gases

He, Xiaoyi; Shan, Xiaowen; Doolen, Gary D.

doi:10.1103/physreve.57.r13

Cited by 562 publications

(396 citation statements)

References 13 publications

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“…The transformation from f i to f i in (26) then coincides with that introduced by He et al [22,19]. Equation (25) and its BGK form (27) may be derived by integrating the discrete Boltzmann equation (5) along a characteristic for time ∆t.…”

Section: Numerical Implementationmentioning

confidence: 99%

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Incompressible limits of lattice Boltzmann equations using multiple relaxation times

Dellar¹

2003

Journal of Computational Physics

159

150

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Lattice Boltzmann equations using multiple relaxation times are intended to be more stable than those using a single relaxation time. The additional relaxation times may be adjusted to suppress non-hydrodynamic modes that do not appear directly in the continuum equations, but may contribute to instabilities on the grid scale. If these relaxation times are fixed in lattice units, as in previous work, solutions computed on a given lattice are found to diverge in the incompressible (small Mach number) limit. This non-existence of an incompressible limit is analysed for an inclined one dimensional jet. An incompressible limit does exist if the nonhydrodynamic relaxation times are not fixed, but scaled by the Mach number in the same way as the hydrodynamic relaxation time that determines the viscosity.

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Section: Numerical Implementationmentioning

confidence: 99%

“…In other words, the f i at time t + ∆t are given explicitly in terms of quantities known at time t by equation (25), while the f i at time t + ∆t would have to be found by solving the system (28) of algebraic equations [22,19].…”

Section: Numerical Implementationmentioning

confidence: 99%

Incompressible limits of lattice Boltzmann equations using multiple relaxation times

Dellar¹

2003

Journal of Computational Physics

159

150

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“…Although the two-phase LBE models mentioned in §1 were developed based on different physical pictures, it can be shown that they can all be reformulated in the following form [9]:…”

Section: Lattice Boltzmann Equation For Two-phase Flowsmentioning

confidence: 99%

“…The forcing term F i represents the effects of the interaction force F and takes different formulations in different two-phase models. Here, we choose the multi-phase LBE based on the extended Boltzmann equation [9], in which F i is expressed as…”

Section: Lattice Boltzmann Equation For Two-phase Flowsmentioning

confidence: 99%

Chequerboard effects on spurious currents in the lattice Boltzmann equation for two-phase flows

Guo

Shi

Zheng

2011

Phil. Trans. R. Soc. A.

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Spurious currents near an interface between different phases are a common undesirable feature of the lattice Boltzmann equation (LBE) method for two-phase systems. In this paper, we show that the spurious currents of a kinetic theory-based LBE have a significant dependence on the parity of the grid number of the underlying lattice, which can be attributed to the chequerboard effect. A technique that uses a Lax-Wendroff streaming is proposed to overcome this anomaly, and its performance is verified numerically.

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“…Boltzmann equation in discrete form for the mass transfer and momentum equations for a system consisting of two non-compressible fluids can be written as follows (He et al, 1998):…”

Section: Two-phase Modelingmentioning

confidence: 99%

LBM Simulation of a Droplet Dripping Down a Hole

Haghani

Rahimian

Taghilou

2013

Engineering Applications of Computational Fluid Mechanics

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ABSTRACT:A droplet dripping through a hole, which is located on a horizontal plate, was simulated in the current work. To overcome the numerical instabilities and accommodate the high density and viscosity ratios, Lee's LBM model was used to simulate the two-phase flow. Also wettability effect was taken into account by imposing the contact angle between solid-liquid and gas phases using Cahn's wetting theory. The effects of gravitational acceleration, surface tension, equilibrium contact angle, viscosity ratio, density ratio, and also the geometrical parameters, such as the height and width of the hole, have been investigated separately. In addition to numerical results, high numerical stability and ease of using surface tension and contact angle for controlling fascinated the authors to model this problem. High numerical stability in capturing the remaining fine particles on the surface and slender strip of a droplet passing through a small hole is a significant contribution. The results show that gravitational force and adhesion force caused by surface tension, are opposing forces influencing droplet behaviour. Enhancing the contact angle to more than 90 degrees makes the surface hydrophobic and the droplet will drip under gravitational force. Also increasing the surface tension causes increasing adhesion force, which leads to droplet decay. In this case some parts of the droplet will remain on the surface.

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Discrete Boltzmann equation model for nonideal gases

Cited by 562 publications

References 13 publications

Incompressible limits of lattice Boltzmann equations using multiple relaxation times

Incompressible limits of lattice Boltzmann equations using multiple relaxation times

Chequerboard effects on spurious currents in the lattice Boltzmann equation for two-phase flows

LBM Simulation of a Droplet Dripping Down a Hole

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