Lattice Boltzmann for Advection-Diffusion Problems

Kusumaatmaja, Halim; Kuzmin, Alexandr; Shardt, Orest; Silva, Gonçalo; Viggen, Erlend Magnus

doi:10.1007/978-3-319-44649-3_8

Cited by 7 publications

(14 citation statements)

References 47 publications

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“…The velocity space is reduced to a finite number of discrete values (i.e., Q j ), and one must have sufficient velocity directions to obey the conservation laws. Yet, for a very wide range of 2‐D flows, a nine velocity set is sufficient to recover the macroscopic hydrodynamics, and 19 velocities in 3‐D …”

Section: Methodsmentioning

confidence: 99%

“…The spatio‐temporal locality of the computations involved makes the method easily parallelizable over distributed computational units unlike conventional FV based solvers where distant units need to communicate for the pressure and velocity coupling of an iterative Navier–Stokes solver. Given these factors, the LB method has gained widespread popularity over the past decades, for both single phase and multiphase flows …”

Section: Methodsmentioning

confidence: 99%

“…The D 3 Q 19 simulations similarly utilize the standard 19 velocity 3‐D lattice, which can be found described in Krüger et al The discretized equilibrium distribution function follows from a multiscale expansion in the incompressible (low Mach number) limit of the Maxwellian:

f_{i}^{σ, italiceq} = w_{i} ρ_{σ} ({}, 1 + \frac{e_{i} \cdot u_{σ}}{RT} + \frac{{((), e_{i} \cdot u_{σ})}^{2}}{2 {(italicRT)}^{2}} - \frac{{boldu}_{σ}^{2}}{2 italicRT})

…”

Section: Methodsmentioning

confidence: 99%

“…The weight factors are w 0 = 4/9, w 1 → 4 = 1/9 and w 5 → 8 = 1/36. ρ σ is the component density and follows from the zeroth moment of the distribution function:

ρ_{σ} = \sum_{i} f_{i}^{σ}

u σ is the bare component velocity and follows from the first moment of the distribution function:

ρ_{σ} boldu = \sum_{i} e_{i} f_{i}^{σ} + \frac{F_{i} normalΔ t}{2}

where F i is the force term. The lattice viscosity is related to the lattice relaxation time by

ν = c_{s}^{2} ((), τ - 1 / 2)

where the pseudosound‐speed

c_{s} = \sqrt{RT}

has the value

1 / \sqrt{3}

for the D 2 Q 9 lattice.…”

Section: Methodsmentioning

confidence: 99%

“…Contrary to the bottom–up PP method, there is the top–down free‐energy method for simulating multiphase flows in LB . Simulations using this approach start with a free‐energy functional with the intended thermodynamics, which is then used to derive other physical quantities, making these methods thermodynamically consistent by definition . This method has the advantage that certain properties like surface tension and interface width can be predefined.…”

Section: Introductionmentioning

confidence: 99%

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A lattice boltzmann approach to surfactant‐laden emulsions

2018

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We present a pseudopotential lattice Boltzmann method to simulate liquid–liquid emulsions with a slightly soluble surfactant. The model is investigated in 2‐D, over a wide parameter space for a single, stationary, immiscible droplet, and surface tension reduction by up to 15% is described in terms of a surfactant strength Λ (which roughly follows a Langmuir isotherm). The basic surfactant model is shown to be insufficient for arresting phase segregation—which is then achieved by changing the liquid–liquid interaction strength locally as a function of the surfactant density. 3‐D spinodal decomposition (phase separation) is simulated, where the surfactant is seen to adapt rapidly to the evolving interfaces. Finally, for pendent droplet formation in an immiscible liquid, the addition of surfactant is shown to alter the droplet‐size distribution and dynamics of newly formed droplets. © 2018 The Authors. AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers. AIChE J, 65: 811–828, 2019

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

f_{i}^{σ, italiceq} = w_{i} ρ_{σ} ({}, 1 + \frac{e_{i} \cdot u_{σ}}{RT} + \frac{{((), e_{i} \cdot u_{σ})}^{2}}{2 {(italicRT)}^{2}} - \frac{{boldu}_{σ}^{2}}{2 italicRT})

…”

Section: Methodsmentioning

confidence: 99%

“…The weight factors are w 0 = 4/9, w 1 → 4 = 1/9 and w 5 → 8 = 1/36. ρ σ is the component density and follows from the zeroth moment of the distribution function:

ρ_{σ} = \sum_{i} f_{i}^{σ}

u σ is the bare component velocity and follows from the first moment of the distribution function:

ρ_{σ} boldu = \sum_{i} e_{i} f_{i}^{σ} + \frac{F_{i} normalΔ t}{2}

where F i is the force term. The lattice viscosity is related to the lattice relaxation time by

ν = c_{s}^{2} ((), τ - 1 / 2)

where the pseudosound‐speed

c_{s} = \sqrt{RT}

has the value

1 / \sqrt{3}

for the D 2 Q 9 lattice.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A lattice boltzmann approach to surfactant‐laden emulsions

2018

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Convection-Diffusion with the Colour Gradient Lattice Boltzmann Method for Three-Component, Two-Phase Flow

et al. 2023

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Supersaturation in the Wake of a Precipitating Hydrometeor and Its Impact on Aerosol Activation

Bhowmick

Wang

Iovieno

et al. 2020

Geophysical Research Letters

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The activation of aerosols impacts the life cycle of a cloud. A detailed understanding is necessary for reliable climate prediction. Recent laboratory experiments demonstrate that aerosols can be activated in the wake of precipitating hydrometeors. However, many quantitative aspects of this wake-induced activation of aerosols remain unclear. Here, we report a detailed numerical investigation of the activation potential of wake-induced supersaturation. By Lagrangian tracking of aerosols, we show that a significant fraction of aerosols are activated in the supersaturated wake. These "lucky aerosols" are entrained in the wake's vortices and reside in the supersaturated environment sufficiently long to be activated. Our analyses show that this wake-induced activation of aerosols can contribute to the life cycle of the clouds. Plain Language Summary We numerically investigate how new water droplets or ice particles are formed within a cloud. Out of several proposed physical processes for droplet generation, recent experimental studies have shown that a large droplet can nucleate aerosols in the wake behind it when falling under gravity. We present a detailed analysis of various physical factors that lead to an excess of water vapor behind the hydrometeors (e.g., droplets, sleet, or hail) and investigate the effectiveness of this process on activation of aerosols to create new cloud particles.

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Lattice Boltzmann for Advection-Diffusion Problems

Cited by 7 publications

References 47 publications

A lattice boltzmann approach to surfactant‐laden emulsions

A lattice boltzmann approach to surfactant‐laden emulsions

Convection-Diffusion with the Colour Gradient Lattice Boltzmann Method for Three-Component, Two-Phase Flow

Supersaturation in the Wake of a Precipitating Hydrometeor and Its Impact on Aerosol Activation

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