A curved no-slip boundary condition for the lattice Boltzmann method

Verschaeve, Joris C. G.; Müller, Bernhard

doi:10.1016/j.jcp.2010.05.022

Cited by 44 publications

(30 citation statements)

References 29 publications

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“…To further confirm our results, a separate control-volume calculation has been performed for System B, and the drag force obtained there is 2.922 × 10 −4 , with a 0.51% relative difference. It is interesting to notice that, in previous models for boundary mass conservation [21][22][23]25,26], normal boundary movement has not been considered in those simulations, even for those models with the boundary velocity included in the formulations [22,23,25].…”

Section: B Lmc Effect On Flow Field and Flow-structure Interactionmentioning

confidence: 99%

“…As we reviewed in the Introduction, typical mass conserving methods [21][22][23]25,26] apply an equal incoming-outgoing PDF-flux requirement at boundary nodes. In addition to the normal boundary movement discussed above, the unbalanced mass flux can also be introduced by the density gradient along the boundary [9,21].…”

Section: Effect Of Tangential Density Gradient On Boundary Mass Trmentioning

confidence: 99%

“…In addition to the velocity accuracy at the boundary, mass transfer across a solid-fluid boundary has also been concerned [5,[19][20][21][22][23][24][25][26]. Soon after the Ladd modification of the classical BB scheme, Aidun and Lu [5] argued that the Ladd method could induce possible mass transfer across an impenetrable surface due the particular PDF correction term.…”

Section: Introductionmentioning

confidence: 99%

“…These methods were presented for flat surfaces, and they might be difficult to be extended to general situations with curved surfaces. To apply the LMC concept for curved boundaries, Bao et al [23] modified the Filippova-Hanel interand extrapolation method [12], and Verschaeve and Müller [25] proposed to interpolate velocity for the equilibrium PDF part and to interpolate stress tensor for the nonequilibrium PDF part. Again, in both methods, the density at the boundary node was tuned to have equal incoming-outgoing PDF amounts at this boundary node.…”

Section: Introductionmentioning

confidence: 99%

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Mass and momentum transfer across solid-fluid boundaries in the lattice-Boltzmann method

Yin

Zhang

2012

Phys. Rev. E

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Mass conservation and momentum transfer across solid-fluid boundaries have been active topics through the development of the lattice-Boltzmann method. In this paper, we review typical treatments to prevent net mass transfer across solid-fluid boundaries in the lattice-Boltzmann method, and argue that such efforts are in general not necessary and could lead to incorrect results. Carefully designed simulations are conducted to examine the effects of normal boundary movement, tangential density gradient, and lattice grid resolution. Our simulation results show that the global mass conservation can be well satisfied even with local unbalanced mass transfer at boundary nodes, while a local mass conservation constraint can produce incorrect flow and pressure fields. These simulations suggest that local mass conservation, at either a fluid or solid boundary node, is not only an unnecessary consequence to maintain the global mass conservation, but also harmful for meaningful simulation results. In addition, the concern on the momentum addition and reduction associated with status-changing nodes is also not technically necessary. Although including this momentum addition or reduction has no direct influence on flow and pressure fields, the incorrect fluid-particle interaction may affect simulation results of particulate suspensions.

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Section: B Lmc Effect On Flow Field and Flow-structure Interactionmentioning

confidence: 99%

Section: Effect Of Tangential Density Gradient On Boundary Mass Trmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mass and momentum transfer across solid-fluid boundaries in the lattice-Boltzmann method

Yin

Zhang

2012

Phys. Rev. E

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“…The lattice Boltzmann equation is regarded as an explicit finite difference approximation of a velocity-discrete Boltzmann equation [7,8]. In describing the macroscopic Navier-Stokes (N-S) equations, it is second order accurate in space and time [1,9,10]. In particular, the spatial second order accuracy for the deviatoric stress tensor is proved theoretically by Luo and Yong [1].…”

Section: Introductionmentioning

confidence: 99%

An alternative lattice Boltzmann model for three-dimensional incompressible flow

Zhang

Zeng

Xie

et al. 2014

Computers & Mathematics with Applications

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a b s t r a c tIn this work, an alternative lattice Boltzmann (LB) model for three-dimensional (3D) incompressible flow is proposed. The equilibrium distribution function (EDF) of the present model is directly derived in accordance with the incompressibility conditions by applying the Hermite expansion. Moreover, an alternative formula for pressure computation is designed from the second order moment of the distribution function. The present 3D LB model inherits the advantageous features of Guo's LB model: the density is a constant, the fluid pressure is independent of density and the Navier-Stokes (N-S) equations for incompressible flow can be derived. Two benchmark tests, flow over a backward-facing step and the lid-driven cavity flow, are applied to validate the present model. Accurate results for these tests are obtained with the present model, and further comparisons with the previous LB models (the standard LB model, the He-Luo model and Guo's LB model) demonstrate that the present model provides better accuracy in the region of high deviatoric stress and such advantage is further enhanced by using the D3Q27 lattice.

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Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Silva

Ginzburg

2022

Numerical Methods in Fluids

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Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second-order boundary (LSOB) Dirichlet fluid flow method [Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two-relaxation-time (TRT) framework. The LSOB follows an in-node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third-order accurate Chapman-Enskog expansion, where the wall slip condition is built-in as a normal Taylor-type condition. The key point of this approach is that the required first-and second-order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called Lnode and Lwall, which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic-based diffusive bounce-back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second-order accuracy within this problem class.

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A curved no-slip boundary condition for the lattice Boltzmann method

Cited by 44 publications

References 29 publications

Mass and momentum transfer across solid-fluid boundaries in the lattice-Boltzmann method

Mass and momentum transfer across solid-fluid boundaries in the lattice-Boltzmann method

An alternative lattice Boltzmann model for three-dimensional incompressible flow

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

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