Boundary conditions of the lattice Boltzmann method for convection–diffusion equations

Huang, Juntao; Yong, Wen‐An

doi:10.1016/j.jcp.2015.07.045

Cited by 66 publications

(34 citation statements)

References 28 publications

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“…The numerical methodology is briefly introduced in Supporting Materials and Methods. The general numerical procedure for the boundary condition and the immersed-boundary method can be found in (19,(26)(27)(28). A similar study, but with a static boundary, has been proposed regarding the drug delivery problem (29,30).…”

Section: Lattice-boltzmann Model For Fluid-membranesolute Couplingmentioning

confidence: 99%

ATP Release by Red Blood Cells under Flow: Model and Simulations

Zhang

Shen

Hogan

et al. 2018

Biophysical Journal

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ATP is a major player as a signaling molecule in blood microcirculation. It is released by red blood cells (RBCs) when they are subjected to shear stresses large enough to induce a sufficient shape deformation. This prominent feature of chemical response to shear stress and RBC deformation constitutes an important link between vessel geometry, flow conditions, and the mechanical properties of RBCs, which are all contributing factors affecting the chemical signals in the process of vasomotor modulation of the precapillary vessel networks. Several in vitro experiments have reported on ATP release by RBCs due to mechanical stress. These studies have considered both intact RBCs as well as cells within which suspected pathways of ATP release have been inhibited. This has provided profound insights to help elucidate the basic governing key elements, yet how the ATP release process takes place in the (intermediate) microcirculation zone is not well understood. We propose here an analytical model of ATP release. The ATP concentration is coupled in a consistent way to RBC dynamics. The release of ATP, or the lack thereof, is assumed to depend on both the local shear stress and the shape change of the membrane. The full chemomechanical coupling problem is written in a lattice-Boltzmann formulation and solved numerically in different geometries (straight channels and bifurcations mimicking vessel networks) and under two kinds of imposed flows (shear and Poiseuille flows). Our model remarkably reproduces existing experimental results. It also pinpoints the major contribution of ATP release when cells traverse network bifurcations. This study may aid in further identifying the interplay between mechanical properties and chemical signaling processes involved in blood microcirculation.Under shear flow, both vesicles (in two and three dimensions) and RBCs exhibit the following two main modes: TT (the cell or vesicle acquires a given orientation while the membrane rotates around the center of mass) and TB (a quasi-solid-like flipping). For vesicles, TB occurs at high enough internal fluid viscosity with respect to the external one, whereas TT prevails at low enough internal viscosity (17). For RBCs (18-21), the transition from TB to TT can be achieved by increasing shear stress. For low shear stress, RBCs exhibit TB, whereas for large shear stress, we have TT. Experiments Modeling ATP Release by RBCs under Flow

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Section: Lattice-boltzmann Model For Fluid-membranesolute Couplingmentioning

confidence: 99%

ATP Release by Red Blood Cells under Flow: Model and Simulations

Zhang

Shen

Hogan

et al. 2018

Biophysical Journal

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“…In this section, we would perform some simulations to validate present LB model for two-phase flows in porous media. Unless otherwise stated, the parameter β is set to be 1.0, the anti-bounce-back scheme is applied for Dirichlet boundary condition [49,[57][58][59][60][61][62],…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

A Lattice Boltzmann Model for Two-Phase Flow in Porous Media

Chai¹,

Liang²,

Du³

et al. 2019

SIAM J. Sci. Comput.

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In this paper, a lattice Boltzmann (LB) model with double distribution functions is proposed for two-phase flow in porous media where one distribution function is used for pressure governed by the Poisson equation, and the other is applied for saturation evolution described by the convection-diffusion equation with a source term. We first performed a Chapman-Enskog analysis, and show that the macroscopic nonlinear equations for pressure and saturation can be recovered correctly from present LB model. Then in the framework of LB method, we develop a local scheme for pressure gradient or equivalently velocity, which may be more efficient than the nonlocal secondorder finite-difference schemes. We also perform some numerical simulations, and the results show that the developed LB model and local scheme for ve- * locity are accurate and also have a second-order convergence rate in space.Finally, compared to the available pore-scale LB models for two-phase flow in porous media, the present LB model has more potential in the study of the large-scale problems.

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“…On the other hand, the present MRT model degenerates to the classical model when the macroscopic equations are linear (see e.g., [29,46]). For the latter, the convergence is established in [46] based on the stability structure proposed in [47,48].…”

Section: Conclusion and Remarksmentioning

confidence: 94%

“…There have been various LB models for CDEs or systems coupling CDEs and flow fields in the literature, e.g., [13,14,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. Among them, most models are concerned with linear isotropic or anisotropic CDEs [14,17,18,20,29,30,31,32,33,34,35] and those for nonlinear CDEs are relatively few. In [19], a Bhatnagar-Gross-Krook (BGK) model for general nonlinear CDEs is proposed by designing appropriate equilibrium and source term, and it is further extended to the anisotropic case in [23] and modified in [13,21,22].…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann method for general convection-diffusion equations: MRT model and boundary schemes

Zhang

Zhao

Lin

2019

Journal of Computational Physics

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This paper is concerned with the lattice Boltzmann method for general convectiondiffusion equations. For such equations, we develop a multiple-relaxation-time lattice Boltzmann model and show its consistency under the diffusive scaling. The secondorder accuracy of the half-way anti-bounce-back scheme accompanying the present M-RT model is justified based on an elegant relation of the collision matrix. Using the half-way anti-bounce-back scheme as a central step, we further construct some parameterized single-node second-order schemes for curved boundaries. The accuracy of the proposed model and boundary schemes are numerically validated with several nonlinear convection-diffusion equations.

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Boundary conditions of the lattice Boltzmann method for convection–diffusion equations

Cited by 66 publications

References 28 publications

ATP Release by Red Blood Cells under Flow: Model and Simulations

ATP Release by Red Blood Cells under Flow: Model and Simulations

A Lattice Boltzmann Model for Two-Phase Flow in Porous Media

Lattice Boltzmann method for general convection-diffusion equations: MRT model and boundary schemes

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