Shear stress in lattice Boltzmann simulations

Krüger, Timm; Varnik, Fathollah; Raabe, Dierk

doi:10.1103/physreve.79.046704

Cited by 107 publications

(80 citation statements)

References 34 publications

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“…(28). However, as shown below, the flux can be computed from the nonequilibrium part of the distribution function with a second-order convergence rate, which is similar to the computation of the strain rate tensor or shear stress in the LBM [35,36]. Substituting Eq.…”

Section: A Local Scheme For the Heat And Mass Fluxesmentioning

confidence: 99%

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Lattice Boltzmann model for the convection-diffusion equation

2013

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We propose a lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) and show that the CDE can be recovered correctly from the model by the Chapman-Enskog analysis. The most striking feature of the present LB model is that it enables the collision process to be implemented locally, making it possible to retain the advantage of the lattice Boltzmann method in the study of the heat and mass transfer in complex geometries. A local scheme for computing the heat and mass fluxes is then proposed to replace conventional nonlocal finite-difference schemes. We further validate the present model and the local scheme for computing the flux against analytical solutions to several classical problems, and we show that both the model for the CDE and the computational scheme for the flux have a second-order convergence rate in space. It is also demonstrated the present model is more accurate than existing LB models for the CDE.

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Section: A Local Scheme For the Heat And Mass Fluxesmentioning

confidence: 99%

“…(we note that this approximation has been widely used to calculate the strain rate tensor or shear stress in the LBM [35,36]), we can obtain the following scheme to compute the gradient term ∇φ:…”

Section: A Local Scheme For the Heat And Mass Fluxesmentioning

confidence: 99%

Lattice Boltzmann model for the convection-diffusion equation

2013

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“…In those methods, higher resolution and higher stability is achieved by increasing (without limit) the number of discretization points. In contrast, with the LB method an increase of n induces higher resolution, but care should be taken not to exceed some given threshold value, beyond which the code destabilizes [42]. Therefore, in all our simulations we have kept a sufficiently small enough number of membrane nodes per lattice grid (by keeping the distance between two adjacent membrane nodes ds close to 1).…”

Section: B Computed Equilibrium Shapesmentioning

confidence: 99%

Two-dimensional vesicle dynamics under shear flow: Effect of confinement

2011

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Dynamics of a single vesicle under shear flow between two parallel plates is studied in two-dimensions using lattice-Boltzmann simulations. We first present how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using an approach known from the immersed boundary method. The fluid flow is computed on an Eulerian regular fixed mesh while the location of the vesicle membrane is tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle equilibrium shapes in a fluid at rest are found and the dynamical behavior of a vesicle under simple shear flow is being reproduced. Further, we focus on investigating the effect of the confinement on the dynamics, a question that has received little attention so far. In particular, we study how the vesicle steady inclination angle in the tank-treading regime depends on the degree of confinement. The influence of the confinement on the effective viscosity of the composite fluid is also analyzed. At a given reduced volume (the swelling degree) of a vesicle we find that both the inclination angle, and the membrane tank-treading velocity decrease with increasing confinement. At sufficiently large degree of confinement the tank-treading velocity exhibits a nonmonotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.

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“…Within the LBM, it is straightforward to evaluate the fluid stress locally (e.g. [2,3]). We thus focus here on a computation of the particle stress at a given position and independent of any further assumptions.…”

Section: Stress Evaluationmentioning

confidence: 99%

“…The total stress is the sum of the fluid and particle stresses, s(r, t) = s f (r, t) + s p (r, t). Usually, the evaluation of the local fluid stress s f (r, t) does not pose a serious problem [1][2][3]. The major difficulty is the computation of the local particle stress s p (r, t).…”

Section: Introductionmentioning

confidence: 99%

Particle stress in suspensions of soft objects

Varnik¹,

Raabe

2011

Phil. Trans. R. Soc. A.

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In a suspension of extended objects such as colloidal particles, capsules or vesicles, the contribution of particles to the stress is usually evaluated by first determining the stress originating from a single particle (e.g. via integrating the fluid stress over the surface of a particle) and then adding up the contributions of individual particles. While adequate for a computation of the average stress over the entire system, this approach fails to correctly reproduce the local stress. In this work, we propose and validate a variant of the method of planes which overcomes this problem. The method is particularly suited for many-body interactions arising from, for example, shear and bending rigidity of red blood cells.

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Shear stress in lattice Boltzmann simulations

Cited by 107 publications

References 34 publications

Lattice Boltzmann model for the convection-diffusion equation

Lattice Boltzmann model for the convection-diffusion equation

Two-dimensional vesicle dynamics under shear flow: Effect of confinement

Particle stress in suspensions of soft objects

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