121 research outputs found
Shear stress in lattice Boltzmann simulations
A thorough study of shear stress within the lattice Boltzmann method is
provided. Via standard multiscale Chapman-Enskog expansion we investigate the
dependence of the error in shear stress on grid resolution showing that the
shear stress obtained by the lattice Boltzmann method is second order accurate.
This convergence, however, is usually spoiled by the boundary conditions. It is
also investigated which value of the relaxation parameter minimizes the error.
Furthermore, for simulations using velocity boundary conditions, an artificial
mass increase is often observed. This is a consequence of the compressibility
of the lattice Boltzmann fluid. We investigate this issue and derive an
analytic expression for the time-dependence of the fluid density in terms of
the Reynolds number, Mach number and a geometric factor for the case of a
Poiseuille flow through a rectangular channel in three dimensions. Comparison
of the analytic expression with results of lattice Boltzmann simulations shows
excellent agreement.Comment: 15 pages, 4 figures, 2 table
Two-dimensional Vesicle dynamics under shear flow: effect of confinement
Dynamics of a single vesicle under shear flow between two parallel plates is
studied using two-dimensional 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
non-monotonous dependence on the reduced volume and the effective viscosity
shows a nonlinear behavior.Comment: 12 pages, 8 figure
Impalement transitions in droplets impacting microstructured superhydrophobic surfaces
Liquid droplets impacting a superhydrophobic surface decorated with
micro-scale posts often bounce off the surface. However, by decreasing the
impact velocity droplets may land on the surface in a fakir state, and by
increasing it posts may impale droplets that are then stuck on the surface. We
use a two-phase lattice-Boltzmann model to simulate droplet impact on
superhydrophobic surfaces, and show that it may result in a fakir state also
for reasonable high impact velocities. This happens more easily if the surface
is made more hydrophobic or the post height is increased, thereby making the
impaled state energetically less favourable.Comment: 8 pages, 4 figures, to appear in Europhysics Letter
Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows
The pseudo-potential lattice Boltzmann (LB) model is a widely used multiphase
model in the LB community. In this model, an interaction force, which is
usually implemented via a forcing scheme, is employed to mimic the molecular
interactions that cause phase segregation. The forcing scheme is therefore
expected to play an important role in the pseudo-potential LB model. In this
paper, we aim to address some key issues about forcing schemes in the
pseudo-potential LB model. Firstly, theoretical and numerical analyses will be
made for Shan-Chen's forcing scheme and the exact-difference-method (EDM)
forcing scheme. The nature of these two schemes and their recovered macroscopic
equations will be shown. Secondly, through a theoretical analysis, we will
reveal the physics behind the phenomenon that different forcing schemes exhibit
different performances in the pseudo-potential LB model. Moreover, based on the
analysis, we will present an improved forcing scheme and numerically
demonstrate that the improved scheme can be treated as an alternative approach
for achieving thermodynamic consistency in the pseudo-potential LB model.Comment: 7 figure
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Lattice Boltzmann simulation of solute transport in heterogeneous porous media with conduits to estimate macroscopic continuous time random walk model parameters
Lattice Boltzmann models simulate solute transport in porous media traversed by conduits. Resulting solute breakthrough curves are fitted with Continuous Time Random Walk models. Porous media are simulated by damping flow inertia and, when the damping is large enough, a Darcy's Law solution instead of the Navier-Stokes solution normally provided by the lattice Boltzmann model is obtained. Anisotropic dispersion is incorporated using a direction-dependent relaxation time. Our particular interest is to simulate transport processes outside the applicability of the standard Advection-Dispersion Equation (ADE) including eddy mixing in conduits. The ADE fails to adequately fit any of these breakthrough curves
Developing Benthic Class Specific, Chlorophyll-a Retrieving Algorithms for Optically-ShallowWater Using SeaWiFS
This study evaluated the ability to improve Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) chl-a retrieval from optically shallow coastal waters by applying algorithms specific to the pixels’ benthic class. The form of the Ocean Color (OC) algorithm was assumed for this study. The operational atmospheric correction producing Level 2 SeaWiFS data was retained since the focus of this study was on establishing the benefit from the alternative specification of the bio-optical algorithm. Benthic class was determined through satellite image-based classification methods. Accuracy of the chl-a algorithms evaluated was determined through comparison with coincident in situ measurements of chl-a. The regionally-tuned models that were allowed to vary by benthic class produced more accurate estimates of chl-a than the single, unified regionally-tuned model. Mean absolute percent difference was approximately 70% for the regionally-tuned, benthic class-specific algorithms. Evaluation of the residuals indicated the potential for further improvement to chl-a estimation through finer characterization of benthic environments. Atmospheric correction procedures specialized to coastal environments were recognized as areas for future improvement as these procedures would improve both classification and algorithm tuning
Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann
On-site boundary conditions are often desired for lattice Boltzmann
simulations of fluid flow in complex geometries such as porous media or
microfluidic devices. The possibility to specify the exact position of the
boundary, independent of other simulation parameters, simplifies the analysis
of the system. For practical applications it should allow to freely specify the
direction of the flux, and it should be straight forward to implement in three
dimensions. Furthermore, especially for parallelized solvers it is of great
advantage if the boundary condition can be applied locally, involving only
information available on the current lattice site. We meet this need by
describing in detail how to transfer the approach suggested by Zou and He to a
D3Q19 lattice. The boundary condition acts locally, is independent of the
details of the relaxation process during collision and contains no artificial
slip. In particular, the case of an on-site no-slip boundary condition is
naturally included. We test the boundary condition in several setups and
confirm that it is capable to accurately model the velocity field up to second
order and does not contain any numerical slip.Comment: 13 pages, 4 figures, revised versio
Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations
During the last decade, lattice-Boltzmann (LB) simulations have been improved
to become an efficient tool for determining the permeability of porous media
samples. However, well known improvements of the original algorithm are often
not implemented. These include for example multirelaxation time schemes or
improved boundary conditions, as well as different possibilities to impose a
pressure gradient. This paper shows that a significant difference of the
calculated permeabilities can be found unless one uses a carefully selected
setup. We present a detailed discussion of possible simulation setups and
quantitative studies of the influence of simulation parameters. We illustrate
our results by applying the algorithm to a Fontainebleau sandstone and by
comparing our benchmark studies to other numerical permeability measurements in
the literature.Comment: 14 pages, 11 figure
Lattice Boltzmann Method for Electromagnetic Wave Propagation
We present a new Lattice Boltzmann (LB) formulation to solve the Maxwell
equations for electromagnetic (EM) waves propagating in a heterogeneous medium.
By using a pseudo-vector discrete Boltzmann distribution, the scheme is shown
to reproduce the continuum Maxwell equations. The technique compares well with
a pseudo-spectral method at solving for two-dimensional wave propagation in a
heterogeneous medium, which by design contains substantial contrasts in the
refractive index. The extension to three dimensions follows naturally and,
owing to the recognized efficiency of LB schemes for parallel computation in
irregular geometries, it gives a powerful method to numerically simulate a wide
range of problems involving EM wave propagation in complex media.Comment: 6 pages, 3 figures, accepted Europhysics letter
Improved axisymmetric lattice Boltzmann scheme
This paper proposes an improved lattice Boltzmann scheme for incompressible
axisymmetric flows. The scheme has the following features. First, it is still
within the framework of the standard lattice Boltzmann method using the
single-particle density distribution function and consistent with the
philosophy of the lattice Boltzmann method. Second, the source term of the
scheme is simple and contains no velocity gradient terms. Owing to this
feature, the scheme is easy to implement. In addition, the singularity problem
at the axis can be appropriately handled without affecting an important
advantage of the lattice Boltzmann method: the easy treatment of boundary
conditions. The scheme is tested by simulating Hagen-Poiseuille flow,
three-dimensional Womersley flow, Wheeler benchmark problem in crystal growth,
and lid-driven rotational flow in cylindrical cavities. It is found that the
numerical results agree well with the analytical solutions and/or the results
reported in previous studies.Comment: 31 pages, 7 figures
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