199 research outputs found
Lattice Boltzmann Models for Complex Fluids
We present various Lattice Boltzmann Models which reproduce the effects of
rough walls, shear thinning and granular flow. We examine the boundary layers
generated by the roughness of the walls. Shear thinning produces plug flow with
a sharp density contrast at the boundaries. Density waves are spontaneously
generated when the viscosity has a nonlinear dependence on density which
characterizes granular flow.Comment: 11 pages, plain TeX, preprint HLRZ 23/9
A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations
Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the thicknesses of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee [J. Comput. Phys. 86, 187] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin [J. Comput. Phys. 163, 216] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving and the statistical average of this method is shown to significantly delay the onset of pinning
Three dimensional hysdrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic flow through porous media
We report the results of a study of multiphase flow in porous media. A
Darcy's law for steady multiphase flow was investigated for both binary and
ternary amphiphilic flow. Linear flux-forcing relationships satisfying Onsager
reciprocity were shown to be a good approximation of the simulation data. The
dependence of the relative permeability coefficients on water saturation was
investigated and showed good qualitative agreement with experimental data.
Non-steady state invasion flows were investigated, with particular interest in
the asymptotic residual oil saturation. The addition of surfactant to the
invasive fluid was shown to significantly reduce the residual oil saturation.Comment: To appear in Phys. Rev.
Lattice Boltzmann Thermohydrodynamics
We introduce a lattice Boltzmann computational scheme capable of modeling
thermohydrodynamic flows of monatomic gases. The parallel nature of this
approach provides a numerically efficient alternative to traditional methods of
computational fluid dynamics. The scheme uses a small number of discrete
velocity states and a linear, single-time-relaxation collision operator.
Numerical simulations in two dimensions agree well with exact solutions for
adiabatic sound propagation and Couette flow with heat transfer.Comment: 11 pages, Physical Review E: Rapid Communications, in pres
Domain Growth, Wetting and Scaling in Porous Media
The lattice Boltzmann (LB) method is used to study the kinetics of domain
growth of a binary fluid in a number of geometries modeling porous media.
Unlike the traditional methods which solve the Cahn-Hilliard equation, the LB
method correctly simulates fluid properties, phase segregation, interface
dynamics and wetting. Our results, based on lattice sizes of up to , do not show evidence to indicate the breakdown of late stage dynamical
scaling, and suggest that confinement of the fluid is the key to the slow
kinetics observed. Randomness of the pore structure appears unnecessary.Comment: 13 pages, latex, submitted to PR
Diffusion in a multi-component Lattice Boltzmann Equation model
Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE)
model are discussed in detail. The mass fluxes associated with different
mechanical driving forces are obtained using a Chapman-Enskog analysis. This
model is found to have correct diffusion behavior and the multiple diffusion
coefficients are obtained analytically. The analytical results are further
confirmed by numerical simulations in a few solvable limiting cases. The LBE
model is established as a useful computational tool for the simulation of mass
transfer in fluid systems with external forces.Comment: To appear in Aug 1 issue of PR
Multi-component lattice-Boltzmann model with interparticle interaction
A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\bf 47}, 1815,
(1993)] lattice Boltzmann model for simulating fluids with multiple components
and interparticle forces is described in detail. Macroscopic equations
governing the motion of each component are derived by using Chapman-Enskog
method. The mutual diffusivity in a binary mixture is calculated analytically
and confirmed by numerical simulation. The diffusivity is generally a function
of the concentrations of the two components but independent of the fluid
velocity so that the diffusion is Galilean invariant. The analytically
calculated shear kinematic viscosity of this model is also confirmed
numerically.Comment: 18 pages, compressed and uuencoded postscript fil
Lattice Boltzmann Simulation of Non-Ideal Fluids
A lattice Boltzmann scheme able to model the hydrodynamics of phase
separation and two-phase flow is described. Thermodynamic consistency is
ensured by introducing a non-ideal pressure tensor directly into the collision
operator. We also show how an external chemical potential can be used to
supplement standard boundary conditions in order to investigate the effect of
wetting on phase separation and fluid flow in confined geometries. The approach
has the additional advantage of reducing many of the unphysical discretisation
problems common to previous lattice Boltzmann methods.Comment: 11 pages, revtex, 4 Postscript figures, uuencode
Scale invariance in coarsening of binary and ternary fluids
Phase separation in binary and ternary fluids is studied using a two
dimensional Lattice Gas Automata. The lengths, given by the the first zero
crossing point of the correlation function and the total interface length is
shown to exhibit power law dependence on time. In binary mixtures, our data
clearly indicate the existence of a regime having more than one length scale
where the coarsening process proceeds through the rupture and reassociation of
domains. In ternary fluids; in the case of symmetric mixtures there exists a
regime with a single length scale having dynamic exponent 1/2, while in
asymmetric mixtures our data establish the break down of scale invariance.Comment: 20 pages, 13 figure
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