157 research outputs found
From the Boltzmann equation to fluid mechanics on a manifold
We apply the Chapman-Enskog procedure to derive hydrodynamic equations on an
arbitrary surface from the Boltzmann equation on the surface
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
Filling a silo with a mixture of grains: Friction-induced segregation
We study the filling process of a two-dimensional silo with inelastic
particles by simulation of a granular media lattice gas (GMLG) model. We
calculate the surface shape and flow profiles for a monodisperse system and we
introduce a novel generalization of the GMLG model for a binary mixture of
particles of different friction properties where, for the first time, we
measure the segregation process on the surface. The results are in good
agreement with a recent theory, and we explain the observed small deviations by
the nonuniform velocity profile.Comment: 10 pages, 5 figures, to be appear in Europhys. Let
Galilean invariance of lattice Boltzmann models
It is well-known that the original lattice Boltzmann (LB) equation deviates
from the Navier-Stokes equations due to an unphysical velocity dependent
viscosity. This unphysical dependency violates the Galilean invariance and
limits the validation domain of the LB method to near incompressible flows. As
previously shown, recovery of correct transport phenomena in kinetic equations
depends on the higher hydrodynamic moments. In this Letter, we give specific
criteria for recovery of various transport coefficients. The Galilean
invariance of a general class of LB models is demonstrated via numerical
experiments
Analytical solutions of the lattice Boltzmann BGK model
Analytical solutions of the two dimensional triangular and square lattice
Boltzmann BGK models have been obtained for the plain Poiseuille flow and the
plain Couette flow. The analytical solutions are written in terms of the
characteristic velocity of the flow, the single relaxation time and the
lattice spacing. The analytic solutions are the exact representation of these
two flows without any approximation.Comment: 10 pages, no postscript figure provide
Spurious diffusion in particle simulations of the Kolmogorov flow
Particle simulations of the Kolmogorov flow are analyzed by the
Landau-Lifshitz fluctuating hydrodynamics. It is shown that a spurious
diffusion of the center of mass corrupts the statistical properties of the
flow. The analytical expression for the corresponding diffusion coefficient is
derived.Comment: 10 pages, no figure
Energy Spectrum in the Dissipation Range of Fluid Turbulence
High resolution, direct numerical simulations of the three-dimensional incompressible Navier-Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/k( sub d))(sup alpha) exp[- betak/k(sub d) is confirmed. The possible values of the parameters alpha and beta, as well as their dependence on Revnolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A "bottleneck'-type effect is reported at k/k(sub d) approximately 4, exhibiting a possible transition from near-dissipation to far- dissipation
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
Chaotic Interaction of Langmuir Solitons and Long Wavelength Radiation
In this work we analyze the interaction of isolated solitary structures and
ion-acoustic radiation. If the radiation amplitude is small solitary structures
persists, but when the amplitude grows energy transfer towards small spatial
scales occurs. We show that transfer is particularly fast when a fixed point of
a low dimensional model is destroyed.Comment: LaTex + 4 eps file
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