66 research outputs found
Stabilized Lattice Boltzmann-Enskog method for compressible flows and its application to one and two-component fluids in nanochannels
A numerically stable method to solve the discretized Boltzmann-Enskog
equation describing the behavior of non ideal fluids under inhomogeneous
conditions is presented. The algorithm employed uses a Lagrangian
finite-difference scheme for the treatment of the convective term and a forcing
term to account for the molecular repulsion together with a
Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious
currents induced by the numerical discretization procedure, we use a
trapezoidal rule for the time integration together with a version of the
two-distribution method of He et al. (J. Comp. Phys 152, 642 (1999)). Numerical
tests show that, in the case of one component fluid in the presence of a
spherical potential well, the proposed method reduces the numerical error by
several orders of magnitude. We conduct another test by considering the flow of
a two component fluid in a channel with a bottleneck and provide information
about the density and velocity field in this structured geometry.Comment: to appear in Physical Review
Entropic Lattice Boltzmann Simulation of the Flow Past Square Cylinder
Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used
as an alternative to the discretization of the Navier-Stokes equations for
hydrodynamic simulations.
Recently, it was argued that modeling sub-grid scale phenomena at the kinetic
level might provide an efficient tool for large scale simulations. Indeed, a
particular variant of this approach, known as the entropic lattice Boltzmann
method (ELBM), has shown that an efficient coarse-grained simulation of
decaying turbulence is possible using these approaches.
The present work investigates the efficiency of the entropic lattice
Boltzmann in describing flows of engineering interest. In order to do so, we
have chosen the flow past a square cylinder, which is a simple model of such
flows. We will show that ELBM can quantitatively capture the variation of
vortex shedding frequency as a function of Reynolds number in the low as well
as the high Reynolds number regime, without any need for explicit sub-grid
scale modeling. This extends the previous studies for this set-up, where
experimental behavior ranging from to were
predicted by a single simulation algorithm.Comment: 12 pages, 5 figures, to appear in Int. J. Mod. Phys.
Quasi-equilibrium lattice Boltzmann method
Abstract.: A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validate
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
Higher-order Galilean-invariant lattice Boltzmann model for microflows: Single-component gas
We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.open252
On the Three-dimensional Central Moment Lattice Boltzmann Method
A three-dimensional (3D) lattice Boltzmann method based on central moments is
derived. Two main elements are the local attractors in the collision term and
the source terms representing the effect of external and/or self-consistent
internal forces. For suitable choices of the orthogonal moment basis for the
three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen
velocity (D3Q15) lattice models, attractors are expressed in terms of
factorization of lower order moments as suggested in an earlier work; the
corresponding source terms are specified to correctly influence lower order
hydrodynamic fields, while avoiding aliasing effects for higher order moments.
These are achieved by successively matching the corresponding continuous and
discrete central moments at various orders, with the final expressions written
in terms of raw moments via a transformation based on the binomial theorem.
Furthermore, to alleviate the discrete effects with the source terms, they are
treated to be temporally semi-implicit and second-order, with the implicitness
subsequently removed by means of a transformation. As a result, the approach is
frame-invariant by construction and its emergent dynamics describing fully 3D
fluid motion in the presence of force fields is Galilean invariant. Numerical
experiments for a set of benchmark problems demonstrate its accuracy.Comment: 55 pages, 8 figure
Capillary filling with wall corrugations] Capillary filling in microchannels with wall corrugations: A comparative study of the Concus-Finn criterion by continuum, kinetic and atomistic approaches
We study the impact of wall corrugations in microchannels on the process of
capillary filling by means of three broadly used methods - Computational Fluid
Dynamics (CFD), Lattice-Boltzmann Equations (LBE) and Molecular Dynamics (MD).
The numerical results of these approaches are compared and tested against the
Concus-Finn (CF) criterion, which predicts pinning of the contact line at
rectangular ridges perpendicular to flow for contact angles theta > 45. While
for theta = 30, theta = 40 (no flow) and theta = 60 (flow) all methods are
found to produce data consistent with the CF criterion, at theta = 50 the
numerical experiments provide different results. Whilst pinning of the liquid
front is observed both in the LB and CFD simulations, MD simulations show that
molecular fluctuations allow front propagation even above the critical value
predicted by the deterministic CF criterion, thereby introducing a sensitivity
to the obstacle heigth.Comment: 25 pages, 8 figures, Langmuir in pres
Lattice Boltzmann simulations in microfluidics: probing the no-slip boundary condition in hydrophobic, rough, and surface nanobubble laden microchannels
In this contribution we review recent efforts on investigations of the effect
of (apparent) boundary slip by utilizing lattice Boltzmann simulations. We
demonstrate the applicability of the method to treat fundamental questions in
microfluidics by investigating fluid flow in hydrophobic and rough
microchannels as well as over surfaces covered by nano- or microscale gas
bubbles.Comment: 11 pages, 6 figure
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