63 research outputs found
Volumetric formulation of lattice Boltzmann models with energy conservation
We analyze a volumetric formulation of lattice Boltzmann for compressible
thermal fluid flows. The velocity set is chosen with the desired accuracy,
based on the Gauss-Hermite quadrature procedure, and tested against controlled
problems in bounded and unbounded fluids. The method allows the simulation of
thermohydrodyamical problems without the need to preserve the exact
space-filling nature of the velocity set, but still ensuring the exact
conservation laws for density, momentum and energy. Issues related to boundary
condition problems and improvements based on grid refinement are also
investigated.Comment: 8 figure
Modelling thermal flow in a transition regime using a lattice Boltzmann approach
Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58
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
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
Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems
In this paper we apply a finite difference lattice Boltzmann model to study
the phase separation in a two-dimensional liquid-vapor system. Spurious
numerical effects in macroscopic equations are discussed and an appropriate
numerical scheme involving flux limiter techniques is proposed to minimize them
and guarantee a better numerical stability at very low viscosity. The phase
separation kinetics is investigated and we find evidence of two different
growth regimes depending on the value of the fluid viscosity as well as on the
liquid-vapor ratio.Comment: 10 pages, 10 figures, to be published in Phys. Rev.
Mesoscopic modeling of a two-phase flow in the presence of boundaries: the Contact Angle
We present a mesoscopic model, based on the Boltzmann Equation, for the
interaction between a solid wall and a non-ideal fluid. We present an analytic
derivation of the contact angle in terms of the surface tension between the
liquid-gas, the liquid-solid and the gas-solid phases. We study the dependency
of the contact angle on the two free parameters of the model, which determine
the interaction between the fluid and the boundaries, i.e. the equivalent of
the wall density and of the wall-fluid potential in Molecular Dynamics studies.
We compare the analytical results obtained in the hydrodynamical limit for
the density profile and for the surface tension expression with the numerical
simulations. We compare also our two-phase approach with some exact results for
a pure hydrodynamical incompressible fluid based on Navier-Stokes equations
with boundary conditions made up of alternating slip and no-slip strips.
Finally, we show how to overcome some theoretical limitations connected with a
discretized Boltzmann scheme and we discuss the equivalence between the surface
tension defined in terms of the mechanical equilibrium and in terms of the
Maxwell construction.Comment: 29 pages, 12 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
Hydrokinetic simulations of nanoscopic precursor films in rough channels
We report on simulations of capillary filling of high-wetting fluids in
nano-channels with and without obstacles. We use atomistic (molecular dynamics)
and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence
of the formation of thin precursor films, moving ahead of the main capillary
front. The dynamics of the precursor films is found to obey a square-root law
as the main capillary front, z^2(t) ~ t, although with a larger prefactor,
which we find to take the same value for the different geometries (2D-3D) under
inspection. The two methods show a quantitative agreement which indicates that
the formation and propagation of thin precursors can be handled at a
mesoscopic/hydrokinetic level. This can be considered as a validation of the
Lattice-Boltzmann (LB) method and opens the possibility of using hydrokinetic
methods to explore space-time scales and complex geometries of direct
experimental relevance. Then, LB approach is used to study the fluid behaviour
in a nano-channel when the precursor film encounters a square obstacle. A
complete parametric analysis is performed which suggests that thin-film
precursors may have an important influence on the efficiency of
nanochannel-coating strategies.Comment: 16 pages, 8 figures; To be published on JSTAT: Journal of statistical
mechanics: Theory and experiment
Capillary filling with pseudo-potential binary Lattice-Boltzmann model
We present a systematic study of capillary filling for a binary fluid by
using a mesoscopic lattice Boltzmann model for immiscible fluids describing a
diffusive interface moving at a given contact angle with respect to the walls.
The phenomenological way to impose a given contact angle is analysed.
Particular attention is given to the case of complete wetting, that is contact
angle equal to zero. Numerical results yield quantitative agreement with the
theoretical Washburn law, provided that the correct ratio of the dynamic
viscosities between the two fluids is used. Finally, the presence of precursor
films is experienced and it is shown that these films advance in time with a
square-root law but with a different prefactor with respect to the bulk
interface.Comment: 13 pages, 8 figures, accepted for publication on The European journal
of physics
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