853 research outputs found
A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas
We investigate sound wave propagation in a monatomic gas using a volume-based
hydrodynamic model. In Physica A vol 387(24) (2008) pp6079-6094, a microscopic
volume-based kinetic approach was proposed by analyzing molecular spatial
distributions; this led to a set of hydrodynamic equations incorporating a
mass-density diffusion component. Here we find that these new mass-density
diffusive flux and volume terms mean that our hydrodynamic model, uniquely,
reproduces sound wave phase speed and damping measurements with excellent
agreement over the full range of Knudsen number. In the high Knudsen number
(high frequency) regime, our volume-based model predictions agree with the
plane standing waves observed in the experiments, which existing kinetic and
continuum models have great difficulty in capturing. In that regime, our
results indicate that the "sound waves" presumed in the experiments may be
better thought of as "mass-density waves", rather than the pressure waves of
the continuum regime.Comment: Revised to aid clarification (no changes to presented model); typos
corrected, figures added, paper title change
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
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Variational approach to gas flows in microchannels on the basis of the Boltzmann equation for hard-sphere molecules
This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.The objective of the present paper is to provide an analytic expression for the first- and second-order velocity slip coefficients. Therefore, gas flow rates in microchannels have been rigorously evaluated in the near-continuum limit by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator. The diffuse-specular reflection condition of Maxwell’s type has been considered in order to take into account the influence of the accommodation coefficient on the slip parameters. The
polynomial form of Knudsen number obtained for the Poiseuille mass flow rate and the values of the second order velocity slip coefficients found on the basis of our variational solution of the linearized Boltzmann equation for hardsphere molecules are analyzed in the frame of potential applications of classical continuum numerical tools (as lattice Boltzmann methods) in simulations of microscale flows
Cauchy problem for the Boltzmann-BGK model near a global Maxwellian
In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK
model for a general class of collision frequencies. We prove that the
Boltzmann-BGK model linearized around a global Maxwellian admits a unique
global smooth solution if the initial perturbation is sufficiently small in a
high order energy norm. We also establish an asymptotic decay estimate and
uniform -stability for nonlinear perturbations.Comment: 26 page
A continuum model of gas flows with localized density variations
We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows
Diffusion in a continuum model of self-propelled particles with alignment interaction
In this paper, we provide the corrections to the hydrodynamic
model derived by Degond and Motsch from a kinetic version of the model by
Vicsek & coauthors describing flocking biological agents. The parameter
stands for the ratio of the microscopic to the macroscopic scales.
The corrected model involves diffusion terms in both the mass and
velocity equations as well as terms which are quadratic functions of the first
order derivatives of the density and velocity. The derivation method is based
on the standard Chapman-Enskog theory, but is significantly more complex than
usual due to both the non-isotropy of the fluid and the lack of momentum
conservation
Fokker-Planck type equations for a simple gas and for a semi-relativistic Brownian motion from a relativistic kinetic theory
A covariant Fokker-Planck type equation for a simple gas and an equation for
the Brownian motion are derived from a relativistic kinetic theory based on the
Boltzmann equation. For the simple gas the dynamic friction four-vector and the
diffusion tensor are identified and written in terms of integrals which take
into account the collision processes. In the case of Brownian motion, the
Brownian particles are considered as non-relativistic whereas the background
gas behaves as a relativistic gas. A general expression for the
semi-relativistic viscous friction coefficient is obtained and the particular
case of constant differential cross-section is analyzed for which the
non-relativistic and ultra relativistic limiting cases are calculated.Comment: To appear in PR
Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains
The formation and propagation of singularities for Boltzmann equation in
bounded domains has been an important question in numerical studies as well as
in theoretical studies. Consider the nonlinear Boltzmann solution near
Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We
demonstrate that discontinuity is created at the non-convex part of the grazing
boundary, then propagates only along the forward characteristics inside the
domain before it hits on the boundary again.Comment: 39 pages, 5 Figure
A fully relativistic lattice Boltzmann algorithm
Starting from the Maxwell-Juettner equilibrium distribution, we develop a
relativistic lattice Boltzmann (LB) algorithm capable of handling
ultrarelativistic systems with flat, but expanding, spacetimes. The algorithm
is validated through simulations of quark-gluon plasma, yielding excellent
agreement with hydrodynamic simulations. The present scheme opens the
possibility of transferring the recognized computational advantages of lattice
kinetic theory to the context of both weakly and ultra-relativistic systems.Comment: 12 pages, 8 figure
Lattice Boltzmann scheme for relativistic fluids
A Lattice Boltzmann formulation for relativistic fluids is presented and
numerically verified through quantitative comparison with recent hydrodynamic
simulations of relativistic shock-wave propagation in viscous quark-gluon
plasmas. This formulation opens up the possibility of exporting the main
advantages of Lattice Boltzmann methods to the relativistic context, which
seems particularly useful for the simulation of relativistic fluids in
complicated geometries.Comment: Submitted to PR
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