400 research outputs found
Monte Carlo simulation of nonlinear Couette flow in a dilute gas
The Direct Simulation Monte Carlo method is applied to solve the Boltzmann
equation in the steady planar Couette flow for Maxwell molecules and hard
spheres. Nonequilibrium boundary conditions based on the solution of the
Bhatnagar-Gross-Krook (BGK) model for the Couette flow are employed to diminish
the influence of finite-size effects. Non-Newtonian properties are
characterized by five independent generalized transport coefficients: a
viscosity function, a thermal conductivity function, two viscometric functions,
and a cross coefficient measuring the heat flux orthogonal to the thermal
gradient. These coefficients depend nonlinearly on the shear rate. The
simulation results are compared with theoretical predictions given by the Grad
method and the BGK and the ellipsoidal statistical (ES) models. It is found
that the kinetic models present a good agreement with the simulation,
especially in the case of the ES model, while the Grad method is only
qualitatively reliable for the momentum transport. In addition, the velocity
distribution function is also measured and compared with the BGK and ES
distributions.Comment: 25 pages (including 15 figures); minor changes; revised version
accepted for publication in Physics of Fluid
Computer simulation of uniformly heated granular fluids
Direct Monte Carlo simulations of the Enskog-Boltzmann equation for a
spatially uniform system of smooth inelastic spheres are performed. In order to
reach a steady state, the particles are assumed to be under the action of an
external driving force which does work to compensate for the collisional loss
of energy. Three different types of external driving are considered: (a) a
stochastic force, (b) a deterministic force proportional to the particle
velocity and (c) a deterministic force parallel to the particle velocity but
constant in magnitude. The Enskog-Boltzmann equation in case (b) is fully
equivalent to that of the homogeneous cooling state (where the thermal velocity
monotonically decreases with time) when expressed in terms of the particle
velocity relative to the thermal velocity. Comparison of the simulation results
for the fourth cumulant and the high energy tail with theoretical predictions
derived in cases (a) and (b) [T. P. C. van Noije and M. H. Ernst, Gran. Matt.
1, 57 (1998)] shows a good agreement. In contrast to these two cases, the
deviation from the Maxwell-Boltzmann distribution is not well represented by
Sonine polynomials in case (c), even for low dissipation. In addition, the high
energy tail exhibits an underpopulation effect in this case.Comment: 18 pages (LaTex), 10 figures (eps); to be published in Granular
Matte
Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas
Motivated by the disagreement found at high dissipation between simulation
data for the heat flux transport coefficients and the expressions derived from
the Boltzmann equation by the standard first Sonine approximation [Brey et al.,
Phys. Rev. E 70, 051301 (2004); J. Phys.: Condens. Matter 17, S2489 (2005)], we
implement in this paper a modified version of the first Sonine approximation in
which the Maxwell-Boltzmann weight function is replaced by the homogeneous
cooling state distribution. The structure of the transport coefficients is
common in both approximations, the distinction appearing in the coefficient of
the fourth cumulant . Comparison with computer simulations shows that the
modified approximation significantly improves the estimates for the heat flux
transport coefficients at strong dissipation. In addition, the slight
discrepancies between simulation and the standard first Sonine estimates for
the shear viscosity and the self-diffusion coefficient are also partially
corrected by the modified approximation. Finally, the extension of the modified
first Sonine approximation to the transport coefficients of the Enskog kinetic
theory is presented.Comment: 10 pages, 6 figures; v2: slightly shortene
DSMC evaluation of the Navier-Stokes shear viscosity of a granular fluid
A method based on the simple shear flow modified by the introduction of a
deterministic non-conservative force and a stochastic process is proposed to
measure the Navier-Stokes shear viscosity in a granular fluid described by the
Enskog equation. The method is implemented in DSMC simulations for a wide range
of values of dissipation and density. It is observed that, after a certain
transient period, the system reaches a hydrodynamic stage which tends to the
Navier-Stokes regime for long times. The results are compared with theoretical
predictions obtained from the Chapman-Enskog method in the leading Sonine
approximation, showing quite a good agreement, even for strong dissipation.Comment: 6 pages, 4 figures; to appear in Rarefied Gas Dynamics: 24th
International Symposium (AIP Conference Proceedings
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