64 research outputs found
Non-linear effects and shock formation in the focusing of a spherical acoustic wave : Numerical simulations and experiments in liquid helium
The focusing of acoustic waves is used to study nucleation phenomena in
liquids. At large amplitude, non-linear effects are important so that the
magnitude of pressure or density oscillations is difficult to predict. We
present a calculation of these oscillations in a spherical geometry.
We show that the main source of non-linearities is the shape of the equation
of state of the liquid, enhanced by the spherical geometry. We also show that
the formation of shocks cannot be ignored beyond a certain oscillation
amplitude. The shock length is estimated by an analytic calculation based on
the characteristics method. In our numerical simulations, we have treated the
shocks with a WENO scheme. We obtain a very good agreement with experimental
measurements which were recently performed in liquid helium. The comparison
between numerical and experimental results allows in particular to calibrate
the vibration of the ceramics used to produce the wave, as a function of the
applied voltage.Comment: 20 pages, 26 figures. Submitted to The European Physical Journal
Lattice gas with ``interaction potential''
We present an extension of a simple automaton model to incorporate non-local
interactions extending over a spatial range in lattice gases. {}From the
viewpoint of Statistical Mechanics, the lattice gas with interaction range may
serve as a prototype for non-ideal gas behavior. {}From the density
fluctuations correlation function, we obtain a quantity which is identified as
a potential of mean force. Equilibrium and transport properties are computed
theoretically and by numerical simulations to establish the validity of the
model at macroscopic scale.Comment: 12 pages LaTeX, figures available on demand ([email protected]
An Euler Solver Based on Locally Adaptive Discrete Velocities
A new discrete-velocity model is presented to solve the three-dimensional
Euler equations. The velocities in the model are of an adaptive nature---both
the origin of the discrete-velocity space and the magnitudes of the
discrete-velocities are dependent on the local flow--- and are used in a finite
volume context. The numerical implementation of the model follows the
near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme
which is second order in space (in the smooth regions and between first and
second order at discontinuities) and second order in time. (The
three-dimensional code is included.) For one choice of the scaling between the
magnitude of the discrete-velocities and the local internal energy of the flow,
the method reduces to a flux-splitting scheme based on characteristics. As a
preliminary exercise, the result of the Sod shock-tube simulation is compared
to the exact solution.Comment: 17 pages including 2 figures and CMFortran code listing. All in one
postscript file (adv.ps) compressed and uuencoded (adv.uu). Name mail file
`adv.uu'. Edit so that `#!/bin/csh -f' is the first line of adv.uu On a unix
machine say `csh adv.uu'. On a non-unix machine: uudecode adv.uu; uncompress
adv.tar.Z; tar -xvf adv.ta
Simulating Three-Dimensional Hydrodynamics on a Cellular-Automata Machine
We demonstrate how three-dimensional fluid flow simulations can be carried
out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for
cellular-automata computations. The principal algorithmic innovation is the use
of a lattice-gas model with a 16-bit collision operator that is specially
adapted to the machine architecture. It is shown how the collision rules can be
optimized to obtain a low viscosity of the fluid. Predictions of the viscosity
based on a Boltzmann approximation agree well with measurements of the
viscosity made on CAM-8. Several test simulations of flows in simple geometries
-- channels, pipes, and a cubic array of spheres -- are carried out.
Measurements of average flux in these geometries compare well with theoretical
predictions.Comment: 19 pages, REVTeX and epsf macros require
Computer simulations of domain growth and phase separation in two-dimensional binary immiscible fluids using dissipative particle dynamics
We investigate the dynamical behavior of binary fluid systems in two
dimensions using dissipative particle dynamics. We find that following a
symmetric quench the domain size R(t) grows with time t according to two
distinct algebraic laws R(t) = t^n: at early times n = 1/2, while for later
times n = 2/3. Following an asymmetric quench we observe only n = 1/2, and if
momentum conservation is violated we see n = 1/3 at early times. Bubble
simulations confirm the existence of a finite surface tension and the validity
of Laplace's law. Our results are compared with similar simulations which have
been performed previously using molecular dynamics, lattice-gas and
lattice-Boltzmann automata, and Langevin dynamics. We conclude that dissipative
particle dynamics is a promising method for simulating fluid properties in such
systems.Comment: RevTeX; 22 pages, 5 low-resolution figures. For full-resolution
figures, connect to http://www.tcm.phy.cam.ac.uk/~ken21/tension/tension.htm
Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains
Modeling blood flow in larger vessels using lattice-Boltzmann methods comes
with a challenging set of constraints: a complex geometry with walls and
inlet/outlets at arbitrary orientations with respect to the lattice,
intermediate Reynolds number, and unsteady flow. Simple bounce-back is one of
the most commonly used, simplest, and most computationally efficient boundary
conditions, but many others have been proposed. We implement three other
methods applicable to complex geometries (Guo, Zheng and Shi, Phys Fluids
(2002); Bouzdi, Firdaouss and Lallemand, Phys. Fluids (2001); Junk and Yang
Phys. Rev. E (2005)) in our open-source application \HemeLB{}. We use these to
simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary
orientation at physiologically relevant Reynolds (1--300) and Womersley (4--12)
numbers and steady flow in a curved pipe at relevant Dean number (100--200) and
compare the accuracy to analytical solutions. We find that both the
Bouzidi-Firdaouss-Lallemand and Guo-Zheng-Shi methods give second-order
convergence in space while simple bounce-back degrades to first order. The BFL
method appears to perform better than GZS in unsteady flows and is
significantly less computationally expensive. The Junk-Yang method shows poor
stability at larger Reynolds number and so cannot be recommended here. The
choice of collision operator (lattice Bhatnagar-Gross-Krook vs.\ multiple
relaxation time) and velocity set (D3Q15 vs.\ D3Q19 vs.\ D3Q27) does not
significantly affect the accuracy in the problems studied.Comment: Submitted to Phys. Rev. E, 14 pages, 6 figures, 5 table
Lattice Boltzmann simulations of soft matter systems
This article concerns numerical simulations of the dynamics of particles
immersed in a continuum solvent. As prototypical systems, we consider colloidal
dispersions of spherical particles and solutions of uncharged polymers. After a
brief explanation of the concept of hydrodynamic interactions, we give a
general overview over the various simulation methods that have been developed
to cope with the resulting computational problems. We then focus on the
approach we have developed, which couples a system of particles to a lattice
Boltzmann model representing the solvent degrees of freedom. The standard D3Q19
lattice Boltzmann model is derived and explained in depth, followed by a
detailed discussion of complementary methods for the coupling of solvent and
solute. Colloidal dispersions are best described in terms of extended particles
with appropriate boundary conditions at the surfaces, while particles with
internal degrees of freedom are easier to simulate as an arrangement of mass
points with frictional coupling to the solvent. In both cases, particular care
has been taken to simulate thermal fluctuations in a consistent way. The
usefulness of this methodology is illustrated by studies from our own research,
where the dynamics of colloidal and polymeric systems has been investigated in
both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures,
76 page
Measuring Corporate Social Responsibility in tourism: Development and validation of an efficient measurement scale in the hospitality industry.
ABSTRAC: This article aims at developing an efficient measurement scale for corporate social responsibility in the tourism industry, given the contextual character that is recognized in the practice of this construct. Indicators were generated on the basis of a literature review and qualitative research. To assess the reliability and validity, first- and second-order confirmatory factor analysis were carried out. Results show a multidimensional structure of this construct—including economic, social, and environmental issues. This study contributes to the advancement of knowledge in the field of social responsibility through its practical application regarding concepts of sustainable development which have mainly been theoretical
Multireflection boundary conditions for lattice Boltzmann models
We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for R
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