437 research outputs found
Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic
fluids recently proposed in Ref. [1], is presented. The method is numerically
validated and applied to the case of two quite different relativistic fluid
dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the
impact of a supernova blast-wave on massive interstellar clouds. Close to
second order convergence with the grid resolution, as well as linear dependence
of computational time on the number of grid points and time-steps, are
reported
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
Excised acoustic black holes: the scattering problem in the time domain
The scattering process of a dynamic perturbation impinging on a draining-tub
model of an acoustic black hole is numerically solved in the time domain.
Analogies with real black holes of General Relativity are explored by using
recently developed mathematical tools involving finite elements methods,
excision techniques, and constrained evolution schemes for strongly hyperbolic
systems. In particular it is shown that superradiant scattering of a
quasi-monochromatic wavepacket can produce strong amplification of the signal,
offering the possibility of a significant extraction of rotational energy at
suitable values of the angular frequency of the vortex and of the central
frequency of the wavepacket. The results show that theoretical tools recently
developed for gravitational waves can be brought to fruition in the study of
other problems in which strong anisotropies are present.Comment: 8 pages, 9 figure
Run-and-tumble particles with hydrodynamics: sedimentation, trapping and upstream swimming
We simulate by lattice Boltzmann the nonequilibrium steady states of
run-and-tumble particles (inspired by a minimal model of bacteria), interacting
by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic
interactions barely perturb the steady state found without them, but for
particles in a harmonic trap such a state is quite changed if the run length is
larger than the confinement length: a self-assembled pump is formed. Particles
likewise confined in a narrow channel show a generic upstream flux in
Poiseuille flow: chiral swimming is not required
Two-dimensional Vesicle dynamics under shear flow: effect of confinement
Dynamics of a single vesicle under shear flow between two parallel plates is
studied using two-dimensional lattice-Boltzmann simulations. We first present
how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using
an approach known from the immersed boundary method. The fluid flow is computed
on an Eulerian regular fixed mesh while the location of the vesicle membrane is
tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle
equilibrium shapes in a fluid at rest are found and the dynamical behavior of a
vesicle under simple shear flow is being reproduced. Further, we focus on
investigating the effect of the confinement on the dynamics, a question that
has received little attention so far. In particular, we study how the vesicle
steady inclination angle in the tank-treading regime depends on the degree of
confinement. The influence of the confinement on the effective viscosity of the
composite fluid is also analyzed. At a given reduced volume (the swelling
degree) of a vesicle we find that both the inclination angle, and the membrane
tank-treading velocity decrease with increasing confinement. At sufficiently
large degree of confinement the tank-treading velocity exhibits a
non-monotonous dependence on the reduced volume and the effective viscosity
shows a nonlinear behavior.Comment: 12 pages, 8 figure
Lattice Boltzmann simulations of apparent slip in hydrophobic microchannels
Various experiments have found a boundary slip in hydrophobic microchannel
flows, but a consistent understanding of the results is still lacking. While
Molecular Dynamics (MD) simulations cannot reach the low shear rates and large
system sizes of the experiments, it is often impossible to resolve the needed
details with macroscopic approaches. We model the interaction between
hydrophobic channel walls and a fluid by means of a multi-phase lattice
Boltzmann model. Our mesoscopic approach overcomes the limitations of MD
simulations and can reach the small flow velocities of known experiments. We
reproduce results from experiments at small Knudsen numbers and other
simulations, namely an increase of slip with increasing liquid-solid
interactions, the slip being independent of the flow velocity, and a decreasing
slip with increasing bulk pressure. Within our model we develop a semi-analytic
approximation of the dependence of the slip on the pressure.Comment: 7 pages, 4 figure
Statistics of precursors to fingering processes
We present an analysis of the statistical properties of hydrodynamic field
fluctuations which reveal the existence of precursors to fingering processes.
These precursors are found to exhibit power law distributions, and these power
laws are shown to follow from spatial -Gaussian structures which are
solutions to the generalized non-linear diffusion equation.Comment: 7 pages incl. 5 figs; tp appear in Europhysics Letter
Finite-Difference Lattice Boltzmann Methods for binary fluids
We investigate two-fluid BGK kinetic methods for binary fluids. The developed
theory works for asymmetric as well as symmetric systems. For symmetric systems
it recovers Sirovich's theory and is summarized in models A and B. For
asymmetric systems it contributes models C, D and E which are especially useful
when the total masses and/or local temperatures of the two components are
greatly different. The kinetic models are discretized based on an octagonal
discrete velocity model. The discrete-velocity kinetic models and the
continuous ones are required to describe the same hydrodynamic equations. The
combination of a discrete-velocity kinetic model and an appropriate
finite-difference scheme composes a finite-difference lattice Boltzmann method.
The validity of the formulated methods is verified by investigating (i) uniform
relaxation processes, (ii) isothermal Couette flow, and (iii) diffusion
behavior.Comment: RevTex, 3 figures. Phys. Rev. E (2005, in press
On the relativistic Lattice Boltzmann method for quark-gluon plasma simulations
In this paper, we investigate the recently developed lattice Boltzmann model
for relativistic hydrodynamics. To this purpose, we perform simulations of
shock waves in quark-gluon plasma in the low and high viscosities regime, using
three different computational models, the relativistic lattice Boltzmann (RLB),
the Boltzmann Approach Multi-Parton Scattering (BAMPS), and the viscous sharp
and smooth transport algorithm (vSHASTA). From the results, we conclude that
the RLB model departs from BAMPS in the case of high speeds and high
temperature(viscosities), the departure being due to the fact that the RLB is
based on a quadratic approximation of the Maxwell-J\"uttner distribution, which
is only valid for sufficiently low temperature and velocity. Furthermore, we
have investigated the influence of the lattice speed on the results, and shown
that inclusion of quadratic terms in the equilibrium distribution improves the
stability of the method within its domain of applicability. Finally, we assess
the viability of the RLB model in the various parameter regimes relevant to
ultra-relativistic fluid dynamics.Comment: 10 pages, 16 Figure
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