21,443 research outputs found
A Hybrid Godunov Method for Radiation Hydrodynamics
From a mathematical perspective, radiation hydrodynamics can be thought of as
a system of hyperbolic balance laws with dual multiscale behavior (multiscale
behavior associated with the hyperbolic wave speeds as well as multiscale
behavior associated with source term relaxation). With this outlook in mind,
this paper presents a hybrid Godunov method for one-dimensional radiation
hydrodynamics that is uniformly well behaved from the photon free streaming
(hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and
to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds
that the technique preserves certain asymptotic limits. The method incorporates
a backward Euler upwinding scheme for the radiation energy density and flux as
well as a modified Godunov scheme for the material density, momentum density,
and energy density. The backward Euler upwinding scheme is first-order accurate
and uses an implicit HLLE flux function to temporally advance the radiation
components according to the material flow scale. The modified Godunov scheme is
second-order accurate and directly couples stiff source term effects to the
hyperbolic structure of the system of balance laws. This Godunov technique is
composed of a predictor step that is based on Duhamel's principle and a
corrector step that is based on Picard iteration. The Godunov scheme is
explicit on the material flow scale but is unsplit and fully couples matter and
radiation without invoking a diffusion-type approximation for radiation
hydrodynamics. This technique derives from earlier work by Miniati & Colella
2007. Numerical tests demonstrate that the method is stable, robust, and
accurate across various parameter regimes.Comment: accepted for publication in Journal of Computational Physics; 61
pages, 15 figures, 11 table
A new model for simulating colloidal dynamics
We present a new hybrid lattice-Boltzmann and Langevin molecular dynamics
scheme for simulating the dynamics of suspensions of spherical colloidal
particles. The solvent is modeled on the level of the lattice-Boltzmann method
while the molecular dynamics is done for the solute. The coupling between the
two is implemented through a frictional force acting both on the solvent and on
the solute, which depends on the relative velocity. A spherical colloidal
particle is represented by interaction sites at its surface. We demonstrate
that this scheme quantitatively reproduces the translational and rotational
diffusion of a neutral spherical particle in a liquid and show preliminary
results for a charged spherical particle. We argue that this method is
especially advantageous in the case of charged colloids.Comment: For a movie click on the link below Fig
Self-consistent modeling of laminar electrohydrodynamic plumes from ultrasharp needles in cyclohexane
This paper presents a self-consistent model of electrohydrodynamic (EHD) laminar plumes produced by electron injection
from ultra-sharp needle tips in cyclohexane. Since the density of electrons injected into the liquid is well described by the
Fowler-Nordheim field emission theory, the injection law is not assumed. Furthermore, the generation of electrons in
cyclohexane and their conversion into negative ions is included in the analysis. Detailed steady-state characteristics of EHD
plumes under weak injection and space-charge limited injection are studied. It is found that the plume characteristics far from
both electrodes and under weak injection can be accurately described with an asymptotic simplified solution proposed by
Vazquez et al. Physics of Fluids 12, 2809 (2000) when the correct longitudinal electric field distribution and liquid velocity
radial profile are used as input. However, this asymptotic solution deviates from the self-consistently calculated plume
parameters under space-charge limited injection since it neglects the radial variations of the electric field produced by a highdensity
charged core. In addition, no significant differences in the model estimates of the plume are found when the
simulations are obtained either with the Finite Element Method or with a diffusion-free particle method. It is shown that the
model also enables the calculation of the current-voltage (IV) characteristic of EHD laminar plumes produced by electron
field emission, with good agreement with measured values reported in the literature.Ministerio de EconomĂa y Competitividad FIS2014-54539-P
Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann vs Brownian dynamics
We present a comparative study of two computer simulation methods to obtain
static and dynamic properties of dilute polymer solutions. The first approach
is a recently established hybrid algorithm based upon dissipative coupling
between Molecular Dynamics and lattice Boltzmann (LB), while the second is
standard Brownian Dynamics (BD) with fluctuating hydrodynamic interactions.
Applying these methods to the same physical system (a single polymer chain in a
good solvent in thermal equilibrium) allows us to draw a detailed and
quantitative comparison in terms of both accuracy and efficiency. It is found
that the static conformations of the LB model are distorted when the box length
L is too small compared to the chain size. Furthermore, some dynamic properties
of the LB model are subject to an finite size effect, while the BD
model directly reproduces the asymptotic behavior. Apart from
these finite size effects, it is also found that in order to obtain the correct
dynamic properties for the LB simulations, it is crucial to properly thermalize
all the kinetic modes. Only in this case, the results are in excellent
agreement with each other, as expected. Moreover, Brownian Dynamics is found to
be much more efficient than lattice Boltzmann as long as the degree of
polymerization is not excessively large.Comment: 11 figures, submitted to J. Chem. Phy
Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
We study the problem of initiation of excitation waves in the FitzHugh-Nagumo
model. Our approach follows earlier works and is based on the idea of
approximating the boundary between basins of attraction of propagating waves
and of the resting state as the stable manifold of a critical solution. Here,
we obtain analytical expressions for the essential ingredients of the theory by
singular perturbation using two small parameters, the separation of time scales
of the activator and inhibitor, and the threshold in the activator's kinetics.
This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2
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