671 research outputs found
Afivo: a framework for quadtree/octree AMR with shared-memory parallelization and geometric multigrid methods
Afivo is a framework for simulations with adaptive mesh refinement (AMR) on
quadtree (2D) and octree (3D) grids. The framework comes with a geometric
multigrid solver, shared-memory (OpenMP) parallelism and it supports output in
Silo and VTK file formats. Afivo can be used to efficiently simulate AMR
problems with up to about unknowns on desktops, workstations or single
compute nodes. For larger problems, existing distributed-memory frameworks are
better suited. The framework has no built-in functionality for specific physics
applications, so users have to implement their own numerical methods. The
included multigrid solver can be used to efficiently solve elliptic partial
differential equations such as Poisson's equation. Afivo's design was kept
simple, which in combination with the shared-memory parallelism facilitates
modification and experimentation with AMR algorithms. The framework was already
used to perform 3D simulations of streamer discharges, which required tens of
millions of cells
Simulating streamer discharges in 3D with the parallel adaptive Afivo framework
We present an open-source plasma fluid code for 2D, cylindrical and 3D
simulations of streamer discharges, based on the Afivo framework that features
adaptive mesh refinement, geometric multigrid methods for Poisson's equation,
and OpenMP parallelism. We describe the numerical implementation of a fluid
model of the drift-diffusion-reaction type, combined with the local field
approximation. Then we demonstrate its functionality with 3D simulations of
long positive streamers in nitrogen in undervolted gaps, using three examples.
The first example shows how a stochastic background density affects streamer
propagation and branching. The second one focuses on the interaction of a
streamer with preionized regions, and the third one investigates the
interaction between two streamers. The simulations run on up to grid
cells within less than a day. Without mesh refinement, they would require
grid cells
Breakdown of the standard Perturbation Theory and Moving Boundary Approximation for "Pulled" Fronts
The derivation of a Moving Boundary Approximation or of the response of a
coherent structure like a front, vortex or pulse to external forces and noise,
is generally valid under two conditions: the existence of a separation of time
scales of the dynamics on the inner and outer scale and the existence and
convergence of solvability type integrals. We point out that these conditions
are not satisfied for pulled fronts propagating into an unstable state: their
relaxation on the inner scale is power law like and in conjunction with this,
solvability integrals diverge. The physical origin of this is traced to the
fact that the important dynamics of pulled fronts occurs in the leading edge of
the front rather than in the nonlinear internal front region itself. As recent
work on the relaxation and stochastic behavior of pulled fronts suggests, when
such fronts are coupled to other fields or to noise, the dynamical behavior is
often qualitatively different from the standard case in which fronts between
two (meta)stable states or pushed fronts propagating into an unstable state are
considered.Comment: pages Latex, submitted to a special issue of Phys. Rep. in dec. 9
Streamers, sprites, leaders, lightning: from micro- to macroscales
"Streamers, sprites, leaders, lightning: from micro- to macroscales" was the
theme of a workshop in October 2007 in Leiden, The Netherlands; it brought
researchers from plasma physics, electrical engineering and industry,
geophysics and space physics, computational science and nonlinear dynamics
together around the common topic of generation, structure and products of
streamer-like electric breakdown. The present cluster issue collects relevant
articles within this area; most of them were presented during the workshop. We
here briefly discuss the research questions and very shortly review the papers
in the cluster issue, and we also refer to a few recent papers in other
journals.Comment: Editorial introduction for the cluster issue on "Streamers, sprites
and lightning" in J. Phys. D, 13 pages, 74 reference
The inception of pulsed discharges in air: simulations in background fields above and below breakdown
We investigate discharge inception in air, in uniform background electric
fields above and below the breakdown threshold. We perform 3D particle
simulations that include a natural level of background ionization in the form
of positive and O ions. When the electric field rises above the
breakdown and the detachment threshold, which are similar in air, electrons can
detach from O and start ionization avalanches. These avalanches
together create one large discharge, in contrast to the `double-headed'
streamers found in many fluid simulations.
On the other hand, in background fields below breakdown, something must
enhance the field sufficiently for a streamer to form. We use a strongly
ionized seed of electrons and positive ions for this, with which we observe the
growth of positive streamers. Negative streamers were not observed. Below
breakdown, the inclusion of electron detachment does not change the results
much, and we observe similar discharge development as in fluid simulations
Spatially hybrid computations for streamer discharges with generic features of pulled fronts: I. Planar fronts
Streamers are the first stage of sparks and lightning; they grow due to a
strongly enhanced electric field at their tips; this field is created by a thin
curved space charge layer. These multiple scales are already challenging when
the electrons are approximated by densities. However, electron density
fluctuations in the leading edge of the front and non-thermal stretched tails
of the electron energy distribution (as a cause of X-ray emissions) require a
particle model to follow the electron motion. As super-particle methods create
wrong statistics and numerical artifacts, modeling the individual electron
dynamics in streamers is limited to early stages where the total electron
number still is limited.
The method of choice is a hybrid computation in space where individual
electrons are followed in the region of high electric field and low density
while the bulk of the electrons is approximated by densities (or fluids). We
here develop the hybrid coupling for planar fronts. First, to obtain a
consistent flux at the interface between particle and fluid model in the hybrid
computation, the widely used classical fluid model is replaced by an extended
fluid model. Then the coupling algorithm and the numerical implementation of
the spatially hybrid model are presented in detail, in particular, the position
of the model interface and the construction of the buffer region. The method
carries generic features of pulled fronts that can be applied to similar
problems like large deviations in the leading edge of population fronts etc.Comment: 33 pages, 15 figures and 2 table
A time scale for electrical screening in pulsed gas discharges
The Maxwell time is a typical time scale for the screening of an electric
field in a medium with a given conductivity. We introduce a generalization of
the Maxwell time that is valid for gas discharges: the \emph{ionization
screening time}, that takes the growth of the conductivity due to impact
ionization into account. We present an analytic estimate for this time scale,
assuming a planar geometry, and evaluate its accuracy by comparing with
numerical simulations in 1D and 3D. We investigate the minimum plasma density
required to prevent the growth of streamers with local field enhancement, and
we discuss the effects of photoionization and electron detachment on ionization
screening. Our results can help to understand the development of pulsed
discharges, for example nanosecond pulsed discharges at atmospheric pressure or
halo discharges in the lower ionosphere
The coherent scattering function in the reptation model: analysis beyond asymptotic limits
We calculate the coherent dynamical scattering function S_c(q,t;N) of a
flexible chain of length N, diffusing through an ordered background of
topological obstacles. As an instructive generalization, we also calculate the
scattering function S_c(q,t;M,N) for the central piece of length M < N of the
chain. Using the full reptation model, we treat global creep, tube length
fluctuations, and internal relaxation within a consistent and unified approach.
Our theory concentrates on the universal aspects of reptational motion, and our
results in all details show excellent agreement with our simulations of the
Evans-Edwards model, provided we allow for a phenomenological prefactor which
accounts for non-universal effects of the micro-structure of the Monte Carlo
chain, present for short times. Previous approaches to the coherent structure
function can be analyzed as special limits of our theory. First, the effects of
internal relaxation can be isolated by studying the limit , M
fixed. The results do not support the model of a `Rouse chain in a tube'. We
trace this back to the non-equilibrium initial conditions of the latter model.
Second, in the limit of long chains and times large
compared to the internal relaxation time , our theory
reproduces the results of the primitive chain model. This limiting form applies
only to extremely long chains, and for chain lengths accessible in practice,
effects of, e.g., tube length fluctuations are not negligible.Comment: 35 pages revtex style, 9 figures, submitted on January 5, 2002,
references updated. Phys. Rev. E, to appea
Simulated avalanche formation around streamers in an overvolted air gap
We simulate streamers in air at standard temperature and pressure in a short
overvolted gap. The simulation is performed with a 3D hybrid model that traces
the single electrons and photons in the low density region, while modeling the
streamer interior as a fluid. The photons are followed by a Monte-Carlo
procedure, just like the electrons. The first simulation result is present
here.Comment: 2 page
The coherent scattering function of the reptation model: simulations compared to theory
We present results of Monte Carlo simulations measuring the coherent
structure function of a chain moving through an ordered lattice of fixed
topological obstacles. Our computer experiments use chains up to 320 beads and
cover a large range of wave vectors and a time range exceeding the reptation
time. -- We compare our results (i) to the predictions of the primitive chain
model, (ii) to an approximate form resulting from Rouse motion in a coiled
tube, and (iii) to our recent evaluation of the full reptation model. (i) The
primitive chain model can fit the data for times t \gt 20 T_2, where T_2 is the
Rouse time of the chain. Besides some phenomenological amplitude factor this
fit involves the reptation time T_3 as a second fit parameter. For the chain
lengths measured, the asymptotic behavior T_3 ~ N^3 is not attained. (ii) The
model of Rouse motion in a tube, which we have criticized before on theoretical
grounds, is shown to fail also on the purely phenomenological level. (iii) Our
evaluation of the full reptation model yields an excellent fit to the data for
both total chains and internal pieces and for all wave vectors and all times,
provided specific micro-structure effects of the MC-dynamics are negligible.
Such micro-structure effects show up for wave vectors of the order of the
inverse segment size. For the dynamics of the total chain our data analysis
based on the full reptation model shows the importance of tube length
fluctuations. Universal (Rouse-type) internal relaxation is unimportant. It can
be observed only in the form of the diffusive motion of a short central
subchain in the tube. -- Finally we present a fit formula which in a large
range of wave vectors and chain lengths reproduces the numerical results of our
theory for the scattering from the total chain.Comment: 26 pages, 12 figure
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