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Author name code: schaffenberger
ADS astronomy entries on 2022-09-14
author:"Schaffenberger, Werner"
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Title: Properties of small-scale magnetism of stellar atmospheres
Authors: Steiner, Oskar; Salhab, René; Freytag, Bernd; Rajaguru,
Paul; Schaffenberger, Werner; Steffen, Matthias
2014PASJ...66S...5S Altcode: 2014PASJ..tmp...95S
The magnetic field outside of sunspots is concentrated in the
intergranular space, where it forms a delicate filigree of bright
ribbons and dots as seen on broad band images of the Sun. We expect this
small-scale magnetic field to exhibit a similar behavior in stellar
atmospheres. In order to find out more about it, we perform numerical
simulations of the surface layers of stellar atmospheres. Here, we
report on preliminary results from simulations in the range between
4000 K and 6500 K effective temperature with an initial vertical,
homogeneous magnetic field of 50 G strength. We find that the field
strength of the strongest magnetic flux concentrations increases with
decreasing effective temperature at the height level where the average
Rosseland optical depth is one. On the other hand, at the same level,
the field is less strong than the thermal equipartition value in the
coolest model but assumes superequipartition in the models hotter
than 5000 K. While the Wilson depression of the strongest field
concentrations is about one pressure scale height in the coolest
model, it is more than four times the pressure scale height in the
hottest one. We also find that the relative contribution of the bright
filigree to the bolometric, vertically directed radiative intensity is
most significant for the T<SUB>eff</SUB> = 5000 K model (0.6%-0.79%)
and least significant for the hottest and coolest models (0.1%-0.46%
and 0.14%-0.32%, respectively). This behavior suggests that the effect
of the small-scale magnetic field on the photometric variability is more
significant for K dwarf stars than for F-type and also M-type stars.
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Title: First steps with CO5BOLD using HLLMHD and PP reconstruction .
Authors: Steiner, O.; Rajaguru, S. P.; Vigeesh, G.; Steffen, M.;
Schaffenberger, W.; Freytag, B.
2013MSAIS..24..100S Altcode:
We report on first experiences with real-life applications using
the MHD-module of CO5BOLD together with the piecewise parabolic
reconstruction scheme and present preliminary results of stellar
magnetic models with T<SUB>eff</SUB> = 4000 K to T<SUB>eff</SUB> =
5770 K.
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Title: Progress in modeling very low mass stars, brown dwarfs,
and planetary mass objects.
Authors: Allard, F.; Homeier, D.; Freytag, B.; Schaffenberger, W.;
Rajpurohit, A. S.
2013MSAIS..24..128A Altcode: 2013arXiv1302.6559A
We review recent advancements in modeling the stellar to substellar
transition. The revised molecular opacities, solar oxygen abundances
and cloud models allow to reproduce the photometric and spectroscopic
properties of this transition to a degree never achieved before,
but problems remain in the important M-L transition characteristic
of the effective temperature range of characterizable exoplanets. We
discuss of the validity of these classical models. We also present
new preliminary global Radiation HydroDynamical M dwarfs simulations.
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Title: Simulations of stellar convection with CO5BOLD
Authors: Freytag, B.; Steffen, M.; Ludwig, H. -G.; Wedemeyer-Böhm,
S.; Schaffenberger, W.; Steiner, O.
2012JCoPh.231..919F Altcode: 2011arXiv1110.6844F
High-resolution images of the solar surface show a granulation
pattern of hot rising and cooler downward-sinking material - the
top of the deep-reaching solar convection zone. Convection plays a
role for the thermal structure of the solar interior and the dynamo
acting there, for the stratification of the photosphere, where most
of the visible light is emitted, as well as for the energy budget of
the spectacular processes in the chromosphere and corona. Convective
stellar atmospheres can be modeled by numerically solving the coupled
equations of (magneto)hydrodynamics and non-local radiation transport
in the presence of a gravity field. The CO5BOLD code described in this
article is designed for so-called "realistic" simulations that take
into account the detailed microphysics under the conditions in solar
or stellar surface layers (equation-of-state and optical properties of
the matter). These simulations indeed deserve the label "realistic"
because they reproduce the various observables very well - with only
minor differences between different implementations. The agreement
with observations has improved over time and the simulations are now
well-established and have been performed for a number of stars. Still,
severe challenges are encountered when it comes to extending these
simulations to include ideally the entire star or substellar object:
the strong stratification leads to completely different conditions in
the interior, the photosphere, and the corona. Simulations have to cover
spatial scales from the sub-granular level to the stellar diameter and
time scales from photospheric wave travel times to stellar rotation
or dynamo cycle periods. Various non-equilibrium processes have to be
taken into account. Last but not least, realistic simulations are based
on detailed microphysics and depend on the quality of the input data,
which can be the actual accuracy limiter. This article provides an
overview of the physical problem and the numerical solution and the
capabilities of CO5BOLD, illustrated with a number of applications.
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Title: Modification of wave propagation and wave travel-time by the
presence of magnetic fields in the solar network atmosphere
Authors: Nutto, C.; Steiner, O.; Schaffenberger, W.; Roth, M.
2012A&A...538A..79N Altcode:
Context. Observations of waves at frequencies above the acoustic cut-off
frequency have revealed vanishing wave travel-times in the vicinity of
strong magnetic fields. This detection of apparently evanescent waves,
instead of the expected propagating waves, has remained a riddle. <BR />
Aims: We investigate the influence of a strong magnetic field on the
propagation of magneto-acoustic waves in the atmosphere of the solar
network. We test whether mode conversion effects can account for the
shortening in wave travel-times between different heights in the solar
atmosphere. <BR /> Methods: We carry out numerical simulations of the
complex magneto-atmosphere representing the solar magnetic network. In
the simulation domain, we artificially excite high frequency waves
whose wave travel-times between different height levels we then
analyze. <BR /> Results: The simulations demonstrate that the wave
travel-time in the solar magneto-atmosphere is strongly influenced by
mode conversion. In a layer enclosing the surface sheet defined by the
set of points where the Alfvén speed and the sound speed are equal,
called the equipartition level, energy is partially transferred from the
fast acoustic mode to the fast magnetic mode. Above the equipartition
level, the fast magnetic mode is refracted due to the large gradient
of the Alfvén speed. The refractive wave path and the increasing phase
speed of the fast mode inside the magnetic canopy significantly reduce
the wave travel-time, provided that both observing levels are above
the equipartition level. <BR /> Conclusions: Mode conversion and the
resulting excitation and propagation of fast magneto-acoustic waves is
responsible for the observation of vanishing wave travel-times in the
vicinity of strong magnetic fields. In particular, the wave propagation
behavior of the fast mode above the equipartition level may mimic
evanescent behavior. The present wave propagation experiments provide an
explanation of vanishing wave travel-times as observed with multi-line
high-cadence instruments. <P />Movies are available in electronic form
at <A href="http://www.aanda.org">http://www.aanda.org</A>
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Title: CO5BOLD: COnservative COde for the COmputation of COmpressible
COnvection in a BOx of L Dimensions with l=2,3
Authors: Freytag, Bernd; Steffen, Matthias; Wedemeyer-Böhm, Sven;
Ludwig, Hans-Günter; Leenaarts, Jorrit; Schaffenberger, Werner;
Allard, France; Chiavassa, Andrea; Höfner, Susanne; Kamp, Inga;
Steiner, Oskar
2010ascl.soft11014F Altcode:
CO5BOLD - nickname COBOLD - is the short form of "COnservative
COde for the COmputation of COmpressible COnvection in a BOx of L
Dimensions with l=2,3". <P />It is used to model solar and stellar
surface convection. For solar-type stars only a small fraction of the
stellar surface layers are included in the computational domain. In
the case of red supergiants the computational box contains the entire
star. Recently, the model range has been extended to sub-stellar objects
(brown dwarfs). <P />CO5BOLD solves the coupled non-linear equations
of compressible hydrodynamics in an external gravity field together
with non-local frequency-dependent radiation transport. Operator
splitting is applied to solve the equations of hydrodynamics (including
gravity), the radiative energy transfer (with a long-characteristics
or a short-characteristics ray scheme), and possibly additional 3D
(turbulent) diffusion in individual sub steps. The 3D hydrodynamics
step is further simplified with directional splitting (usually). The 1D
sub steps are performed with a Roe solver, accounting for an external
gravity field and an arbitrary equation of state from a table. <P
/>The radiation transport is computed with either one of three
modules: <P />MSrad module: It uses long characteristics. The lateral
boundaries have to be periodic. Top and bottom can be closed or open
("solar module"). <P />LHDrad module: It uses long characteristics
and is restricted to an equidistant grid and open boundaries at all
surfaces (old "supergiant module"). <P />SHORTrad module: It uses
short characteristics and is restricted to an equidistant grid and
open boundaries at all surfaces (new "supergiant module"). <P />The
code was supplemented with an (optional) MHD version [Schaffenberger
et al. (2005)] that can treat magnetic fields. There are also modules
for the formation and advection of dust available. The current version
now contains the treatment of chemical reaction networks, mostly used
for the formation of molecules [Wedemeyer-Böhm et al. (2005)], and
hydrogen ionization [Leenaarts & Wedemeyer-Böhm (2005)], too. <P
/>CO5BOLD is written in Fortran90. The parallelization is done with
OpenMP directives.
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Title: Supergranulation-Scale Convection Simulations
Authors: Stein, R. F.; Nordlund, Å.; Georgoviani, D.; Benson, D.;
Schaffenberger, W.
2009ASPC..416..421S Altcode:
Results of realistic simulations of solar surface convection on the
scale of supergranules (96 Mm wide by 20 Mm deep) are presented. The
simulations cover only 10% of the geometric depth of the solar
convection zone, but half its pressure scale heights. They include the
hydrogen ionization zone, and the first and most of the second helium
ionization zones. The horizontal velocity spectrum is a power law,
and the horizontal size of the dominant convective cells increases
with increasing depth. Convection is driven by buoyancy work, which
is largest close to the surface, but significant over the entire
domain. Close to the surface, buoyancy driving is balanced by the
divergence of the kinetic energy flux, but deeper down it is balanced
by dissipation. The damping length of the turbulent kinetic energy
is 4 pressure scale heights. The mass mixing length is 1.8 scale
heights. Two thirds of the area is upflowing fluid except very close
to the surface. The internal (ionization) energy flux is the largest
contributor to the convective flux for temperatures less than 40,000
K and the thermal energy flux is the largest contributor at higher
temperatures. This data set is useful for validating local helioseismic
inversion methods. Sixteen hours of data are available as four hour
averages, with two hour cadence, at steinr.msu.edu/~bob/96averages,
as idl save files. The variables stored are the density, temperature,
sound speed, and three velocity components. In addition, the three
velocity components at 200 km above mean continuum optical depth unity
are available at 30 second cadence.
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Title: The Horizontal Magnetic Field of the Quiet Sun: Numerical
Simulations in Comparison to Observations with Hinode
Authors: Steiner, O.; Rezaei, R.; Schlichenmaier, R.; Schaffenberger,
W.; Wedemeyer-Böhm, S.
2009ASPC..415...67S Altcode: 2009arXiv0904.2030S
Three-dimensional magnetohydrodynamic simulations of the surface layers
of the Sun intrinsically produce a predominantly horizontal magnetic
field in the photosphere. This is a robust result in the sense that it
arises from simulations with largely different initial and boundary
conditions for the magnetic field. While the disk-center synthetic
circular and linear polarization signals agree with measurements from
Hinode, their center-to-limb variation sensitively depends on the
height variation of the horizontal and the vertical field component
and they seem to be at variance with the observed behavior.
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Title: Supergranulation Scale Convection Simulations
Authors: Stein, R. F.; Lagerfjård, A.; Nordlund, Å.; Georgobiani,
D.; Benson, D.; Schaffenberger, W.
2009ASPC..415...63S Altcode:
Results of realistic simulations of solar surface convection on
the scale of supergranules (48 and 96 Mm wide by 20 Mm deep) are
presented. The simulations include the hydrogen, first and most
of the second helium ionization zones. Horizontal magnetic field is
advected into the domain by upflows at the bottom. Upflows stretch the
field lines upward, while downflows push them down, thus producing
loop like magnetic structures. The mass mixing length is 1.8 scale
heights. Two thirds of the area is upflowing fluid except very close
to the surface. The internal (ionization) energy flux is the largest
contributor to the convective flux for temperatures less than 40,000
K and the thermal energy flux is the largest contributor at higher
temperatures. The data is available for evaluating local helioseismic
procedures.
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Title: Magnetohydrodynamic Characteristic Boundary Conditions
Authors: Schaffenberger, Werner; Stein, R.
2009SPD....40.0930S Altcode:
We implemented MHD characteristic boundary conditions for a non-ideal
plasma in the "stagger-code" (Gudiksen and Nordlund, 2005, ApJ 618,
1020). The aim of these boundary conditions is to reduce reflection
at the boundaries which is important for the simulation of wave
propagation. We present some test simulations of propagating waves
demonstrating the capability of these boundary conditions.
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Title: Solar Magneto-Convection Simulations
Authors: Stein, Robert F.; Lagerfjard, A.; Nordlund, A.; Benson, D.;
Georgobiani, D.; Schaffenberger, W.
2009SPD....40.0401S Altcode:
We present preliminary results of magneto-convection simulations
of the rise of initially horizontal magnetic flux from 20 Mm deep
through the solar surface in a domain 48 Mm wide. The magnetic field
is stretched upward in the diverging upflows and pulled down in the
downdrafts which produces a hierarchy of loop like structures. The
strength varies with depth as the square root of the density. The field
is swept to the boundaries of small supergranular like structures to
form a magnetic network.
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Title: Supergranulation Scale Connection Simulations
Authors: Stein, R. F.; Nordlund, A.; Georgobiani, D.; Benson, D.;
Schaffenberger, W.
2008arXiv0811.0472S Altcode:
Results of realistic simulations of solar surface convection on the
scale of supergranules (96 Mm wide by 20 Mm deep) are presented. The
simulations cover only 10% of the geometric depth of the solar
convection zone, but half its pressure scale heights. They include the
hydrogen, first and most of the second helium ionization zones. The
horizontal velocity spectrum is a power law and the horizontal
size of the dominant convective cells increases with increasing
depth. Convection is driven by buoyancy work which is largest close
to the surface, but significant over the entire domain. Close to the
surface buoyancy driving is balanced by the divergence of the kinetic
energy flux, but deeper down it is balanced by dissipation. The
damping length of the turbulent kinetic energy is 4 pressure scale
heights. The mass mixing length is 1.8 scale heights. Two thirds of the
area is upflowing fluid except very close to the surface. The internal
(ionization) energy flux is the largest contributor to the convective
flux for temperatures less than 40,000 K and the thermal energy flux is
the largest contributor at higher temperatures. This data set is useful
for validating local helioseismic inversion methods. Sixteen hours
of data are available as four hour averages, with two hour cadence,
at steinr.msu.edu/~bob/96averages, as idl save files. The variables
stored are the density, temperature, sound speed, and three velocity
components. In addition, the three velocity components at 200 km above
mean continuum optical depth unity are available at 30 sec. cadence.
---------------------------------------------------------
Title: Numerical Experiments with Magnetoacoustic Waves in the
Solar Atmosphere
Authors: Nutto, C.; Schaffenberger, W.; Steiner, O.
2008ESPM...12.3.23N Altcode:
With numerical experiments we explore the feasibility of using high
frequency waves for probing the magnetic field in the photosphere
and the chromosphere of the Sun. We track monochromatic wave trains
that propagates through a magnetically structured, realistic solar
atmosphere. When entering the magnetically dominated chromosphere,
the waves undergo partial mode conversion and get refracted and
reflected. We explore the relationship between wave travel times and
the topography of the surface of equal Alfven and sound speeds, viz.,
the magnetic canopy.
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Title: The Horizontal Internetwork Magnetic Field: Numerical
Simulations in Comparison to Observations with Hinode
Authors: Steiner, O.; Rezaei, R.; Schaffenberger, W.; Wedemeyer-Böhm,
S.
2008ESPM...12.3.22S Altcode:
Observations with the Hinode space observatory led to the discovery
of predominantly horizontal magnetic fields in the photosphere of the
quiet internetwork region. Here we investigate realistic numerical
simulations of the surface layers of the Sun with respect to horizontal
magnetic fields and compute the corresponding polarimetric response
in the Fe I 630 nm line pair. We find a local maximum in the mean
strength of the horizontal field component at a height of around 500
km in the photosphere, where, depending on the initial state or the
boundary condition, it surpasses the vertical component by a factor
of 2.0 or 5.6. From the synthesized Stokes profiles, we derive a mean
horizontal field component that is 1.6 or 4.3 times stronger than
the vertical component, depending on the initial state or the boundary
condition. This is a consequence of both the intrinsically stronger flux
density of and the larger area occupied by the horizontal fields. We
find that convective overshooting expels horizontal fields to the upper
photosphere, making the Poynting flux positive in the photosphere,
whereas it is negative in the convectively unstable layer below it.
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Title: The Horizontal Internetwork Magnetic Field: Numerical
Simulations in Comparison to Observations with Hinode
Authors: Steiner, O.; Rezaei, R.; Schaffenberger, W.; Wedemeyer-Böhm,
S.
2008ApJ...680L..85S Altcode: 2008arXiv0801.4915S
Observations with the Hinode space observatory led to the discovery
of predominantly horizontal magnetic fields in the photosphere of the
quiet internetwork region. Here we investigate realistic numerical
simulations of the surface layers of the Sun with respect to horizontal
magnetic fields and compute the corresponding polarimetric response
in the Fe I 630 nm line pair. We find a local maximum in the mean
strength of the horizontal field component at a height of around 500
km in the photosphere, where, depending on the initial state or the
boundary condition, it surpasses the vertical component by a factor
of 2.0 or 5.6. From the synthesized Stokes profiles, we derive a mean
horizontal field component that is 1.6 or 4.3 times stronger than
the vertical component, depending on the initial state or the boundary
condition. This is a consequence of both the intrinsically stronger flux
density of and the larger area occupied by the horizontal fields. We
find that convective overshooting expels horizontal fields to the upper
photosphere, making the Poynting flux positive in the photosphere,
whereas the Poynting flux is negative in the convectively unstable
layer below it.
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Title: Surface Convection
Authors: Stein, Robert F.; Benson, David; Georgobiani, Dali; Nordlund,
Åke; Schaffenberger, Werner
2007AIPC..948..111S Altcode:
What are supergranules? Why do they stand out? Preliminary results from
realistic simulations of solar convection on supergranule scales (96 Mm
wide by 20 Mm deep) are presented. The solar surface velocity amplitude
is a decreasing power law from the scale of granules up to giant cells
with a slight enhancement at supergranule scales. The simulations show
that the size of the horizontal convective cells increases gradually
and continuously with increasing depth. Without magnetic fields
present there is, as yet, no enhancement at supergranule scales at the
surface. A hypothesis is presented that it is the balance between the
rate of magnetic flux emergence and the horizontal sweeping of magnetic
flux by convective motions that determines the size of the magnetic
network and produces the extra power at supergranulation scales.
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Title: First local helioseismic experiments with CO<SUP>5</SUP>BOLD
Authors: Steiner, O.; Vigeesh, G.; Krieger, L.; Wedemeyer-Böhm, S.;
Schaffenberger, W.; Freytag, B.
2007AN....328..323S Altcode: 2007astro.ph..1029S
With numerical experiments we explore the feasibility of using high
frequency waves for probing the magnetic fields in the photosphere and
the chromosphere of the Sun. We track a plane-parallel, monochromatic
wave that propagates through a non-stationary, realistic atmosphere,
from the convection-zone through the photosphere into the magnetically
dominated chromosphere, where it gets refracted and reflected. We
compare the wave travel time between two fixed geometrical height levels
in the atmosphere (representing the formation height of two spectral
lines) with the topography of the surface of equal magnetic and thermal
energy density (the magnetic canopy or β=1 contour) and find good
correspondence between the two. We conclude that high frequency waves
indeed bear information on the topography of the `magnetic canopy'.
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Title: Holistic MHD-Simulation from the Convection Zone to the
Chromosphere
Authors: Schaffenberger, W.; Wedemeyer-Böhm, S.; Steiner, O.;
Freytag, B.
2006ASPC..354..345S Altcode:
A three-dimensional magnetohydrodynamic simulation of the integral
layers from the convection zone to the chromosphere has been
carried out. The simulation represents magnetoconvection in a quiet
network-cell interior. The following preliminary new results are
obtained: The chromospheric magnetic field is very dynamic with a
continuous rearrangement of magnetic flux on a time scale of less than
one~minute. Rapidly moving magnetic filaments (rarely exceeding 40~G)
form in the compression zone downstream and along propagating shock
fronts that are present throughout the chromosphere. The magnetic
filaments rapidly move, form, and dissolve with the shock waves. Flux
concentrations strongly expand through the photosphere into a more
homogeneous, space filling chromospheric field. “Canopy fields”
form on a granular scale above largely field-free granule centers
leading to a mesh-work of current sheets in a height range between
approximately 400 and 900~km.
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Title: Simulations of Magnetohydrodynamics and CO Formation from
the Convection Zone to the Chromosphere
Authors: Wedemeyer-Böhm, S.; Schaffenberger, W.; Steiner, O.; Steffen,
M.; Freytag, B.; Kamp, I.
2005ESASP.596E..16W Altcode: 2005ccmf.confE..16W
No abstract at ADS
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Title: Magnetohydrodynamic Simulation from the Convection Zone to
the Chromosphere
Authors: Schaffenberger, W.; Wedemeyer-Böhm, S.; Steiner, O.;
Freytag, B.
2005ESASP.596E..65S Altcode: 2005ccmf.confE..65S
No abstract at ADS
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Title: Analysis of mirror modes convected from the bow shock to
the magnetopause
Authors: Erkaev, N. V.; Schaffenberger, W.; Biernat, H. K.; Farrugia,
C. J.; Vogl, D. F.
2001P&SS...49.1359E Altcode:
Spacecraft observations confirm the existence of mirror fluctuations
in the magnetosheath. The mirror instability occurs in an anisotropic
magnetized plasma when the difference between perpendicular and
parallel (with respect to the magnetic field) plasma pressure exceeds
a threshold depending on the perpendicular plasma beta. The anisotropy
of the plasma pressure increases from the shock to the magnetopause as
a result of magnetic field line stretching. This gives rise to plasma
fluctuations which in turn lead to a relaxation between parallel and
perpendicular temperatures. Mirror perturbations do not propagate
and are convected with plasma flow along the streamlines. Using an
anisotropic steady-state MHD flow model, we calculate the growth
of mirror fluctuations from the bow shock to the magnetopause along
the subsolar streamline. For the anisotropic MHD model, we use the
empirical closure equation suitable for the AMPTE/IRM observations. The
amplitudes of mirror fluctuations, which are obtained as a function of
distance from the magnetopause, are directly compared with AMPTE/IRM
observations on October 24, 1985. With regard to both the amplification
of the magnetic field and the plasma density oscillations, as well
as the location of maximum amplitudes, model calculations are in good
agreement with values obtained from the AMPTE/IRM data.
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Title: A Lattice Gas Model for Twodimensional Boussinesq Convection
Authors: Schaffenberger, W.; Hanslmeier, A.; Messerotti, M.
2001HvaOB..25...49S Altcode:
In this paper, we present a 2-D model for simulating the convection of
an incompressible fluid between two walls of different temperatures. In
particular, a bidimensional cellular automaton (CA) was developed to
study the evolution of a discrete particle system, which represents a
modified Frisch-Hasslacher-Pomeau (FHP) lattice gas. The derivation of
the model equations and some relevant diagnostics, such as the Rayleigh,
Prandtl and Nusselt numbers, are briefly outlined. The diagnostics
computed for test runs indicate the consistency of the model as well
as the preliminary simulation performed with a CA.
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Title: MHD effects of the solar wind flow around planets
Authors: Biernat, H. K.; Erkaev, N. V.; Farrugia, C. J.; Vogl, D. F.;
Schaffenberger, W.
2000NPGeo...7..201B Altcode:
The study of the interaction of the solar wind with magnetized and
unmagnetized planets forms a central topic of space research. Focussing
on planetary magnetosheaths, we review some major developments in this
field. Magnetosheath structures depend crucially on the orientation of
the interplanetary magnetic field, the solar wind Alfvén Mach number,
the shape of the obstacle (axisymmetric/non-axisymmetric, etc.), the
boundary conditions at the magnetopause (low/high magnetic shear),
and the degree of thermal anisotropy of the plasma. We illustrate the
cases of Earth, Jupiter and Venus. The terrestrial magnetosphere is
axisymmetric and has been probed in-situ by many spacecraft. Jupiter's
magnetosphere is highly non-axisymmetric. Furthermore, we study
magnetohydrodynamic effects in the Venus magnetosheath.
---------------------------------------------------------
Title: Cellular Automata Models for Convection
Authors: Schaffenberger, W.; Hanslmeier, A.; Messerotti, M.
1999ASSL..239..267S Altcode: 1999msa..proc..267S
We present here three models for convection. The models make use of
the concept of cellular automata (CA). CA are discrete systems. The
advantages of CA are their simple and parallel structure. The
simplest of the presented models simulates two-dimensional Boussinesq
convection. The two other models are extensions to compressible fluids
and three-dimensional convection, respectively. We derive the model
equations for the simplest model and present some of our results.
---------------------------------------------------------
Title: Simulating convection with cellular automata.
Authors: Schaffenberger, W.; Hanslmeier, A.; Messerotti, M.
1997AGAb...13..175S Altcode:
No abstract at ADS
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Title: On the Influence of Supernova Shockfronts on the Stability
of the Solar System
Authors: Schaffenberger, W.; Hanslmeier, A.
1997dbps.conf..393S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Simulation of solar convection with cellular automata -
first results.
Authors: Schaffenberger, W.; Hanslmeier, A.; Messerotti, M.
1997joso.proc...82S Altcode:
No abstract at ADS
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Title: A cellulare automaton for modelling the convection.
Authors: Schaffenberger, W.; Hanslmeier, A.; Messerotti, M.
1996AGAb...12..162S Altcode:
No abstract at ADS
