32 research outputs found
The discontinuous Galerkin method for fractional degenerate convection-diffusion equations
We propose and study discontinuous Galerkin methods for strongly degenerate
convection-diffusion equations perturbed by a fractional diffusion (L\'evy)
operator. We prove various stability estimates along with convergence results
toward properly defined (entropy) solutions of linear and nonlinear equations.
Finally, the qualitative behavior of solutions of such equations are
illustrated through numerical experiments
A high-order Godunov scheme for global 3D MHD accretion disks simulations. I. The linear growth regime of the magneto-rotational instability
We employ the PLUTO code for computational astrophysics to assess and compare
the validity of different numerical algorithms on simulations of the
magneto-rotational instability in 3D accretion disks. In particular we stress
on the importance of using a consistent upwind reconstruction of the
electro-motive force (EMF) when using the constrained transport (CT) method to
avoid the onset of numerical instabilities. We show that the electro-motive
force (EMF) reconstruction in the classical constrained transport (CT) method
for Godunov schemes drives a numerical instability. The well-studied linear
growth of magneto-rotational instability (MRI) is used as a benchmark for an
inter-code comparison of PLUTO and ZeusMP. We reproduce the analytical results
for linear MRI growth in 3D global MHD simulations and present a robust and
accurate Godunov code which can be used for 3D accretion disk simulations in
curvilinear coordinate systems
Collapse and Fragmentation of Rotating Magnetized Clouds. I. Magnetic Flux - Spin Relation
We discuss evolution of the magnetic flux density and angular velocity in a
molecular cloud core, on the basis of three-dimensional numerical simulations,
in which a rotating magnetized cloud fragments and collapses to form a very
dense optically thick core of > 5 times 10 ^10 cm^-3 . As the density increases
towards the formation of the optically thick core, the magnetic flux density
and angular velocity converge towards a single relationship between the two
quantities. If the core is magnetically dominated its magnetic flux density
approaches 1.5 (n/5 times 10^10 cm^-3)^1/2 mG, while if the core is
rotationally dominated the angular velocity approaches 2.57 times 10^-3, (n/5
times 10^10 cm^-3)^1/2 yr^-1, where n is the density of the gas. We also find
that the ratio of the angular velocity to the magnetic flux density remains
nearly constant until the density exceeds 5 times 10^10 cm^-3. Fragmentation of
the very dense core and emergence of outflows from fragments are shown in the
subsequent paper.Comment: 17 pages, 12 figures, accepted for publication in MNRA
Modeling of Protostellar Clouds and their Observational Properties
A physical model and two-dimensional numerical method for computing the
evolution and spectra of protostellar clouds are described. The physical model
is based on a system of magneto-gasdynamical equations, including ohmic and
ambipolar diffusion, and a scheme for calculating the thermal and ionization
structure of a cloud. The dust and gas temperatures are determined during the
calculations of the thermal structure of the cloud. The results of computing
the dynamical and thermal structure of the cloud are used to model the
radiative transfer in continuum and in molecular lines. We presented the
results for clouds in hydrostatic and thermal equilibrium. The evolution of a
rotating magnetic protostellar cloud starting from a quasi-static state is also
considered. Spectral maps for optically thick lines of linear molecules are
analyzed. We have shown that the influence of the magnetic field and rotation
can lead to a redistribution of angular momentum in the cloud and the formation
of a characteristic rotational velocity structure. As a result, the
distribution of the velocity centroid of the molecular lines can acquire an
hourglass shape. We plan to use the developed program package together with a
model for the chemical evolution to interpret and model observed starless and
protostellar cores.Comment: Accepted to Astronomy Report
The Dune framework: Basic concepts and recent developments
This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state Bastian etal. (2008a, 2008b). This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut cells, grid modifications such as adaptation and moving domains, high order discretizations and node level performance, non-smooth multigrid methods, and multiscale methods. A brief discussion on current and future development directions of the framework concludes the paper
Magnetic Field Amplification in Galaxy Clusters and its Simulation
We review the present theoretical and numerical understanding of magnetic
field amplification in cosmic large-scale structure, on length scales of galaxy
clusters and beyond. Structure formation drives compression and turbulence,
which amplify tiny magnetic seed fields to the microGauss values that are
observed in the intracluster medium. This process is intimately connected to
the properties of turbulence and the microphysics of the intra-cluster medium.
Additional roles are played by merger induced shocks that sweep through the
intra-cluster medium and motions induced by sloshing cool cores. The accurate
simulation of magnetic field amplification in clusters still poses a serious
challenge for simulations of cosmological structure formation. We review the
current literature on cosmological simulations that include magnetic fields and
outline theoretical as well as numerical challenges.Comment: 60 pages, 19 Figure
A fully covariant mean-field dynamo closure for numerical 3+1 resistive GRMHD
The powerful high-energy phenomena typically encountered in astrophysics
invariably involve physical engines, like neutron stars and black hole
accretion disks, characterized by a combination of highly magnetized plasmas,
strong gravitational fields, and relativistic motions. In recent years
numerical schemes for General Relativistic MHD (GRMHD) have been developed to
model the multidimensional dynamics of such systems, including the possibility
of an evolving spacetime. Such schemes have been also extended beyond the ideal
limit including the effects of resistivity, in an attempt to model dissipative
physical processes acting on small scales (sub-grid effects) over the global
dynamics. Along the same lines, magnetic fields could be amplified by the
presence of turbulent dynamo processes, as often invoked to explain the high
values of magnetization required in accretion disks and neutron stars. Here we
present, for the first time, a further extension to include the possibility of
a mean-field dynamo action within the framework of numerical 3+1 (resistive)
GRMHD. A fully covariant dynamo closure is proposed, in analogy with the
classical theory, assuming a simple alpha-effect in the comoving frame. Its
implementation into a finite-difference scheme for GRMHD in dynamical
spacetimes [the X-ECHO code: (Bucciantini and Del Zanna 2011)] is described,
and a set of numerical test is presented and compared with analytical solutions
wherever possible.Comment: 16 pages, 11 figures, accepted for publication in MNRA
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas