658 research outputs found
A Godunov Method for Multidimensional Radiation Magnetohydrodynamics based on a variable Eddington tensor
We describe a numerical algorithm to integrate the equations of radiation
magnetohydrodynamics in multidimensions using Godunov methods. This algorithm
solves the radiation moment equations in the mixed frame, without invoking any
diffusion-like approximations. The moment equations are closed using a variable
Eddington tensor whose components are calculated from a formal solution of the
transfer equation at a large number of angles using the method of short
characteristics. We use a comprehensive test suite to verify the algorithm,
including convergence tests of radiation-modified linear acoustic and
magnetosonic waves, the structure of radiation modified shocks, and
two-dimensional tests of photon bubble instability and the ablation of dense
clouds by an intense radiation field. These tests cover a very wide range of
regimes, including both optically thick and thin flows, and ratios of the
radiation to gas pressure of at least 10^{-4} to 10^{4}. Across most of the
parameter space, we find the method is accurate. However, the tests also reveal
there are regimes where the method needs improvement, for example when both the
radiation pressure and absorption opacity are very large. We suggest
modifications to the algorithm that will improve accuracy in this case. We
discuss the advantages of this method over those based on flux-limited
diffusion. In particular, we find the method is not only substantially more
accurate, but often no more expensive than the diffusion approximation for our
intended applications.Comment: 42 pages, 22 figures, 2 tables, accepted by ApJ
New numerical solver for flows at various Mach numbers
Many problems in stellar astrophysics feature flows at low Mach numbers.
Conventional compressible hydrodynamics schemes frequently used in the field
have been developed for the transonic regime and exhibit excessive numerical
dissipation for these flows. While schemes were proposed that solve
hydrodynamics strictly in the low Mach regime and thus restrict their
applicability, we aim at developing a scheme that correctly operates in a wide
range of Mach numbers. Based on an analysis of the asymptotic behavior of the
Euler equations in the low Mach limit we propose a novel scheme that is able to
maintain a low Mach number flow setup while retaining all effects of
compressibility. This is achieved by a suitable modification of the well-known
Roe solver. Numerical tests demonstrate the capability of this new scheme to
reproduce slow flow structures even in moderate numerical resolution. Our
scheme provides a promising approach to a consistent multidimensional
hydrodynamical treatment of astrophysical low Mach number problems such as
convection, instabilities, and mixing in stellar evolution.Comment: 16 pages, 8 figures, accepted for publication by A&
Reminiscences about numerical schemes
This preprint appeared firstly in Russian in 1997. Some truncated versions of this preprint were published in English and French, here a fully translated version is presented. The translation in English was done by O. V. Feodoritova and V. Deledicque to whom I express my gratitude
Numerics and Theory of High-Energy Relativistic Astrophysical Transients:(Alternative Format Thesis)
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Small Collaboration: Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and Their Applications (hybrid meeting)
This small collaborative workshop brought together
experts from the Sino-German project working in the field of advanced numerical methods for
hyperbolic balance laws. These are particularly important for compressible fluid flows and related systems of equations. The investigated numerical methods were finite volume/finite difference, discontinuous Galerkin methods, and kinetic-type schemes. We have discussed challenging open mathematical research problems in this field, such as multidimensional shock waves, interfaces with different phases or efficient and problem suited adaptive algorithms. Consequently, our main objective was to discuss novel high-order accurate schemes that reliably approximate underlying physical models and preserve important physically relevant properties. Theoretical questions concerning the
convergence of numerical methods and proper solution concepts were addressed as well
Thermodynamics of the dead-zone inner edge in protoplanetary disks
In protoplanetary disks, the inner boundary between the turbulent and laminar
regions could be a promising site for planet formation, thanks to the trapping
of solids at the boundary itself or in vortices generated by the Rossby wave
instability. At the interface, the disk thermodynamics and the turbulent
dynamics are entwined because of the importance of turbulent dissipation and
thermal ionization. Numerical models of the boundary, however, have neglected
the thermodynamics, and thus miss a part of the physics. The aim of this paper
is to numerically investigate the interplay between thermodynamics and dynamics
in the inner regions of protoplanetary disks by properly accounting for
turbulent heating and the dependence of the resistivity on the local
temperature. Using the Godunov code RAMSES, we performed a series of 3D global
numerical simulations of protoplanetary disks in the cylindrical limit,
including turbulent heating and a simple prescription for radiative cooling. We
find that waves excited by the turbulence significantly heat the dead zone, and
we subsequently provide a simple theoretical framework for estimating the wave
heating and consequent temperature profile. In addition, our simulations reveal
that the dead-zone inner edge can propagate outward into the dead zone, before
staling at a critical radius that can be estimated from a mean-field model. The
engine driving the propagation is in fact density wave heating close to the
interface. A pressure maximum appears at the interface in all simulations, and
we note the emergence of the Rossby wave instability in simulations with
extended azimuth. Our simulations illustrate the complex interplay between
thermodynamics and turbulent dynamics in the inner regions of protoplanetary
disks. They also reveal how important activity at the dead-zone interface can
be for the dead-zone thermodynamic structure.Comment: 16 pages, 16 figures. Accepted in Astronomy and Astrophysic
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