1,569 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 Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren & Hauck [29] suggests that the filtered spherical
harmonics method represents an efficient, robust, and accurate method for
radiation transport, at least in the two-dimensional (2D) case. We extend their
work to the three-dimensional (3D) case and find that all of the advantages of
the filtering approach identified in 2D are present also in the 3D case. We
reformulate the filter operation in a way that is independent of the timestep
and of the spatial discretization. We also explore different second- and
fourth-order filters and find that the second-order ones yield significantly
better results. Overall, our findings suggest that the filtered spherical
harmonics approach represents a very promising method for 3D radiation
transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of
Computational Physic
A radiation-hydrodynamics scheme valid from the transport to the diffusion limit
We present in this paper the numerical treatment of the coupling between
hydrodynamics and radiative transfer. The fluid is modeled by classical
conservation laws (mass, momentum and energy) and the radiation by the grey
moment system. The scheme introduced is able to compute accurate
numerical solution over a broad class of regimes from the transport to the
diffusive limits. We propose an asymptotic preserving modification of the HLLE
scheme in order to treat correctly the diffusion limit. Several numerical
results are presented, which show that this approach is robust and have the
correct behavior in both the diffusive and free-streaming limits. In the last
numerical example we test this approach on a complex physical case by
considering the collapse of a gas cloud leading to a proto-stellar structure
which, among other features, exhibits very steep opacity gradients.Comment: 29 pages, submitted to Journal of Computational physic
General relativistic radiation hydrodynamics of accretion flows. I: Bondi-Hoyle accretion
We present a new code for performing general-relativistic
radiation-hydrodynamics simulations of accretion flows onto black holes. The
radiation field is treated in the optically-thick approximation, with the
opacity contributed by Thomson scattering and thermal bremsstrahlung. Our
analysis is concentrated on a detailed numerical investigation of hot
two-dimensional, Bondi-Hoyle accretion flows with various Mach numbers. We find
significant differences with respect to purely hydrodynamical evolutions. In
particular, once the system relaxes to a radiation-pressure dominated regime,
the accretion rates become about two orders of magnitude smaller than in the
purely hydrodynamical case, remaining however super-Eddington as are the
luminosities. Furthermore, when increasing the Mach number of the inflowing
gas, the accretion rates become smaller because of the smaller cross section of
the black hole, but the luminosities increase as a result a stronger emission
in the shocked regions. Overall, our approach provides the first
self-consistent calculation of the Bondi-Hoyle luminosity, most of which is
emitted within r~100 M from the black hole, with typical values L/L_Edd ~ 1-7,
and corresponding energy efficiencies eta_BH ~ 0.09-0.5. The possibility of
computing luminosities self-consistently has also allowed us to compare with
the bremsstrahlung luminosity often used in modelling the electromagnetic
counterparts to supermassive black-hole binaries, to find that in the
optically-thick regime these more crude estimates are about 20 times larger
than our radiation-hydrodynamics results.Comment: With updated bibliographyc informatio
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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
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