1,816 research outputs found
Local characteristic algorithms for relativistic hydrodynamics
Numerical schemes for the general relativistic hydrodynamic equations are
discussed. The use of conservative algorithms based upon the characteristic
structure of those equations, developed during the last decade building on
ideas first applied in Newtonian hydrodynamics, provides a robust methodology
to obtain stable and accurate solutions even in the presence of
discontinuities. The knowledge of the wave structure of the above system is
essential in the construction of the so-called linearized Riemann solvers, a
class of numerical schemes specifically designed to solve nonlinear hyperbolic
systems of conservation laws. In the last part of the review some astrophysical
applications of such schemes, using the coupled system of the
(characteristic) Einstein and hydrodynamic equations, are also briefly
presented.Comment: 20 pages, 4 figures, To appear in the proceedings of the workshop
"The conformal structure of space-time", J. Frauendiener, H. Friedrich, eds,
Springer Lecture Notes in Physic
Compton Scattering in Static and Moving Media. II. System-Frame Solutions for Spherically Symmetric Flows
I study the formation of Comptonization spectra in spherically symmetric,
fast moving media in a flat spacetime. I analyze the mathematical character of
the moments of the transfer equation in the system-frame and describe a
numerical method that provides fast solutions of the time-independent radiative
transfer problem that are accurate in both the diffusion and free-streaming
regimes. I show that even if the flows are mildly relativistic (V~0.1, where V
is the electron bulk velocity in units of the speed of light), terms that are
second-order in V alter the emerging spectrum both quantitatively and
qualitatively. In particular, terms that are second-order in V produce
power-law spectral tails, which are the dominant feature at high energies, and
therefore cannot be neglected. I further show that photons from a static source
are upscattered by the bulk motion of the medium even if the velocity field
does not converge. Finally, I discuss these results in the context of radial
accretion onto and outflows from compact objects.Comment: 28 pages, 9 figures; minor changes, to appear in the Astrophysical
Journa
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