4,930 research outputs found
Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity
A recent paper by Lucas-Serrano et al. indicates that a high-resolution
central (HRC) scheme is robust enough to yield accurate hydrodynamical
simulations of special relativistic flows in the presence of ultrarelativistic
speeds and strong shock waves. In this paper we apply this scheme in full
general relativity (involving {\it dynamical} spacetimes), and assess its
suitability by performing test simulations for oscillations of rapidly rotating
neutron stars and merger of binary neutron stars. It is demonstrated that this
HRC scheme can yield results as accurate as those by the so-called
high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers.
Furthermore, the adopted HRC scheme has increased computational efficiency as
it avoids the costly solution of Riemann problems and has practical advantages
in the modeling of neutron star spacetimes. Namely, it allows simulations with
stiff equations of state by successfully dealing with very low-density
unphysical atmospheres. These facts not only suggest that such a HRC scheme may
be a desirable tool for hydrodynamical simulations in general relativity, but
also open the possibility to perform accurate magnetohydrodynamical simulations
in curved dynamic spacetimes.Comment: 4 pages, to be published in Phys. Rev. D (brief report
Numerical evolution of matter in dynamical axisymmetric black hole spacetimes. I. Methods and tests
We have developed a numerical code to study the evolution of self-gravitating
matter in dynamic black hole axisymmetric spacetimes in general relativity. The
matter fields are evolved with a high-resolution shock-capturing scheme that
uses the characteristic information of the general relativistic hydrodynamic
equations to build up a linearized Riemann solver. The spacetime is evolved
with an axisymmetric ADM code designed to evolve a wormhole in full general
relativity. We discuss the numerical and algorithmic issues related to the
effective coupling of the hydrodynamical and spacetime pieces of the code, as
well as the numerical methods and gauge conditions we use to evolve such
spacetimes. The code has been put through a series of tests that verify that it
functions correctly. Particularly, we develop and describe a new set of testbed
calculations and techniques designed to handle dynamically sliced,
self-gravitating matter flows on black holes, and subject the code to these
tests. We make some studies of the spherical and axisymmetric accretion onto a
dynamic black hole, the fully dynamical evolution of imploding shells of dust
with a black hole, the evolution of matter in rotating spacetimes, the
gravitational radiation induced by the presence of the matter fields and the
behavior of apparent horizons through the evolution.Comment: 42 pages, 20 figures, submitted to Phys Rev
Turbulence Time Series Data Hole Filling using Karhunen-Loeve and ARIMA methods
Measurements of optical turbulence time series data using unattended
instruments over long time intervals inevitably lead to data drop-outs or
degraded signals. We present a comparison of methods using both Principal
Component Analysis, which is also known as the Karhunen--Loeve decomposition,
and ARIMA that seek to correct for these event-induced and mechanically-induced
signal drop-outs and degradations. We report on the quality of the correction
by examining the Intrinsic Mode Functions generated by Empirical Mode
Decomposition. The data studied are optical turbulence parameter time series
from a commercial long path length optical anemometer/scintillometer, measured
over several hundred metres in outdoor environments.Comment: 8 pages, 9 figures, submitted to ICOLAD 2007, City University,
London, U
Numerical 3+1 general relativistic magnetohydrodynamics: a local characteristic approach
We present a general procedure to solve numerically the general relativistic
magnetohydrodynamics (GRMHD) equations within the framework of the 3+1
formalism. The work reported here extends our previous investigation in general
relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not
considered. The GRMHD equations are written in conservative form to exploit
their hyperbolic character in the solution procedure. All theoretical
ingredients necessary to build up high-resolution shock-capturing schemes based
on the solution of local Riemann problems (i.e. Godunov-type schemes) are
described. In particular, we use a renormalized set of regular eigenvectors of
the flux Jacobians of the relativistic magnetohydrodynamics equations. In
addition, the paper describes a procedure based on the equivalence principle of
general relativity that allows the use of Riemann solvers designed for special
relativistic magnetohydrodynamics in GRMHD. Our formulation and numerical
methodology are assessed by performing various test simulations recently
considered by different authors. These include magnetized shock tubes,
spherical accretion onto a Schwarzschild black hole, equatorial accretion onto
a Kerr black hole, and magnetized thick accretion disks around a black hole
prone to the magnetorotational instability.Comment: 18 pages, 8 figures, submitted to Ap
Nonlinear r-modes in Rapidly Rotating Relativistic Stars
The r-mode instability in rotating relativistic stars has been shown recently
to have important astrophysical implications (including the emission of
detectable gravitational radiation, the explanation of the initial spins of
young neutron stars and the spin-distribution of millisecond pulsars and the
explanation of one type of gamma-ray bursts), provided that r-modes are not
saturated at low amplitudes by nonlinear effects or by dissipative mechanisms.
Here, we present the first study of nonlinear r-modes in isentropic, rapidly
rotating relativistic stars, via 3-D general-relativistic hydrodynamical
evolutions. Our numerical simulations show that (1) on dynamical timescales,
there is no strong nonlinear coupling of r-modes to other modes at amplitudes
of order one -- unless nonlinear saturation occurs on longer timescales, the
maximum r-mode amplitude is of order unity (i.e., the velocity perturbation is
of the same order as the rotational velocity at the equator). An absolute upper
limit on the amplitude (relevant, perhaps, for the most rapidly rotating stars)
is set by causality. (2) r-modes and inertial modes in isentropic stars are
predominantly discrete modes and possible associated continuous parts were not
identified in our simulations. (3) In addition, the kinematical drift
associated with r-modes, recently found by Rezzolla, Lamb and Shapiro (2000),
appears to be present in our simulations, but an unambiguous confirmation
requires more precise initial data. We discuss the implications of our findings
for the detectability of gravitational waves from the r-mode instability.Comment: 4 pages, 4 eps figures, accepted in Physical Review Letter
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