60 research outputs found
Towards a gauge-polyvalent Numerical Relativity code
The gauge polyvalence of a new numerical code is tested, both in
harmonic-coordinate simulations (gauge-waves testbed) and in
singularity-avoiding coordinates (simple Black-Hole simulations, either with or
without shift). The code is built upon an adjusted first-order
flux-conservative version of the Z4 formalism and a recently proposed family of
robust finite-difference high-resolution algorithms. An outstanding result is
the long-term evolution (up to 1000M) of a Black-Hole in normal coordinates
(zero shift) without excision.Comment: to appear in Physical Review
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a
test-bed for constraint-preserving boundary conditions in the non-linear
regime. As an illustration, energy-constraint preservation is separately tested
in the Z4 framework. Both algebraic conditions, derived from energy estimates,
and derivative conditions, deduced from the constraint-propagation system, are
considered. The numerical errors at the boundary are of the same order than
those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting
200
Efficient implementation of finite volume methods in Numerical Relativity
Centered finite volume methods are considered in the context of Numerical
Relativity. A specific formulation is presented, in which third-order space
accuracy is reached by using a piecewise-linear reconstruction. This
formulation can be interpreted as an 'adaptive viscosity' modification of
centered finite difference algorithms. These points are fully confirmed by 1D
black-hole simulations. In the 3D case, evidence is found that the use of a
conformal decomposition is a key ingredient for the robustness of black hole
numerical codes.Comment: Revised version, 10 pages, 6 figures. To appear in Phys. Rev.
Conformal and covariant formulation of the Z4 system with constraint-violation damping
We present a new formulation of the Einstein equations based on a conformal
and traceless decomposition of the covariant form of the Z4 system. This
formulation combines the advantages of a conformal decomposition, such as the
one used in the BSSNOK formulation (i.e. well-tested hyperbolic gauges, no need
for excision, robustness to imperfect boundary conditions) with the advantages
of a constraint-damped formulation, such as the generalized harmonic one (i.e.
exponential decay of constraint violations when these are produced). We
validate the new set of equations through standard tests and by evolving binary
black hole systems. Overall, the new conformal formulation leads to a better
behavior of the constraint equations and a rapid suppression of the violations
when they occur. The changes necessary to implement the new conformal
formulation in standard BSSNOK codes are very small as are the additional
computational costs.Comment: 12 pages, 7 figures. Version matching the one in press on PR
New Formalism for Numerical Relativity
We present a new formulation of the Einstein equations that casts them in an
explicitly first order, flux-conservative, hyperbolic form. We show that this
now can be done for a wide class of time slicing conditions, including maximal
slicing, making it potentially very useful for numerical relativity. This
development permits the application to the Einstein equations of advanced
numerical methods developed to solve the fluid dynamic equations, {\em without}
overly restricting the time slicing, for the first time. The full set of
characteristic fields and speeds is explicitly given.Comment: uucompresed PS file. 4 pages including 1 figure. Revised version adds
a figure showing a comparison between the standard ADM approach and the new
formulation. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ Appeared
in Physical Review Letters 75, 600 (1995
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