36,464 research outputs found
Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity
We describe a numerical code that solves Einstein's equations for a
Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation
introduced by Choquet-Bruhat and York. This is the first time this formulation
has been used to evolve a numerical spacetime containing a black hole. We
excise the hole from the computational grid in order to avoid the central
singularity. We describe in detail a causal differencing method that should
allow one to stably evolve a hyperbolic system of equations in three spatial
dimensions with an arbitrary shift vector, to second-order accuracy in both
space and time. We demonstrate the success of this method in the spherically
symmetric case.Comment: 23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev.
A unified IMEX Runge-Kutta approach for hyperbolic systems with multiscale relaxation
In this paper we consider the development of Implicit-Explicit (IMEX)
Runge-Kutta schemes for hyperbolic systems with multiscale relaxation. In such
systems the scaling depends on an additional parameter which modifies the
nature of the asymptotic behavior which can be either hyperbolic or parabolic.
Because of the multiple scalings, standard IMEX Runge-Kutta methods for
hyperbolic systems with relaxation loose their efficiency and a different
approach should be adopted to guarantee asymptotic preservation in stiff
regimes. We show that the proposed approach is capable to capture the correct
asymptotic limit of the system independently of the scaling used. Several
numerical examples confirm our theoretical analysis
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