arXiv subjects

C. Bona

Publications and source records attributed to C. Bona.

22 records · Page 2Linked to original sources

arXiv2002

Flux Limiter Methods in 3D Numerical Relativity

New numerical methods have been applied in relativity to obtain a numerical evolution of Einstein equations much more robust and stable. Starting from 3+1 formalism and with the evolution equations written as a FOFCH (first-order flux conservative hyperbolic) system, advanced numerical methods from CFD (Computational Fluid Dynamics) have been successfully applied. A flux limiter mechanism has been implemented in order to deal with steep gradients like the ones usually associated with black hole spacetimes. As a test bed, the method has been applied to 3D metrics describing propagation of nonlinear gauge waves. Results are compared with the ones obtained with standard methods, showing a great increase in both robustness and stability of the numerical algorithm.

gr-qc↗

arXiv1999

Robust evolution system for Numerical Relativity

The paper combines theoretical and applied ideas which have been previously considered separately into a single set of evolution equations for Numerical Relativity. New numerical ingredients are presented which avoid gauge pathologies and allow one to perform robust 3D calculations. The potential of the resulting numerical code is demonstrated by using the Schwarzschild black hole as a test-bed. Its evolution can be followed up to times greater than one hundred black hole masses.

gr-qc↗

arXiv1998

Dealing with the center and boundary problems in 1D Numerical Relativity

Instabilities in finite difference codes due to the singularity of spherical coordinates at the center are studied. In typical Numerical Relativity applications, standard regularization techniques by themselves do not ensure long term stability. A proposal to remedy that problem is presented, which takes advantage of redundant quantities introduced in recent hyperbolic formulations of Einstein's evolution equations. The results are discussed through the example case of a boson star, where a significant improvement in the implementation of boundary conditions is also presented.

gr-qc↗

arXiv1998

Stuffed Black Holes

Initial data corresponding to spacetimes containing black holes are considered in the time symmetric case. The solutions are obtained by matching across the apparent horizon different, conformally flat, spatial metrics. The exterior metric is the vacuum solution obtained by the well known conformal imaging method. The interior metric for every black hole is regular everywhere and corresponds to a positive energy density. The resulting matched solutions cover then the whole initial (Cauchy) hypersurface, without any singularity, and can be useful for numerical applications. The simpler cases of one black hole (Schwarzschild data) or two identical black holes (Misner data) are explicitly solved. A procedure for extending this construction to the multiple black hole case is also given, and it is shown to work for all time symmetric vacuum solutions obtained by the conformal imaging method. The numerical evolution of one such 'stuffed' black hole is compared with that of a pure vacuum or 'plain' black hole in the spherically symmetric case.

gr-qc↗