On discretizations of axisymmetric systems

Details On discretizations of axisymmetric systems On discretizations of axisymmetric systems

2002-07-24

arxiv.org/abs/gr-qc/0207092v1

Phys.Rev. D66 (2002) 104027

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1103/PhysRevD.66.104027

In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so called cartoon method which was proposed by Alcubierre, Brandt et.al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.

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