On discretizations of axisymmetric systems

Abstract

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.

References in corpus (2)

• On the Stability of the Iterated Crank-Nicholson Method in Numerical Relativity
• Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids

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