Numerical Analysis of a Canonical Shock Wave Interaction Problem in General Relativity
Vol. 11 No. 1 (2016) P.217~P.234
We present the analysis of convergence of the locally inertial Godunov method with
dynamical time dilation applied to a canonical initial data set which is arguably the simplest
initial data that creates a point of shock wave interaction in General Relativity. New
applications include the analysis of convergence in the presence of new boundary conditions
which enables one to test the validity of the Einstein constraint equations numerically in
new Lipschitz continuous space-time metrics. The numerical method, introduced in [14,
15], is an algorithm for simulating general relativistic shock-waves in spherically symmetric
spacetimes, and the analysis here rigorously establishes claims made in authors’ PRSA
General Relativity, Shock Wave Interactions, Numerical Relativity, Godunov Method, Locally Inertial.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 83C10, 76L05, 35L65, 32D20.
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Revised : 2015-09-30