Time Step Size Limitation Introduced by the BSSN Gamma Driver

Abstract

Many mesh refinement simulations currently performed in numerical relativity counteract instabilities near the outer boundary of the simulation domain either by changes to the mesh refinement scheme or by changes to the gauge condition. We point out that the BSSN Gamma Driver gauge condition introduces a time step size limitation in a similar manner as a CFL condition, but which is independent of the spatial resolution. We give a didactic explanation of this issue, show why especially mesh refinement simulations suffer from it, and point to a simple remedy.