Time Step Size Limitation Introduced by the BSSN Gamma Driver

TL;DR

This paper reveals that the BSSN Gamma Driver gauge condition imposes a time step size limitation in numerical relativity simulations, independent of spatial resolution, affecting mesh refinement stability and suggesting a simple fix.

Contribution

It identifies a previously overlooked time step restriction caused by the BSSN Gamma Driver gauge, providing a clear explanation and a straightforward remedy.

Findings

The Gamma Driver gauge introduces a CFL-like time step limit.

Mesh refinement simulations are particularly affected by this limitation.

A simple method to mitigate the issue is proposed.

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.