Evolving a puncture black hole with fixed mesh refinement

TL;DR

This paper introduces a new algorithm for mesh refinement in numerical relativity, enabling stable, accurate simulations of black hole spacetimes with improved boundary handling and convergence properties.

Contribution

It presents a novel method for mesh refinement interfaces in numerical relativity that maintains second order convergence near black hole punctures.

Findings

Achieved second order convergence near the puncture

Extended outer boundary beyond 100M for better wave extraction

Demonstrated stable evolution of puncture initial data

Abstract

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.