Dynamical Excision Boundaries in Spectral Evolutions of Binary Black Hole Spacetimes

TL;DR

This paper introduces a dynamic boundary management technique for spectral simulations of binary black holes, enabling stable evolution even in extreme configurations by adjusting excision boundaries through a feedback control system.

Contribution

It presents a novel time-dependent mapping and control system to maintain outflow excision boundaries in binary black hole simulations with complex dynamics.

Findings

Effective handling of high spin and mass ratio binaries

Stable evolution through merger phases

Enhanced grid adaptability during extreme distortions

Abstract

Simulations of binary black hole systems using the Spectral Einstein Code (SpEC) are done on a computational domain that excises the regions inside the black holes. It is imperative that the excision boundaries are outflow boundaries with respect to the hyperbolic evolution equations used in the simulation. We employ a time-dependent mapping between the fixed computational frame and the inertial frame through which the black holes move. The time-dependent parameters of the mapping are adjusted throughout the simulation by a feedback control system in order to follow the motion of the black holes, to adjust the shape and size of the excision surfaces so that they remain outflow boundaries, and to prevent large distortions of the grid. We describe in detail the mappings and control systems that we use. We show how these techniques have been essential in the evolution of binary black hole systems with extreme configurations, such as large spin magnitudes and high mass ratios, especially during the merger, when apparent horizons are highly distorted and the computational domain becomes compressed. The techniques introduced here may be useful in other applications of partial differential equations that involve time-dependent mappings.