Reducing phase error in long numerical binary black hole evolutions with sixth order finite differencing

TL;DR

This paper introduces a sixth-order finite differencing scheme in a numerical relativity code, significantly improving the accuracy of long binary black hole simulations compared to previous fourth-order methods.

Contribution

The authors modify a moving puncture evolution code by replacing fourth-order differencing with sixth-order stencils, enhancing simulation precision for binary black holes.

Findings

Improved accuracy in long binary black hole evolutions.

Successful implementation of sixth-order differencing in a numerical relativity code.

Simulation covering nine orbits demonstrating the method's effectiveness.

Abstract

We describe a modification of a fourth-order accurate ``moving puncture'' evolution code, where by replacing spatial fourth-order accurate differencing operators in the bulk of the grid by a specific choice of sixth-order accurate stencils we gain significant improvements in accuracy. We illustrate the performance of the modified algorithm with an equal-mass simulation covering nine orbits.