A new dissipation term for finite-difference simulations in Relativity

TL;DR

This paper introduces a new numerical dissipation algorithm for finite-difference simulations in Numerical Relativity, enhancing stability and accuracy in 3D black hole simulations by combining centered finite-volume methods with adaptive dissipation.

Contribution

The paper presents a simplified, efficient dissipation algorithm compatible with centered finite-difference methods, improving numerical stability in relativistic simulations.

Findings

Effective in 3D black hole simulations

Combines finite-volume methods with adaptive dissipation

Achieves third-order spatial accuracy

Abstract

We present a new numerical dissipation algorithm, which can be efficiently used in combination with centered finite-difference methods. We start from a formulation of centered finite-volume methods for Numerical Relativity, in which third-order space accuracy can be obtained by employing just piecewise-linear reconstruction. We obtain a simplified version of the algorithm, which can be viewed as a centered finite-difference method plus some 'adaptive dissipation'. The performance of this algorithm is confirmed by numerical results obtained from 3D black hole simulations.