Efficient implementation of finite volume methods in Numerical Relativity

TL;DR

This paper presents a finite volume method with third-order accuracy for Numerical Relativity, demonstrating its effectiveness in black hole simulations and highlighting the importance of conformal decomposition for robustness.

Contribution

It introduces a novel finite volume formulation with adaptive viscosity for Numerical Relativity, validated through black hole simulations and emphasizing conformal decomposition.

Findings

Third-order accuracy achieved with piecewise-linear reconstruction.

The method is validated in 1D black hole simulations.

Conformal decomposition enhances robustness in 3D simulations.

Abstract

Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be interpreted as an 'adaptive viscosity' modification of centered finite difference algorithms. These points are fully confirmed by 1D black-hole simulations. In the 3D case, evidence is found that the use of a conformal decomposition is a key ingredient for the robustness of black hole numerical codes.