Flux Limiter Methods in 3D Numerical Relativity

TL;DR

This paper introduces a flux limiter method from CFD applied to 3D numerical relativity, significantly enhancing the robustness and stability of Einstein equation simulations involving black hole spacetimes.

Contribution

The paper presents a novel flux limiter technique integrated into 3D numerical relativity to improve stability in simulations with steep gradients.

Findings

Enhanced robustness in black hole spacetime simulations

Increased stability compared to standard methods

Successful application to nonlinear gauge wave propagation

Abstract

New numerical methods have been applied in relativity to obtain a numerical evolution of Einstein equations much more robust and stable. Starting from 3+1 formalism and with the evolution equations written as a FOFCH (first-order flux conservative hyperbolic) system, advanced numerical methods from CFD (Computational Fluid Dynamics) have been successfully applied. A flux limiter mechanism has been implemented in order to deal with steep gradients like the ones usually associated with black hole spacetimes. As a test bed, the method has been applied to 3D metrics describing propagation of nonlinear gauge waves. Results are compared with the ones obtained with standard methods, showing a great increase in both robustness and stability of the numerical algorithm.