Flux-Vector-Splitting (FVS) method for Z4 formalism and its numerical analysis

TL;DR

This paper develops and analyzes a Flux-Vector-Splitting (FVS) numerical method tailored for the Z4 formalism in general relativity, comparing its performance with other schemes through black hole simulations.

Contribution

It introduces the first first-order FVS method for Z4 formalism and evaluates its effectiveness in black hole evolution simulations.

Findings

FVS method successfully applied to Z4 formalism.

Numerical solutions depend on the choice of scheme.

FVS shows comparable or improved accuracy over Lax Friedrichs methods.

Abstract

The previously developed Flux-Vector-Splitting (FVS) method was formulated here for the first-order version of Z4 formalism. Then, the characteristics of this method formulated for Z4 formalism were studied by numerically analyzing the evolution of two types of black holes (free and stuffed). Finally, these numerical results from the FVS method were compared with those from the Local Lax Friedrichs and Modified Local Lax Friedrichs methods to reveal the dependency of numerical solution by Z4 formalism on the choice of numerical scheme.