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arXiv · 1703.10241

A novel scheme for simulating the force-free equations: boundary conditions and the evolution of solutions towards stationarity

Federico Carrasco·Oscar Reula
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Abstract

Force-Free Electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arises on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In this article, we present a full 3D numerical implementation of the FFE evolution around a Kerr black hole. The novelty of our approach is three-folded: i) We use the "multi-block" technique to represent a domain with $S^2 \times \mathbb{R}^{+}$ topology within a stable finite-differences scheme. ii) We employ as evolution equations those arising from a covariant hyperbolization of the FFE system. iii) We implement stable and constraint-preserving boundary conditions to represent an outer region given by a uniform magnetic field aligned or misaligned respect to the symmetry axis. We find stationary jet solutions which reach equilibrium --through boundary conditions-- with the outer numerical surface. This is so, even when the outer boundary is located very close to the central region (i.e. $r_{out}\sim 10M $). These numerical solutions reproduce most of the known results for analogue astrophysical settings.

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Federico Carrasco, Oscar Reula. 2017-03-29. A novel scheme for simulating the force-free equations: boundary conditions and the evolution of solutions towards stationarity. https://doi.org/10.1103/physrevd.96.063006

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