Computational General Relativistic Force-Free Electrodynamics: II. Characterization of Numerical Diffusivity

Abstract

Scientific codes are an indispensable link between theory and experiment; in (astro-)plasma physics, such numerical tools are one window into the universe's most extreme flows of energy. The discretization of Maxwell's equations - needed to make highly magnetized (astro)physical plasma amenable to its numerical modeling - introduces numerical diffusion. It acts as a source of dissipation independent of the system's physical constituents. Understanding the numerical diffusion of scientific codes is the key to classify their reliability. It gives specific limits in which the results of numerical experiments are physical. We aim at quantifying and characterizing the numerical diffusion properties of our recently developed numerical tool for the simulation of general relativistic force-free electrodynamics, by calibrating and comparing it with other strategies found in the literature. Our code correctly models smooth waves of highly magnetized plasma. We evaluate the limits of general relativistic force-free electrodynamics in the context of current sheets and tearing mode instabilities. We identify that the current parallel to the magnetic field (${\mathbf{j}}_{\parallel }$), in combination with the break-down of general relativistic force-free electrodynamics across current sheets, impairs the physical modeling of resistive instabilities. We find that at least eight numerical cells per characteristic size of interest (e.g. the wavelength in plasma waves or the transverse width of a current sheet) are needed to find consistency between resistivity of numerical and of physical origins. High-order discretization of the force-free current allows us to provide almost ideal orders of convergence for (smooth) plasma wave dynamics. The physical modeling of resistive layers requires suitable current prescriptions or a sub-grid modeling for the evolution of ${\mathbf{j}}_{\parallel }$.

arXiv comment15 pages, 9 figures, Accepted by A&A

References in corpus (21)

• Electrodynamics of black hole magnetospheres
• Explosive reconnection in magnetars
• Resistive Solutions for Pulsar Magnetospheres
• Beyond ideal MHD: towards a more realistic modeling of relativistic astrophysical plasmas
• First-Principles Plasma Simulations of Black-Hole Jet Launching
• Plasmoid formation in global GRMHD simulations and AGN flares
• Accurate Simulations of Binary Black-Hole Mergers in Force-Free Electrodynamics
• Black-hole jets without large-scale net magnetic flux
• Tearing instability in relativistic magnetically dominated plasmas
• Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
• Triggering magnetar outbursts in 3D force-free simulations
• Simulations of the magnetospheres of accreting millisecond pulsars
• Dissipation of Alfvén Waves in Relativistic Magnetospheres of Magnetars
• Particle acceleration in explosive relativistic reconnection events and Crab Nebula gamma-ray flares
• Particle acceleration in explosive relativistic reconnection events and Crab Nebula gamma-ray flares
• Striped Blandford/Znajek jets from advection of small scale magnetic field
• A High-Order WENO-based Staggered Godunov-type Scheme with Constrained Transport for Force-free Electrodynamics
• 3+1 Magnetodynamics
• An HLLC Riemann Solver for Resistive Relativistic Magnetohydrodynamics
• Instability of twisted magnetar magnetospheres
• Force Free Waves and Black Hole Magnetospheric Causality

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