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We present a new numerical method of special relativistic resistive magnetohydrodynamics with scalar resistivity that can treat a range of phenomena, from non-relativistic to relativistic (shock, contact discontinuity, and Alfvén wave). The present scheme calculates the numerical flux of fluid by using an approximate Riemann solver and electromagnetic field by using the method of characteristics. Since this scheme uses appropriate characteristic velocities, it is capable of accurately solving problems that cannot be approximated as ideal magnetohydrodynamics and whose characteristic velocity is much lower than the velocity of light. The numerical results show that our scheme can solve the above problems as well as nearly ideal MHD problems. Our new scheme is particularly well suited to systems with initially weak magnetic field and mixed phenomena of relativistic and non-relativistic velocity, for example magnetorotational instability in an accretion disk and super Alfvénic turbulence. [ABSTRACT FROM AUTHOR]

In this paper we propose a new mechanism describing the initial spike of giant flares in the framework of the starquake model. We investigate the evolution of a plasma on a closed magnetic flux tube in the magnetosphere of a magnetar in the case of a sudden energy release, and discuss the relationship with observations of giant flares. We perform one-dimensional, numerical simulations of the relativistic magnetohydrodynamics in Schwarzschild geometry. We assume energy is injected at the footpoints of the loop by a hot star surface containing random perturbations of the transverse velocity. Alfvén waves are generated and propagate upward, accompanying very hot plasma which is also continuously heated by nonlinearly generated compressive waves. We find that the front edges of the fireball regions collide at the top of the tube with their symmetrically launched counterparts. This collision results in an energy release that can describe the light curve of the initial spikes of giant flares. [ABSTRACT FROM AUTHOR]

In this paper, we report on turbulent acceleration of the dissipation of the magnetic field in the post-shock region of a Poynting flux-dominated flow, such as the Crab pulsar wind nebula. We have performed two-dimensional resistive relativistic magnetohydrodynamics simulations of subsonic turbulence driven by the Richtmyer-Meshkov instability at the shock fronts of the Poynting flux-dominated flows in pulsar winds. We find that turbulence stretches current sheets which substantially enhances the dissipation of the magnetic field, and that most of the initial magnetic field energy is dissipated within a few eddy-turnover times. We also develop a simple analytical model for turbulent dissipation of the magnetic field that agrees well with our simulations. The analytical model indicates that the dissipation rate does not depend on resistivity even in the small resistivity limit. Our findings can possibly alleviate the σ-problem in the Crab pulsar wind nebulae. [ABSTRACT FROM AUTHOR]