Numerical Magnetohydrodynamics in Astrophysics

Abstract

Newtonian magnetohydrodynamics (MHD) is a very special limit of Maxwell's equations and plasma dynamics. In the last 10 years, powerful numerical algorithms and computational methods have been developed for simulating thetime-evolution of magnetic field configurations in the astrophysical environment. The most recent trends go in the direction of fully conservative schemes and adaptive mesh refinement for large-scale supercoinputing. The most popular codes in use in astrophysics are briefly discussed, together with their strengths and pitfalls. Progress in understanding fundamental MHD processes have been achieved in the field of flux tube dynamics, magnetic turbulence in accretion and galactic disks, magnetic Herbig- Haro flows from young stellar objects and the evolution of primordial magnetic fields in galaxy clusters. The true relativistic magnetohydrodynamics includes various terms which are completely neglected in the classical MHD. Some progress has been achieved in the last few years in the numerical modelling of special relativistic MHD (SRMHD), with main applications to the simulation of the propagation of relativistic extragalactic jets. While this field of research is presently under a high dynamical pressure, the development of codes for General Relativistic MHD (GRMHD) is still in its infancy phase. The main application for such schemes is for understanding the extraction of rotational energy of rapidly rotating compact objects, such as neutron stars and Black Holes. In particular; the extraction of rotational energy from Black Holes in microquasars, quasars and radio galaxies and their transformation into collimated jet outflows is one of the main unsolved problem in modern astrophysics.