This volume contains the lecture notes of the Third JETSET School on Jets from Young Stars focussing on Numerical MHD and Instabilities. The introductory lectures presented here cover the basic concepts of the numerical methods for the integration of hydrodynamic and magnetohydrodynamic equations and of the applications of these methods to the treatment of the instabilities relevant for the physics of stellar jets. The first part of the book contains an introduction to the finite difference and finite volume methods for computing the solutions of hyperbolic partial differential equations and a discussion of approximate Riemann solvers for both hydrodynamic and magnetohydrodynamic problems. The second part is devoted to the discussion of some of the main instability processes that may take place in stellar jets, namely: the Kelvin-Helmholtz, the radiative shock, the pressure driven and the thermal instabilities. Graduate students and young scientists will benefit from this book by learning how to use the fundamental tools used in computational astrophysical jet research.

Klappentext

The study of the mechanisms that govern origin and propagation of stellar jets involves the treatment of many concurrent physical processes such as gravitation, hydrodynamics and magnetohydrodynamics, atomic physics and radiation. In the past years, an intensive work has been done looking for so- tions of the ideal MHD equations in the steady state limit as well as studying the stability of out?ows in the linear regime. These kind, of approaches have provided a contribution to the understanding of jets that can hardly be ov- estimated. However, the extension of the analyses to the time-dependent and nonlinear regimes could not be avoided, and the MHD numerical simulations were the only mean to achieve this goal. Intherecentyears,considerableprogresseshavebeenmadebythecom- tational?uiddynamiccommunityinthedevelopmentofnumericaltechniques, theso-calledhighresolutionshockcapturingschemes,wellsuitedforthetre- ment of supersonic ?ows with discontinuities. The numerical simulations of astrophysical jets took advantage of these developments; however new physics needed to be incorporated, such as magnetic ?eld e?ects, radiation losses by diluted gases, and proper astrophysics environments. These needs led to the nontrivial extension of the methods devised for the Euler equations of g- dynamics to the magneto-hydrodynamical system. On the other hand, the possibility of carrying out numerical calculations has been greatly facilitated bytheavailability, ononehand,ofpowerfulsupercomputersand,ontheother hand, of fast processors at low cost. Large scale 3D simulations of jets at high resolution are now possible thanks to supercomputers, but also high reso- tion 2D MHD simulations can be performed routinely on desktop computers.

Inhalt

Numerical Methods.- Computational Methods for Hyperbolic Equations.- Shock-Capturing Schemes in Computational MHD.- Hydrodynamic and Magneto-Hydrodynamic Instabilities.- The Kelvin-Helmholtz Instability.- Pressure-Driven Instabilities in Astrophysical Jets.- Thermal Instabilities.- The Oscillatory Instability of Radiative Shock Waves.