Relativistic Hydrodynamics

AbstractThe book provides a lively and approachable introduction to the main concepts and techniques of relativistic hydrodynamics in a form which will appeal to physicists at advanced undergraduate and postgraduate levels. The book is divided into three parts. The first part deals with the physical aspects of relativistic hydrodynamics, touching on fundamental topics such as kinetic theory, equations of state, mathematical aspects of hyperbolic partial differential equations, linear and nonlinear waves in fluids, reaction fronts, and the treatment of non-ideal fluids. The second part provides an introductory but complete description of those numerical methods currently adopted in the solution of the relativistic-hydrodynamic equations. Starting from traditional finite-difference methods, modern high-resolution shock-capturing methods are discussed with special emphasis on Godunov upwind schemes based on Riemann solvers. High-order schemes are also treated, focusing on essentially non-oscillatory and weighted non-oscillatory methods, Galerkin methods and on modern ADER approaches. Finally, the third part of the book is devoted to applications and considers several physical and astrophysical systems for which relativistic hydrodynamics plays a crucial role. Several non-self-gravitating systems are first studied, including self-similar flows, relativistic blast waves, spherical flows onto a compact object, relativistic accreting disks, relativistic jets and heavy-ion collisions. Self-gravitating systems are also considered, from isolated stars, to more dynamical configurations such as the collapse to a black hole or the dynamics of binary systems. The book is especially recommended to astrophysicists, particle physicists and applied mathematicians.