This Volume contains the proceedings of ASTRONUM-2009 — the fourth in a series of international conferences now organized by the Center for Space Plasma and Aeronomic Research at the University of Alabama in Huntsville and the Laboratory for Research into the Fundamental Laws of the Universe at the French Commissariat of Atomic Energy. The subjects of the conference included such topics as turbulence and cosmic ray transport, astrophysical flows, space plasma flows, kinetic and hybrid simulations, numerical methods, algorithms, and frameworks, and data handling and visualization. All of these topics are of great importance for scientists investigating solar structure, the heliosphere, the Sun-Earth connection, and various astrophysical phenomena.

The problems discussed at the conference are characterized by different time and space scales, regions, or particle populations, for which different sets of defning equations or concepts are necessary to understand the physical system in its entirety. This book will be of interest to specialists in applied mathematics, astrophysics, space physics, and computer science working on the application of novel numerical algorithms to contemporary problems arising in these fields. It can also be used by graduate students to get acquainted with the fundamental approaches to solving the fluid dynamic and kinetic equations governing space plasma flows.