Applied gas dynamics. Numerical methods for solving hyperbolic systems of equations. Tutorial

The manual is devoted to modern high -precision methods of computing gas -dynamics used in solving complex tasks of modeling currents that occur in various fields of science and engineering applications. The book gives a description of mathematical models of hydro- and gas-dynamics, the general properties of hyperbolic equations and systems associated with these models are considered, as well as methods of their numerical solution. The main attention is paid to the methods of approximation of Euler"s equations, which are a basic model for describing the fluid and gas currents.
Unlike classic textbooks, in this book the emphasis is placed precisely on modern numerical methods that have been developed and gained widely (such as Weno and DG methods) In detail, methods of approximation of the solution of the problem of Riman, which underlies these numerical methods, are examined in detail.
These methods have high accuracy and can be used for calculations of geometrically complex areas on unstructured nets.
This book can be used as a textbook for students of senior courses studying in the areas of training “Mechanics and mathematical modeling”, “Applied mathematics”, “Applied mathematics and computer science”, “Applied mechanics”, as well as graduate students, specializing in applied mathematics and computing gas -dynamics. It can also be used as a reference for engineers and scientists working in these and related fields