Modern Solution Methods for Nonlinear Multidimensional Problems Mathematics, Mechanics, Turbulence

Unique monograph which sums up the current results of the world-known school of Academician O.M. Belotserkovskii. Preparing the English translation the author has completely revised the Russian edition of 1994. The new versions and generalizations of computational algorithms which were intensively developed by the method of splitting with respect to physical processes are described. The problems described by the Euler equations (chapter 1), the Naiver-Stokes equations (chapters 2,3), and the Bolzmann equations (chapter 4) as applied to nonlinear problems in computational fluid dynamics, mechanics of a rigid deformable body, plasma physics, rarefied gas dynamics and so on, are considered successively. Chapter 5 deals with a grid-characteristic method which is suitable for solving multidimensional equations of hyperbolic type. Chapter 6, specially for the English edition, gives a detailed description of the concept of the direct numerical simulation of a free developed turbulence with shear. As the author demonstrates in this monograph the questions of “rational” numerical simulation are rather urgent nowadays. This permits us to reduce considerably the demands for computer resources.