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.

Monograph presents the newest results in the numerical modeling and computer simulation of turbulence. Treated in Chapter 1 is one of the complicated types of fully developed shear turbulent flows, namely – the phenomena within the wake (both the close-range and long-range one) behind the moving body, oceanic flows, etc. Apart of the three-dimensionality and unsteadiness, here one takes into account, as well, the medium’s compressibility and the effect of viscosity. All the observations, as a whole, form the basis for the “rational” approach, which is not quite ordinary for the numerical modeling of turbulence. The studies of various kinds of hydrodynamic instabilities (chapters 2 and 3) are of unquestionable interest, especially by three-dimensional calculations extended to large temporal intervals, up to the turbulent stage. Finally, chapter 4 is devoted to an investigation of the problems of turbulence, using the statistical Monte-Carlo method. That approach proved to be highly effective when considering the problems of rarefied gas dynamics. In English