by Oleg M Belotserkovskii (Russian Academy of Sciences, Russia) & Yury Iv Khlopkov (Russian Academy of Natural Sciences, Russia)

This book is devoted to analysis of Monte Carlo methods developed in rarefied gas dynamics. Presented is the short history of the development of such methods, described are their main properties, their advantages and deficiencies. It is shown that the contemporary stage in the progress of computational methods cannot be regarded without a complex approach to the preparation of algorithms taking into account all the peculiarities of the problem under consideration, that is, of the physical nature of a process, the mathematical model and the theoretical aspects of computational mathematics and stochastic processes. Thoroughly investigated is the possibility of application of Monte Carlo methods in some kindred areas of science which are non-traditional for the use of statistical modeling (continuous media, turbulence). Considered are the possible directions of development of statistical modeling.

• The Main Equations and Approaches to Solution of the Problems in Rarefied Gas Dynamics
• Development of the Numerical Methods of Solution of the Linear Kinetic Equations
• Methods of Solution of the Nonlinear Problems in rarefied Gas Dynamics
• Modeling of the Flows of Continuous Media
• Solution of the Navier–Stokes Equations
• Studies of the Weakly Perturbed Flows of Rarefied Gas
• Study of the Flows about Different Bodies in Transitional Regime
• Determination of the Aerodynamical Characteristics of the Returnable Cosmic Systems (RCS)
• Supersonic Flow about Blunted Bodies with Energy Addition
• The General Models of Description of the Turbulent Flows
• Studies as the Turbulent Flows of Fluid and Gas
• The Possible Directions of Development of the Methods of Statistical Modeling of the Flows of Fluid and Gas