This volume is dedicated to modeling in fluid mechanics and is divided into four chapters, which contain a significant number of useful exercises with solutions. The authors provide relatively complete references on relevant topics in the bibliography at the end of each chapter.

The book is devoted to calculation methods of a converging-diverging nozzle used in propulsion and the high velocity flow. The algorithms and programs given in the book are intended to help engineers and students to design and calculate the nozzle parameters to provide optimal parameters for compressible supersonic flows. The present monograph is a tutorial (handbook) to calculate and determine the optimal parameters for converging-diverging nozzles provided supersonic flow. The main program consists from three main parts: programs for calculation the profile of the Contraction zone, EOD code for the flow in the Contraction zone, the program Rott-Crabtree for calculation the pressure gradient Pohlhausen parameter, the program for the aerodynamic design of axisymmetric and two-dimensional nozzles for supersonic and hypersonic wind tunnels, programs for solving laminar, transitional, or turbulent compressible boundary layer equations for two-dimensional and axisymmetric flow, and the program to obtain hypersonic boundary layer stability. The book is designed to be an instrument for students and scientists interested in study supersonic flow and high-temperature gas dynamics.

Nonlinear phenomena and instabilities arise in all fields of physics, chemistry, biology, and engineering. The book consists of six chapters. Chapter 1 contains preliminary topics from analysis: elements of set theory, measure theory, integration theory, asymptotic expansions, continued fractions and Pad'e approximations. Chapters 2 and 3 are devoted to basic and advanced methods of ODE's and their visualization: attractors, fractals, bifurcations, chaos, and elements of stability theory. Chapter 4 studies analytical and geometrical aspects of perturbation theory and contains many examples. Chapter 5 represents the basic knowledge in turbulence theory and introduces to Richardson-Kolmogorov concept, deals with bifurcations in Kuramoto-Sivashinsky equation, and develops multifractal and hierarchical (shell) models of turbulence. The main hydrodynamic instabilities (Rayleigh-Taylor, Kelvin-Helmholtz, and Richtmyer-Meshkov) are studied in Chapter 6. The book contains theoretical and practical materials, examples and exercises and can be recommended to students and specialists of mathematics and physics, chemistry, biology and engineering.