This book is a guide to a wide spectrum of mathematical models, problems, methods and techniques used in modern fluid dynamics. It contains the derivation of the fundamental equations of fluid flow and presents the formulation of mathematical models and boundary value problems describing a number of flows important in applied research. Particular attention is paid to the investigation of qualitative properties of models and to their numerical solution. In particular, the existence and uniqueness of the solution to incompressible and compressible inviscid as well as viscous flow is studied using the theory of complex functions, integral equations, and partial differential equations, including the concepts of weak and measure-valued solutions. Furthermore, theoretical analyses and practical implementations of basic methods of computational fluid dynamics, i.e., finite difference, finite element, and finite volume methods are presented. The treatment is accompanied by a number of examples of computed flow fields.

The book contains a balance between the derivations of equations and models, the theory of boundary value problems of fluid dynamics and numerical methods. Accompanied by examples, it fills the gap between the engineering literature and highly specialized mathematical monographs in a mathematically precise but accessible way.

Quantities and equations describing the flow

irrotational incompressible flow

models of compressible and rotational inviscid flow

mathematical theory and numerical solution of inviscid flow

problems with trailing conditions

stationary inviscid transonic flow

the Euler quations and nonlinear hyperbolic systems

mathematical theory and numerical solution of viscous flow.

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