Kiselev Duke. These notes will be a valuable asset for researchers and advanced graduate students in several aspects of mathematicsl fluid mechanics. Score: 4. The goal of the course was not to provide an exhaustive account of fluid mechanics, nor to assess the engineering value of various approxima tion procedures.
The goals were: i to present some of the basic ideas of fluid mechanics in a mathematically attractive manner which does not mean "fully rigorous" ; ii to present the physical back ground and motivation for some constructions which have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems; iil.
The notes are divided into three chapters. The first chapter contains an elementary derivation of the equations; the concept of vorticity is introduced at an early stage. The second chapter contains a discussion of potential flow, vortex motion, and boundary layers.
A construction of boundary layers using vortex sheets and random walks is presented; it is hoped that it helps to clarify the ideas. The third chapter contains an analysis of one-dimensional gas iv flow, from a mildly modern point of view.
Weak solutions, Riemann problems, Glimm's scheme, and combustion waves are discussed. The style is informal and no attempt was made to hide the authors' biases and interests. The author guides readers through mathematical modelling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behaviour of the dynamics of physical flow.
Both students and experts intending to control or predict the behavior of fluid flows by theoretical and computational fluid dynamics will benefit from the combination of all relevant aspects in one handy volume. The book consists of three main parts: - The design of mathematical models of physical fluid flow; - A theoretical treatment of the equations representing the model, as Navier-Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as quantitative insights into the processes of flow events; - The construction and effective use of numerical procedures in order to find quantitative descriptions of concrete physical or technical fluid flow situations.
This is the first text of its kind to merge all these subjects so thoroughly. Elementary Fluid Dynamics Author : D. It has a wide scope, with frequent references to experiments, and numerous exercises illustrating the main ideas. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics.
The book is intended to prepare the reader for more advanced topics of current research interest. Konstantin Pikeckas, K. Fluid Mechanics. Computational Fluid Dynamics with Moving Boundaries. Introduction to the Physics of Fluids and Solids. Mathematics of Classical and Quantum Physics. Mathematics for Physicists. Mathematical Tools for Physics.
Mathematical Theory of Compressible Fluid Flow. Dynamics of Fluids in Porous Media. Microhydrodynamics: Principles and Selected Applications. Fundamentals of Mathematical Physics. Mathematical Modelling Techniques. Mathematics for the Physical Sciences.
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