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**Computational fluid mechanics and heat transfer.**
*(English)*
Zbl 0569.76001

Series in computational methods in mechanics and thermal sciences. Washington - New York - London: Hemisphere Publishing Corporation; New York etc.: McGraw-Hill Book Company. XII, 599 p. $ 39.95 (1984).

This is one of the good books written by a team of experienced research workers who are themselves experts in different branches of computational fluid mechanics. There is an urgent need of such a book for students of engineering and science since it is very difficult for a student to search for all these articles which appeared in different journals.

In chapter 1, an introduction to the broad subject of numerical analysis is presented in a very interesting manner. The most important paper by Courant, Friedrichs and Lewy is cited as the beginning of modern numerical analysis. Then the authors give the most important names of books and papers published on this topic in chronological order. A beginner gets a good idea of the literature on numerical analysis.

In chapter 2, the authors discuss in short the mathematical aspect of partial differential equations. - In chapter 3, fundamentals of finite- difference methods are discussed. The concepts of stability, convergence, well-posed problems are clearly discussed. This is the most important step which every student or research worker must study thoroughly from this book. For establishing stability of the finite-difference scheme, different methods are discussed in this chapter. - Then in chapter 4, the authors have presented different types of finite-difference schemes in case of some standard partial differential equations. Both advantages and disadvantages of different schemes are brought out. Then the methods of solving the system of algebraic equations and their advantages and disadvantages are discussed. This is a good topic in this book which is presented at length and will help the student or research worker to get a good grasp of the finite-difference methods.

In chapter 5, all the differential equations of fluid-mechanics for laminar and turbulent flows are given. Different models for turbulent flows are also presented. - In chapters 6 and 7, these methods are applied for solving differential equations for inviscid and viscous flows. In viscous flow theory, the boundary layer equations for flat horizontal bodies in 2 and 3 dimensions are solved by finite-difference equations. The discussion for solving these problems is very good.

The most important part of the book is chapter 8 where the material presented is quite new in the sense that these topics do not appear in any standard book on fluid-mechanics. Boundary layer flow, in the presence of shock waves, near a corner or thin layer flow in which boundary layer concept fails completely, are solved most systematically giving all the details. A number of physical situations in fluid mechanics can be discussed by these methods in future. The authors are to be congratulated for presenting a consolidated account of these topics.

In chapter 9, equations governing the compressible flows are solved by finite-difference methods. - In solving problems in fluid mechanics, geometry of the shape of the body is very important and the grid-system must be applicable to all types of shapes. So transformations for different types of grids are discussed in chapter 10. This is very important when the geometrical shape of the body is complicated.

In general, the reviewer feels that this book should be recommended to all undergraduate and post-graduate courses in fluid mechanics. But some topics which need introduction in present day technology as free convective flows, mixed convective flows (both steady and unsteady flows) stability of flows etc. are not included. Finite-difference methods applied to these problems are found most powerful methods in present day research. I am sure, the authors will add a few more chapters on these topics in their next edition. Then definitely, the book will be an ideal text-book in engineering fields.

In chapter 1, an introduction to the broad subject of numerical analysis is presented in a very interesting manner. The most important paper by Courant, Friedrichs and Lewy is cited as the beginning of modern numerical analysis. Then the authors give the most important names of books and papers published on this topic in chronological order. A beginner gets a good idea of the literature on numerical analysis.

In chapter 2, the authors discuss in short the mathematical aspect of partial differential equations. - In chapter 3, fundamentals of finite- difference methods are discussed. The concepts of stability, convergence, well-posed problems are clearly discussed. This is the most important step which every student or research worker must study thoroughly from this book. For establishing stability of the finite-difference scheme, different methods are discussed in this chapter. - Then in chapter 4, the authors have presented different types of finite-difference schemes in case of some standard partial differential equations. Both advantages and disadvantages of different schemes are brought out. Then the methods of solving the system of algebraic equations and their advantages and disadvantages are discussed. This is a good topic in this book which is presented at length and will help the student or research worker to get a good grasp of the finite-difference methods.

In chapter 5, all the differential equations of fluid-mechanics for laminar and turbulent flows are given. Different models for turbulent flows are also presented. - In chapters 6 and 7, these methods are applied for solving differential equations for inviscid and viscous flows. In viscous flow theory, the boundary layer equations for flat horizontal bodies in 2 and 3 dimensions are solved by finite-difference equations. The discussion for solving these problems is very good.

The most important part of the book is chapter 8 where the material presented is quite new in the sense that these topics do not appear in any standard book on fluid-mechanics. Boundary layer flow, in the presence of shock waves, near a corner or thin layer flow in which boundary layer concept fails completely, are solved most systematically giving all the details. A number of physical situations in fluid mechanics can be discussed by these methods in future. The authors are to be congratulated for presenting a consolidated account of these topics.

In chapter 9, equations governing the compressible flows are solved by finite-difference methods. - In solving problems in fluid mechanics, geometry of the shape of the body is very important and the grid-system must be applicable to all types of shapes. So transformations for different types of grids are discussed in chapter 10. This is very important when the geometrical shape of the body is complicated.

In general, the reviewer feels that this book should be recommended to all undergraduate and post-graduate courses in fluid mechanics. But some topics which need introduction in present day technology as free convective flows, mixed convective flows (both steady and unsteady flows) stability of flows etc. are not included. Finite-difference methods applied to these problems are found most powerful methods in present day research. I am sure, the authors will add a few more chapters on these topics in their next edition. Then definitely, the book will be an ideal text-book in engineering fields.

Reviewer: V.M.Soundalgekar

### MSC:

76-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics |

76M99 | Basic methods in fluid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |