Computational techniques for fluid dynamics. Vol. 1: Fundamental and general techniques. Vol. 2: Specific techniques for different flow categories.

*(English)*Zbl 0706.76001
Springer Series in Computational Physics. Berlin etc.: Springer-Verlag. xiv, 409 p./vol.1; xi, 484 p./vol.2; DM 198.00/set (1988).

These are two volumes written by the author specifically useful to research workers and engineers in fluid dynamics. Volume I is devoted to fundamental and general techniques useful in fluid mechanics. Author assumes that the student should have basic knowledge of fluid mechanics and elementary knowledge of numerical analysis. With this background, author discusses in the first chapter some typical problems with both simple and complex geometry and reviews some of the recent literature on this topic. This is a good information collected in one book so that the student can get good information of the development in this field. The second chapter deals with different types of partial differential equations and the field of fluid mechanics where such equations appear. This is the most important chapter one should master before one proceeds to apply the numerical methods, because computer methods depend upon the nature of the partial differential equation governing the flow phenomenon.

In chapter 3, different methods are discussed regarding the conversion of a partial differential equation into finite-difference form, and error analysis. But attention is focused on linear partial differential equations. (As request to the next edition, discretization of systems of nonlinear partial differential equations should also be discussed.)

In chapter 4, author discusses the basic concepts of consistency, stability and convergence of finite-difference schemes. Chapter 5 deals with other methods available to solve partial differential equations viz. i) weighted residual method and its applications, ii) finite volume method and its applications iii) finite element method and its applications. This is a good chapter in the sense that while considering the applications to different partial differential equations, author has provided actual computer programs and the computer results. This helps a beginner to try these programs by himself on his PC, making necessary changes as per the computer model and get the results which can be checked and compared with author’s results. This creates confidence in the mind of a beginner and hence this book will be found most useful to a beginner to learn these techniques.

Now chapter 6 deals with the applications of these methods to linear and nonlinear equations of fluid dynamics. Computer programs are provided along with computer results. Here advantages and disadvantages of different methods are discussed, which is the most important aspect for a beginner.

Chapters 7,8,9 are devoted to the applications of such schemes to one or two dimensional linear differential equations. Computer programs are provided with computer results. It helps a beginner to learn the art of programming and then to check their results on those obtained by the author.

In chapter 10, some nonlinear convection problems are studied with the help of both computer programs and their results. Author is requested to add to this chapter computer problems for coupled nonlinear equations governing convection problems. This is because, many problems are still incomplete in this field especially with irregular surfaces.

Volume II of this book is actually devoted to different types of problems of fluid dynamics. In chapter 11, fundamental equations in Cartesian form are derived. When boundary shapes of the bodies are complicated, equations in curvilinear coordinates are useful to solve such problems. So in chapter 12, author has discussed the discretization methods for such equations. This is most useful for modern fluid mechanics where only flows past complicated shaped bodies are still remaining unsolved.

Grid generation technique is the most important technique of computer science and this is discussed in chapter 13. Advantages of such a procedure are also discussed. Chapter 14 is devoted to compressible inviscid flows. Many computer programs are given. Subsonic, transonic and supersonic flows are studied by finite-difference and finite-volume methods.

Chapter 15 is devoted to study the finite-difference methods for boundary layer flow, and the advantages of different schemes. Both two and three dimensional boundary layers are studied.

The boundary layer approximation is valid in a thin viscous layer near the surface of a body, otherwise the flow has a thick viscous layer and is to be studied with the help of full Navier-Stokes equations, which is very expensive. So reduced forms of Navier-Stokes equations are constructed making computation more economical and giving accurate physical models also. Author has discussed in chapter 16, the derivation of a reduced Navier-Stokes form and solved both internal and external flow problems. Computer programs and their results are given so that it helps a researcher to understand the fundamentals of such a physical phenomenon. Many types of problems are discussed in this chapter.

In chapter 17 and 18, full Navier-Stokes equations, both incompressible and compressible, are solved. All types of difficulties encountered in such computations are discussed.

In general, for an engineer and a research worker in the field of fluid mechanics, these two volumes will serve as good guidance-books.

Lastly, it is to be noted here that other types of problems in fluid mechanics which are important from the practical and design point of view are free convection, mixed convection flows and stability of fluid flows. These have not been included in these two volumes. After the inclusion of these topics, the two volumes can be considered as most useful to fluid mechanics researchers.

The style of explaining different methods is quite satisfactory. These books can be found most useful at both under- and post-graduate level.

In chapter 3, different methods are discussed regarding the conversion of a partial differential equation into finite-difference form, and error analysis. But attention is focused on linear partial differential equations. (As request to the next edition, discretization of systems of nonlinear partial differential equations should also be discussed.)

In chapter 4, author discusses the basic concepts of consistency, stability and convergence of finite-difference schemes. Chapter 5 deals with other methods available to solve partial differential equations viz. i) weighted residual method and its applications, ii) finite volume method and its applications iii) finite element method and its applications. This is a good chapter in the sense that while considering the applications to different partial differential equations, author has provided actual computer programs and the computer results. This helps a beginner to try these programs by himself on his PC, making necessary changes as per the computer model and get the results which can be checked and compared with author’s results. This creates confidence in the mind of a beginner and hence this book will be found most useful to a beginner to learn these techniques.

Now chapter 6 deals with the applications of these methods to linear and nonlinear equations of fluid dynamics. Computer programs are provided along with computer results. Here advantages and disadvantages of different methods are discussed, which is the most important aspect for a beginner.

Chapters 7,8,9 are devoted to the applications of such schemes to one or two dimensional linear differential equations. Computer programs are provided with computer results. It helps a beginner to learn the art of programming and then to check their results on those obtained by the author.

In chapter 10, some nonlinear convection problems are studied with the help of both computer programs and their results. Author is requested to add to this chapter computer problems for coupled nonlinear equations governing convection problems. This is because, many problems are still incomplete in this field especially with irregular surfaces.

Volume II of this book is actually devoted to different types of problems of fluid dynamics. In chapter 11, fundamental equations in Cartesian form are derived. When boundary shapes of the bodies are complicated, equations in curvilinear coordinates are useful to solve such problems. So in chapter 12, author has discussed the discretization methods for such equations. This is most useful for modern fluid mechanics where only flows past complicated shaped bodies are still remaining unsolved.

Grid generation technique is the most important technique of computer science and this is discussed in chapter 13. Advantages of such a procedure are also discussed. Chapter 14 is devoted to compressible inviscid flows. Many computer programs are given. Subsonic, transonic and supersonic flows are studied by finite-difference and finite-volume methods.

Chapter 15 is devoted to study the finite-difference methods for boundary layer flow, and the advantages of different schemes. Both two and three dimensional boundary layers are studied.

The boundary layer approximation is valid in a thin viscous layer near the surface of a body, otherwise the flow has a thick viscous layer and is to be studied with the help of full Navier-Stokes equations, which is very expensive. So reduced forms of Navier-Stokes equations are constructed making computation more economical and giving accurate physical models also. Author has discussed in chapter 16, the derivation of a reduced Navier-Stokes form and solved both internal and external flow problems. Computer programs and their results are given so that it helps a researcher to understand the fundamentals of such a physical phenomenon. Many types of problems are discussed in this chapter.

In chapter 17 and 18, full Navier-Stokes equations, both incompressible and compressible, are solved. All types of difficulties encountered in such computations are discussed.

In general, for an engineer and a research worker in the field of fluid mechanics, these two volumes will serve as good guidance-books.

Lastly, it is to be noted here that other types of problems in fluid mechanics which are important from the practical and design point of view are free convection, mixed convection flows and stability of fluid flows. These have not been included in these two volumes. After the inclusion of these topics, the two volumes can be considered as most useful to fluid mechanics researchers.

The style of explaining different methods is quite satisfactory. These books can be found most useful at both under- and post-graduate level.

Reviewer: V.M.Soundalgekar

##### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76Mxx | Basic methods in fluid mechanics |

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

76-04 | Software, source code, etc. for problems pertaining to fluid mechanics |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |