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Computational fluid dynamics
286
Book reviews
C. BLANC. Equations aux d&ivkes partielles. Un cows pour in&nieuts. 136 p. (Intemat. Ser. of Numer. Math. Vol. 34), Birkhiiuser, Stuttgart, 1976. This is a textbook on the partial differential equations of mathematical physics. Attention is concentrated on the formulation of problems and methods of solving them, delicate and lengthy theorems on the existence of solutions are omitted. The features of partial differential equations are demonstrated by examples of the solution of some actual problems of mathematical physics (for example, of the theory of elasticity). Variational and numerical methods (for example, the method of finite elements) are also discussed. Chapter headings: 1. Some problems concerning differential equations; 2. The Laplace and Poisson equations; 3. The equations of plane elasticity theory; 4. Some partial differential equations for evolution problems; 5. Problems of the theory of oscillations; 6. Continuous perturbed systems. M. K. Kerimov
P. J. ROACHE. Cbmputationalj7uid dynamics. vii+446 p. Hermosa Publs., Albuquerque, 1976. This monograph is devoted to the numerical integration of the equations of the unsteady motion of viscous incompressible and compressible fluids. Considering this problem, the author expounds the fundamental methods for the numerical solution of the partial differential equations. Here the hydrodynamic, and not the purely mathematical approach, is used. Particular attention is paid to heuristic justifications and to the results of numerical experiments. The technical aspect of the derivation and interpretation of the numerical solution of problems of the mechanics of a liquid and gas is extensively illuminated. The book consists of seven chapters, differing greatly in length. In Ch. 1 the subject of numerical hydrodynamics and its actual position at the junction of numerical mathematics and theoretical hydromechanics is discussed. A short historical survey of the development of this department of science is given. A considerable part of the book is occupied by Ch. 3, where a description is given of various numerical methods for integrating these equations in the two-dimensional case - the parabolic equation for vortex transport with initial conditions and Poisson’s equation for the stream function with boundary conditions. The numerical realization of boundary conditions of a different kind on the boundaries of the flow region is analyzed in detail, and their extreme importance is emphasized. Questions of the stability and convergence of the numerical solutions are discussed, and the types of errors due to the use of difference schemes are also investigated. The calculation of the pressure and temperature fields for the solution obtained for the vortex and stream function are explained separately. The equations of motion of a viscous fluid in physical variables, including the threedimensional case are also considered. The subject of Chaps. 4 and 5 is the numerical integration of the Navier-Stokes equations for a compressible gas. Various methods of the computation of unsteady flows with shock waves are presented. The principal position is allotted to methods of solution on Eulerlan meshes, enabling a through calculation to be made without the isolation of shock waves, due to the presence in the scheme of explicit or implicit (scheme) artificial viscosity. In the analysis of the computational boundary conditions aspects characteristic of compressible fluid flow are stressed.
287
Book reviews
The use of special computing meshes and coordinate transformations is discussed in Ch. 6. Ch. 7 contains practical advice on the construction and debugging of programs, on the checking of computational algorithms and the processing of the information obtained, in particular, on the computer plotting of graphs. The book is provided with an extremely extensive bibliography on computational hydrodynamics, but unfortunately the list of references ends in 1972 and includes an insufficient number of the papers by soviet authors. The main text and the special section contain many training exercises and problems. Using extensive and interesting material on topical questions of numerical hydrodynamics, the author presents it in accessible form. A special merit of the monograph is the fact that it presents a comparative analysis of various methods, gives recommendations on their practical use, and generalizes the accumulated experience of many workers in computational hydromechanics. Drawbacks are some superficiality in the treatment in individual places and numerous misprints. The book is of considerable interest to scientists and engineers conducting research in both fluid mechanics and computational mathematics. It can also be used as a textbook for postgraduates and students. At the present time a Russian translation of it is being published by “Mif’. P. I. Chushkin Translated by J. Berry.
Book reviews
C. BLANC. Equations aux d&ivkes partielles. Un cows pour in&nieuts. 136 p. (Intemat. Ser. of Numer. Math. Vol. 34), Birkhiiuser, Stuttgart, 1976. This is a textbook on the partial differential equations of mathematical physics. Attention is concentrated on the formulation of problems and methods of solving them, delicate and lengthy theorems on the existence of solutions are omitted. The features of partial differential equations are demonstrated by examples of the solution of some actual problems of mathematical physics (for example, of the theory of elasticity). Variational and numerical methods (for example, the method of finite elements) are also discussed. Chapter headings: 1. Some problems concerning differential equations; 2. The Laplace and Poisson equations; 3. The equations of plane elasticity theory; 4. Some partial differential equations for evolution problems; 5. Problems of the theory of oscillations; 6. Continuous perturbed systems. M. K. Kerimov
P. J. ROACHE. Cbmputationalj7uid dynamics. vii+446 p. Hermosa Publs., Albuquerque, 1976. This monograph is devoted to the numerical integration of the equations of the unsteady motion of viscous incompressible and compressible fluids. Considering this problem, the author expounds the fundamental methods for the numerical solution of the partial differential equations. Here the hydrodynamic, and not the purely mathematical approach, is used. Particular attention is paid to heuristic justifications and to the results of numerical experiments. The technical aspect of the derivation and interpretation of the numerical solution of problems of the mechanics of a liquid and gas is extensively illuminated. The book consists of seven chapters, differing greatly in length. In Ch. 1 the subject of numerical hydrodynamics and its actual position at the junction of numerical mathematics and theoretical hydromechanics is discussed. A short historical survey of the development of this department of science is given. A considerable part of the book is occupied by Ch. 3, where a description is given of various numerical methods for integrating these equations in the two-dimensional case - the parabolic equation for vortex transport with initial conditions and Poisson’s equation for the stream function with boundary conditions. The numerical realization of boundary conditions of a different kind on the boundaries of the flow region is analyzed in detail, and their extreme importance is emphasized. Questions of the stability and convergence of the numerical solutions are discussed, and the types of errors due to the use of difference schemes are also investigated. The calculation of the pressure and temperature fields for the solution obtained for the vortex and stream function are explained separately. The equations of motion of a viscous fluid in physical variables, including the threedimensional case are also considered. The subject of Chaps. 4 and 5 is the numerical integration of the Navier-Stokes equations for a compressible gas. Various methods of the computation of unsteady flows with shock waves are presented. The principal position is allotted to methods of solution on Eulerlan meshes, enabling a through calculation to be made without the isolation of shock waves, due to the presence in the scheme of explicit or implicit (scheme) artificial viscosity. In the analysis of the computational boundary conditions aspects characteristic of compressible fluid flow are stressed.
287
Book reviews
The use of special computing meshes and coordinate transformations is discussed in Ch. 6. Ch. 7 contains practical advice on the construction and debugging of programs, on the checking of computational algorithms and the processing of the information obtained, in particular, on the computer plotting of graphs. The book is provided with an extremely extensive bibliography on computational hydrodynamics, but unfortunately the list of references ends in 1972 and includes an insufficient number of the papers by soviet authors. The main text and the special section contain many training exercises and problems. Using extensive and interesting material on topical questions of numerical hydrodynamics, the author presents it in accessible form. A special merit of the monograph is the fact that it presents a comparative analysis of various methods, gives recommendations on their practical use, and generalizes the accumulated experience of many workers in computational hydromechanics. Drawbacks are some superficiality in the treatment in individual places and numerous misprints. The book is of considerable interest to scientists and engineers conducting research in both fluid mechanics and computational mathematics. It can also be used as a textbook for postgraduates and students. At the present time a Russian translation of it is being published by “Mif’. P. I. Chushkin Translated by J. Berry.