Mathematical methods in aerodynamics. (Q2718880)

This book presents mathematical methods used in aerodynamics, both theoretical and numerical, and consists of 11 chapters and 6 appendices. The chapter headings are: 1. The equations of ideal fluids; 2. The equations of linear aerodynamics; 3. The infinite span airfoil in subsonic flow; 4. The applications of the boundary element method; 5. The theory of finite span airfoil and the lifting surface theory; 6. The lifting line theory; 7. The application of the boundary integral equation method to three-dimensional airfoils; 8. The supersonic steady flow; 9. The transonic steady flow; 10. The unsteady flow; 11. The theory of slender bodies. The appendices are: A. Fourier transform and notions of distribution theory; B. Cauchy type integrals; C. Singular integral equations; D. Finite part of integrals; E. Multiple singular integrals; F. Gauss quadrature formulae.NEWLINENEWLINENEWLINEAs regards the most interesting characteristics of the work, they are the following, given without any order of importance.NEWLINENEWLINENEWLINE1. The author presents the entire domain of modern aerodynamics. His attention is paid both to theoretical considerations and to applications, going till numerical results. Each chapter has nearly the same plan: it begins with a short historical presentation of the problem, continues with the results of the most important contributors to the solution methods, and ends with mathematical results obtained by the author himself or by his collaborators.NEWLINENEWLINENEWLINE2. The method called by the author ``fundamental solutions method'' runs through the book and is presented as ``unitary method'' in aerodynamics. It consists in considering a field of unknown forces on the body boundary which perturbates the fluid motion, and in determining this distribution by means of boundary conditions. In other words, the author considers the reaction of the body on the fluid action and, by virtue of Cauchy's stress principle, he equals action and reaction. This method is a variant of similar methods used by pioneers of aerodynamics (L. Prandtl, R. von Mises, L. M. Milne-Thomson and others), who replaced the perturbing body with distributions of sources, vortices or dipoles, without a mechanical support. The results obtained with the fundamental solution method are compared with the results obtained by other authors with other methods.NEWLINENEWLINENEWLINE3. The six appendices contain not only general mathematical results useful for a better understanding of the book, but they also contain suggestions about the numerical methods which can be used by the analysis of problems, many of them established by the author himself. Additionally, the volume contains a rich and useful bibliography, about 500 titles, where the contributions of the author and his associates occupy a large part. The mathematical tools used along the book are up-to-date ones, which makes this modern treatise on aerodynamics useful, in our opinion, both to the beginners and to the scientists working in the domain.