Most of the fundamental concepts of unsteady viscous flows have been known since the early part of the century. However, the past decade has seen an unprecedented number of publications in this area. In this monograph I try to connect materials of earlier contributions and synthesize them into a comprehensive entity. One of the main purposes of a monograph, in my opinion, is to fit together in a comprehensive way scattered contributions that provide fragmented information to the readers. The collection of such contributions should be presented in a unified way; continuity of thought and logical sequence of the presentation of ideas and methods are essential. The reader should be able to follow through without having to resort to other references, something that is unavoidable in the case of a research paper or even a review paper. Many of the solutions discussed in the literature address specific practical problems. In fact, in the process of collecting information, I discovered independent lines of investigations, dealing with the same physical problem, but inspired by different practical applications. For example, I found that two groups of investigators have been studying independently the response of a viscous layer to a harmonic external disturbance. One group is con cerned with mass transport and the transport of sediment over the bottom of the ocean, and the other is interested in the aerodynamics of lifting surfaces in harmonically changing environments.

The GAMM-Commi ttee for Numerical Methods in Fluid Mechanics (GAMM-Fachausschuss für Numerische Methoden in der Strömungsmechanik) has sponsored the organization of a GAMM Workshop dedicated to the numerical simulation of three dimensional incompressible unsteady viscous laminar flows to test Navier-Stokes solvers. The Workshop was held in Paris from June 12th to June 14th, 1991 at the Ecole Nationale Superieure des Arts et Metiers. Two test problems were set up. The first one is the flow in a driven-lid parallelepipedic cavity at Re = 3200 . The second problem is a flow around a prolate spheroid at incidence. These problems are challenging as fully transient solutions are expected to show up. The difficulties for meaningful calculations come from both space and temporal discretizations which have to be sufficiently accurate to resol ve detailed structures like Taylor-Görtler-like vortices and the appropriate time development. Several research teams from academia and industry tackled the tests using different formulations (veloci ty-pressure, vortici ty velocity), different numerical methods (finite differences, finite volumes, finite elements), various solution algorithms (splitting, coupled ...), various solvers (direct, iterative, semi-iterative) with preconditioners or other numerical speed-up procedures. The results show some scatter and achieve different levels of efficiency. The Workshop was attended by about 25 scientists and drove much interaction between the participants. The contributions in these proceedings are presented in alphabetical order according to the first author, first for the cavi ty problem and then for the prolate spheroid problem. No definite conclusions about benchmark solutions can be drawn.

This unique book provides a unified and systematic account of internal, external and unsteady slow viscous flows, including the latest advances of the last decade, some of which are due to the author. The book shows how the method of eigenfunctions, in conjunction with least squares, can be used to solve problems of low Reynolds number flows, including three-dimensional internal and unsteady flows, which until recently were considered intractable. Although the methods used are quantitative, much stress is laid on understanding the qualitative nature of these intriguing flows. A secondary purpose of the book is to explain how the complex eigenfunction method can be used to solve problems in science and engineering.Although primarily aimed at graduate students, academics and research engineers in the areas of fluid mechanics and applied mathematics, care has been taken, through the use of numerous diagrams and much discussion, to explain to the non-specialist the qualitative features of these complex flows./a

Applications of computational aerodynamics to aeronautical research, design, and analysis have increased rapidly over the past decade, and these applications offer significant benefits to aeroelasticians. This paper traces the past developments by means of a number of specific examples, and projects the trends over the next several years. The crucial factors that limit the present capabilities for unsteady analyses are identified; they include computer speed and memory, algorithm and solution methods, grid generation, turbulence modeling, vortex modeling, data processing, and coupling of the aerodynamic and structural dynamic analyses. The prospects for overcoming these limitations are presented, and many improvements appear to be readily attainable. If so, a complete and reliable numerical simulation of the unsteady, transonic viscous flow around a realistic fighter aircraft configuration could become possible within the next decade. The possibilities of using artificial intelligence concepts to hasten the achievement of this goal are also discussed. Key words include: Flutter predictions; Oscillating wings; and Unsteady computational aerodynamics.