Gesamtwerk: In diesem Werk der beiden bedeutenden Aerodynamiker wird das gesamte Gebiet der Flugzeugaerodynamik von den Grundlagen bis zu den Entwicklungen der 60er Jahre des 20.Jahrhunderts in klarer, ingenieursgemasser Form dargestellt. Das Hauptgewicht liegt dabei auf den physikalisch und technisch wichtigen Sachverhalten. Die erlauterten Berechnungsverfahren werden durch zahlreiche Beispielrechnungen und Abbildungen veranschaulicht sowie durch Vergleich mit experimentellen Werten uberpruft. Erster Band: Der erste Band behandelt die Grundlagen der Stromungsmechanik einschliesslich der Gasdynamik und der Grenzschichttheorie, und zwar mit besonderer Betonung der Anwendungen in der Flugtechnik. Ausserdem enthalt der erste Band die Profiltheorie, d.h. den ersten Teil der Aerodynamik des Tragflugels."

One cannot overemphasize the importance of studying fluids in motion or at rest for a variety of scientific and engineering endeavors. Fluid mechanics as an art reaches back into antiquity, but its rational formulation is a relatively recent undertaking. Much of the physics of a particular flow situation can be understood by conducting appropriate experiments. Flow visualization techniques offer a useful tool to establish an overall picture of a flow field and to delineate broadly its salient features before embarking on more detailed quantitative measurements. Among the single-point measurements that are particularly difficult are those in separated flows, non-Newtonian fluids, rotating flows, and nuclear aerosols. Pressure, shear stress, vorticity, and heat transfer coefficient are also difficult quantities to measure, particularly for time-dependent flows. These and other special situations are among the topics covered in this volume. Each article emphasizes the development of a particular measuring technique. The topics covered were chosen because of their importance to the field, recent appeal, and potential for future development. The articles are comprehensive and coverage is pedagogical with a bias towards recent developments.

This is a text/reference illustrating thermal and hydraulic design of heat exchangers. The book shows how to apply the fundamentals of thermodynamics, heat transfer, and fluid dynamics for a systematic analysis of the phenomena in heat exchangers, important to energy effective operation in process plants.

Dynamical systems theory and flow control are two research areas of great current interest. These and other special situations are among the topics covered in this volume. Each article emphasizes the use of experiments to achieve better physical understanding of a particular class of flow problems. The topics covered were chosen because of their importance to the field, recent appeal, and potential for future development. The articles are comprehensive and coverage is pedagogical with a bias towards recent developments.

In recent years, the performance of digital computers has been improved by the rapid development of electronics at remarkable speed. In addition, substantial research has been carried out in developing numerical analysis techniques. Nowadays, a variety of problems in the engineering and scientific fields can be solved by using not only super computers but also personal computers. After the first book titled "Boundary Element" was published by Brebbia in 1978, the boundary element method (BEM) has been recognized as a powerful numerical technique which has some advantages over the finite difference method (FDM) and finite element method (FEM). A great amount of research has been carried out on the applications of BEM to various problems. The numerical analysis of fluid mechanics and heat transfer problems plays a key role in analysing some phenomena and it has become recognized as a new research field called "Computational Fluid Dynamics". In partic ular, the analysis of viscous flow including thermal convection phenomena is one of the most important problems in engineering fields. The FDM and FEM have been generally .applied to solve these problems because of non singularities of governing equations.

This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications.

This book offers timely insights into research on numerical and experimental fluid mechanics and aerodynamics, mainly for (but not limited to) aerospace applications. It reports on findings by members of the STAB (German Aerospace Aerodynamics Association) and DGLR (German Society for Aeronautics and Astronautics) and covers both nationally and EC-funded projects. Continuing on the tradition of the previous volumes, the book highlights innovative solutions, promoting translation from fundamental research to industrial applications. It addresses academics and professionals in the field of aeronautics, astronautics, ground transportation, and energy alike.

This revised edition provides updated fluid mechanics measurement techniques as well as a comprehensive review of flow properties required for research, development, and application. Fluid-mechanics measurements in wind tunnel studies, aeroacoustics, and turbulent mixing layers, the theory of fluid mechanics, the application of the laws of fluid mechanics to measurement techniques, techniques of thermal anemometry, laser velocimetry, volume flow measurement techniques, and fluid mechanics measurement in non-Newtonian fluids, and various other techniques are discussed.

The GAMM Committee for Efficient Numerical Methods for Par tial Differential Equations (GAMM-FachausschuB "Effiziente numerische Verfahren fUr partielle Differenzialgleichungen") organizes conferences and seminars on subjects concerning the algorithmic treatment of partial differential equation prob lems. The first seminar "Efficient Solution of Elliptic Systems" was followed by a second one held at the University of Kiel from January 17th to January 19th, 1986. The title was "Efficient Numerical Methods in Continuum Mechanics." The equations arising in continuum mechanics have many con nections to those of fluid mechanics, but are usually more complex. Therefore, much attention has to be paid to the ef ficient discretization, postprocessing and extrapolation. The seminar was attended by 66 scientists from 10 countries. Most of the 21 lectures presented at the seminar treated the discretization of equations in continuum mechanics by finite elements, methods for improving the accuracy of these approx imations and the use of boundary elements. Other contribu tions presented efficient methods for investigating bifurca tions which play an essential role in practical applications. These proceedings contain 11 contributions in alphabetical order. The editors and organizers of the seminar would like to thank the land Schleswig-Holstein and the DFG (Deutsche Forschungs gemeinschaft) for their support. Kiel, November 1986 W. Hackbusch K. Witsch v Contents Page K. ERIKSSON, C. JOHNSON, J. LENNBLAD: Optimal error estimates and adaptive time and space step control for linear parabolic problems ....................... ."

During the week of December 8-13, 1984, a conference on Multi-Grid Methods was held at the Mathematisches Forschungs- institut (Mathematical Research Institute) in Oberwolfach. The conference was suggested by the GAMM-Committee "Effiziente numerische Verfahren fUr partielle Differentialgleichungen". We were pleased to have 42 participants from 12 countries. These proceedings contain some contributions to the confe- rence. The centre of interest in the more theoretical contri- butions were exact convergence proofs for multi-grid method. Here, the theoretical foundation for the application of the method to the Stokes equations, the biharmonic equation in its formulation as a mixed finite element problem and other more involved problems were investigated. Moreover, improvements and new attacks for getting quantitative results on convergence rates were reported. Another series of contributions was concerned with the de- velopment of highly efficient and fast algorithms for various partial differential equations. Also in this framework, the Stokes and the biharmonic equations were investigated. Other lectures treated problems from fluid mechanics (as Navier- Stokes and Euler equations), the dam-problem and eigenvalue problems. The editors would like to thank Professor M. Barner, the director of Mathematisches Forschungsinstitut Oberwolfach for making this conference possible. D. Braess, Bochum W. Hackbusch, Kiel U. Trottenberg, St. Augustin v CONTENTS O. AXELSSON: A mixed variable finite element method for the efficient solution of nonlinear diffusion and pot- tial flow equations ................................... .

INTRODUCTION 1. - The problem for analysis and requirements 2. - Results 3. - Comparison of computer times 4. - Conclusion. INTRODUCTION In 1981 it appeared to the organizers that a workshop to compare codes to solve the Navier -Stokes equations would be of great interest to the community of numerical analysts and users working on CFD (Computer fluid Dynamics}. A test problem would have to be selected with the following features: 1. it should be suited for all known methods (finite differences, finite elements, spectral ... ) thus the geometry should be simple. 2. it should be simple so that scientists with small computer facilities can test it and the gradients in the flow should be reasonable in size so that algo rithms don't blow up with a limited number of points and iterations. In practice one would have to select a stationary flow at moderate Reynolds number. 3. it should be a real flow to allow experimental asurements. The simplest problem used previously was the cavity flow problem; however the singularity of the data at the boundary (point A and B on figure 1} makes it difficult for the Finite Element and Spectral methods; furthermore it is not such an easy experiment to set up. A B .... u = 2 Flow around a cylinder, although most interesting of all, is too difficult because it is unbounded (many grid points) and very quickly unsteady {Re 30)."

One studying the motion of fluids relative to particulate systems is soon impressed by the dichotomy which exists between books covering theoretical and practical aspects. Classical hydrodynamics is largely concerned with perfect fluids which unfortunately exert no forces on the particles past which they move. Practical approaches to subjects like fluidization, sedimentation, and flow through porous media abound in much useful but uncorrelated empirical information. The present book represents an attempt to bridge this gap by providing at least the beginnings of a rational approach to fluid particle dynamics, based on first principles. From the pedagogic viewpoint it seems worthwhile to show that the Navier-Stokes equations, which form the basis of all systematic texts, can be employed for useful practical applications beyond the elementary problems of laminar flow in pipes and Stokes law for the motion of a single particle. Although a suspension may often be viewed as a continuum for practical purposes, it really consists of a discrete collection of particles immersed in an essentially continuous fluid. Consideration of the actual detailed boundary value problems posed by this viewpoint may serve to call attention to the limitation of idealizations which apply to the overall transport properties of a mixture of fluid and solid particles."

The advent of the computer has drastically changed and widened the field of applied mathematics. The "graphical and numerical methods" taught some thirty years ago rather incoherently in small courses have given way to a broad and complex treatment from very different view-points, and the struggle for ever-in-creasing accuracy has brought forth a considerable diver- sification according to the different fields of application. The mathematical theorist, striving for general theorems and unified methods, might regret this development but as long as the demands of practical problems surpass what can be achieved by purely mathematical reasoning, the physicist and the engineer will also base their endeavours on physical grounds. In the wide field of fluid mechanics this development is marked by an in- creasing number of conferences, lecture series and periodicals. It was felt, however, that the nature of the subject required a more extensive coverage of information than is possible in a ] 5 minute-8 pages paper, and that it was necessary, for instance, to give detailed reasoning, comparisons and even critical coding samples. Thus ultimately a monograph form of publication seemed desirable to back up the other channels and the idea of a specialized series was brought forth in the GAMM-Fachausschu for Numerical Methods in Fluid Mechanics. We are happy to have found in the Vieweg-Verlag a potent and understanding partner for this task and we hope for a lasting resonance both from readers and writers in this interesting field.

This book provides a general introduction to fluid mechanics in the form of biographies and popular science. Based on the author's extensive teaching experience, it combines natural science and human history, knowledge inheritance and cognition law to replace abstract concepts of fluid mechanics with intuitive and understandable physical concepts. In seven chapters, it describes the development of fluid mechanics, aerodynamics, hydrodynamics, computational fluid dynamics, experimental fluid dynamics, wind tunnel and water tunnel equipment, the mystery of flight and aerodynamic principles, and leading figures in fluid mechanics in order to spark beginners' interest and allow them to gain a comprehensive understanding of the field's development. It also provides a list of references for further study.

1. 1 Preamble The science to which this work is appended is termed rheology and rheology means the study of flow and deformation of liquids and solids with emphasis on the underlying physical processes. Characteristic for solids is that they respond to a force by deforming, and, on removal of the force, by returning to their original shape. This type of re sponse is termed elastic. Characteristic for liquids is that they deform and continue to deform as long as the force is present. This type of response is termed viscous. The two definitions just given for viscous and elastic response represent wo extremes of response to an external force. Materials do not always fall readily into one or the other of the above-mentioned categories. An additional parameter is needed to describe material response more fully. The extra param eter is time. As a general rule the faster the deformation the closer the re sponse is to being elastic, the slower the deformation the closer the response is to being viscous. Slow and fast . are factors relative to some natural time, T, of the material. This natural time may be thought connected with the rates of spontaneous diffusion of its molecular and atomic constituents. For every day fluids as water, the natural time is very short, of the order of 10-10s 1) and hence for most purposes is considered as being viscous."

Die Neuauflage halt am bewahrten und anerkannten Konzept der Vorauflage fest: ein Grundlagenwerk zum Einsatz in der universitaren Lehre, aber vor allem ein Nachschlagewerk fur den Beruf zum tieferen Verstandnis der verfahrenstechnischen Zusammenhange. Gegenuber der Vorauflage wurde das Werk allerdings erheblich erweitert sowie durch aktuelle Forschungsergebnisse und ein Kapitel zur konzeptuellen Prozessentwicklung erganzt.

Die Grundverfahren werden auf der Basis der Thermodynamik, der Warme- und Stoffubertragung und der Fluiddynamik ubergreifend dargestellt. Damit erhalt der Praktiker erste Informationen uber die Auswahl, die Auslegung und den Betrieb von Apparaten. Nach einer komprimierten Darstellung wichtiger Grundlagen werden u.a. das Destillieren, die Rektifikation, die Absorption, die Kristallisation und die Adsorption behandelt. Es wird aufgezeigt, wie sich grundlagenorientierte Berechnungsansatze fur fluiddynamische und kinetische Vorgange in bekannten und neuen Apparaten finden lassen."

Flowing matter is all around us, from daily-life vital processes (breathing, blood circulation), to industrial, environmental, biological, and medical sciences. Complex states of flowing matter are equally present in fundamental physical processes, far remote from our direct senses, such as quantum-relativistic matter under ultra-high temperature conditions (quark-gluon plasmas). Capturing the complexities of such states of matter stands as one of the most prominent challenges of modern science, with multiple ramifications to physics, biology, mathematics, and computer science. As a result, mathematical and computational techniques capable of providing a quantitative account of the way that such complex states of flowing matter behave in space and time are becoming increasingly important. This book provides a unique description of a major technique, the Lattice Boltzmann method to accomplish this task. The Lattice Boltzmann method has gained a prominent role as an efficient computational tool for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales; from fully-developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic sub-nuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this text provides a survey of the major developments which have led to the impressive growth of the Lattice Boltzmann across most walks of fluid dynamics and its interfaces with allied disciplines. Included are recent developments of Lattice Boltzmann methods for non-ideal fluids, micro- and nanofluidic flows with suspended bodies of assorted nature and extensions to strong non-equilibrium flows beyond the realm of continuum fluid mechanics. In the final part, it presents the extension of the Lattice Boltzmann method to quantum and relativistic matter, in an attempt to match the major surge of interest spurred by recent developments in the area of strongly interacting holographic fluids, such as electron flows in graphene.

Applied Research in Hydraulics and Heat Flow covers modern subjects of mechanical engineering such as fluid mechanics, heat transfer, and flow control in complex systems as well as new aspects related to mechanical engineering education. The chapters help to enhance the understanding of both the fundamentals of mechanical engineering and their application to the solution of problems in modern industry. The book includes the most popular applications-oriented approach to engineering fluid mechanics and heat transfer. It offers a clear and practical presentation of all basic principles of fluid mechanics and heat transfer, tying theory directly to real devices and systems used in mechanical and chemical engineering. It presents new procedures for problem-solving and design, including measurement devices and computational fluid mechanics and heat transfer. This book is suitable for students, both in upper-level undergraduate and graduate mechanical engineering courses. The book also serves as a useful reference for academics, hydraulic engineers, and professionals in fields related to mechanical engineering who want to review basic principles and their applications in hydraulic engineering systems. This fundamental treatment of engineering hydraulics balances theory with practical design solutions to common engineering problems. The authors examine the most common topics in hydraulics, including hydrostatics, pipe flow, pipelines, pipe networks, pumps, hydraulic structures, water measurement devices, and hydraulic similitude and model studies. A glossary of terms, case studies, list of abbreviations, and recent references are included.