Whatdoasupernovaexplosioninouterspace, ?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally. The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In ?ows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that in?uence the stability of the wings as well as fuel consumption in ?ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for e?ciency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial di?erential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scienti?c progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua, partial di?erential equationsareamajor?eldofresearchinmathematics. Asubstantialportionof mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more spacedimensionsstillposeoneofthemainchallengestomodernmathematics

This book provides concise, up-to-date and easy-to-follow information on certain aspects of an ever important research area: multiphase flow in porous media. This flow type is of great significance in many petroleum and environmental engineering problems, such as in secondary and tertiary oil recovery, subsurface remediation and CO2 sequestration. This book contains a collection of selected papers (all refereed) from a number of well-known experts on multiphase flow. The papers describe both recent and state-of-the-art modeling and experimental techniques for study of multiphase flow phenomena in porous media. Specifically, the book analyses three advanced topics: upscaling, pore-scale modeling, and dynamic effects in multiphase flow in porous media. This will be an invaluable reference for the development of new theories and computer-based modeling techniques for solving realistic multiphase flow problems. Part of this book has already been published in a journal. Audience This book will be of interest to academics, researchers and consultants working in the area of flow in porous media.

This monograph on fluid mechanics is not only a superb and unique textbook but also an impressive piece of research. The author writes from the vantage point of a mathematical physicist: Having in mind the important applications and approximation techniques used in physics and engineering, he carefully analyses the power of the theory. He examines, among others, the theories of Leray, Ruelle and Takens, and discusses Lorenz's ideas of attractors. This is the only textbook that fully covers turbulence, all the way from the works of Kolmogorov to modern dynamics.

ThisvolumeispublishedastheproceedingsoftheRussian-GermanAdvanced Research workshop on Computational Science and High Performance C- puting in Novosibirsk Academgorodok in September 2003. The contributions of these proceedings were provided and edited by the authors, chosen after a careful selection and reviewing. The workshop was organized by the Institute of Computational Techno- gies SB RAS (Novosibirsk, Russia) and the High Performance Computing Center Stuttgart (Stuttgart, Germany). The objective was the discussion of the latest results in computational science and to develop a close coope- tion between Russian and German specialists in the above-mentioned ?eld. The main directions of the workshop are associated with the problems of computational hydrodynamics, application of mathematical methods to the development of new generation of materials, environment protection pr- lems, development of algorithms, software and hardware support for hi- performance computation, and designing modern facilities for visualization of computational modelling results. The importance of the workshop topics was con?rmed by the partici- tion of representatives of major research organizations engaged in the so- tion of the most complex problems of mathematical modelling, development of new algorithms, programs and key elements of new information techno- gies. Among the Russian participants were researchers of the Institutes of the Siberian Branch of the Russian Academy of Sciences: Institute of Com- tational Technologies, Institute of Computational Mathematics and Mat- matical Geophysics, Institute of Computational Modelling, Russian Federal Nuclear Center, All-Russian Research Institute of Experimental Physics, - merovo State University.

Despite dramatic advances in numerical and experimental methods of fluid mechanics, the fundamentals are still the starting point for solving flow problems. This textbook introduces the major branches of fluid mechanics of incompressible and compressible media, the basic laws governing their flow, and gas dynamics. Fluid Mechanics demonstrates how flows can be classified and how specific engineering problems can be identified, formulated and solved, using the methods of applied mathematics. The material is elaborated in special applications sections by more than 200 exercises and separately listed solutions. The final section comprises the Aerodynamics Laboratory, an introduction to experimental methods treating eleven flow experiments. This class-tested textbook offers a unique combination of introduction to the major fundamentals, many exercises, and a detailed description of experiments.

Luminescent molecule sensors, called pressure-sensitive paint (PSP) and temperature-sensitive paint (TSP), measure factors essential for understanding the aerodynamic performance and heat transfer characteristics of flight vehicles. They provide a powerful tool for experimental aerodynamicists to obtain a deeper understanding of the rich physical phenomena in complex flows around a flight vehicle. This book helps the reader to understand the physics and chemistry and the capabilities of PSP and TSP. It provides an overview of the wide scope of applications and explains the system requirements for using these sensors. The book also includes an extensive table of properties of PTP and TSP. As such, it is a thorough and up-to-date coverage of the underlying physics and applications of luminescent molecules designed for global pressure and temperature mapping

Modelling Fluid Flow presents invited lectures, workshop summaries and a selection of papers from a recent international conference CMFF '03 on fluid technology. The lectures follow the current evolution and the newest challenges of the computational methods and measuring techniques related to fluid flow. The workshop summaries reflect the recent trends, open questions and unsolved problems in the mutually inspiring fields of experimental and computational fluid mechanics. The papers cover a wide range of fluids engineering, including reactive flow, chemical and process engineering, environmental fluid dynamics, turbulence modelling, numerical methods, and fluid machinery.

This book contains papers presented at a workshop, jointly organized by the EUROPIV 2 project, the PivNet 2 Thematic Network, and the ERCOFTAC Spe cial Interest Group on PIV (SIG 32). EUROPIV 2 was a research program, funded by the European Community which started in April 2000 and ended in June 2003. The aim of this project was to develop and demonstrate the Particle Image Velocimetry technique (PIV), which allows to measure the velocity of large flow fields instantaneously, in order to make it available as an operational tool for the European aeronautical industry. A total of 17 teams from 5 different countries cooperated during these 3 years to im prove the method, both hardware and software, and to demonstrate its capabilities in large industrial wind tunnels. PivNet 2 is a European thematic network devoted to the transfer of the PIV technique to IndUStry. It has started in April 2002 for four years. It is coordinated by Dr J. Kompenhans from DLR Gottingen. Details on PivNnet 2 can be found at http: //pivnet.sm.go.dlr.de. ERCOFTAC (European Research Community on Flow, Turbulence and Com bustion) is an international association with the aim to promote research and coop eration in Europe on fluid flows, turbulence and combustion. Details can be found at http: //www.ercoftac.org and http: //www.univ-lillellpivnet."

Why are propeller blades of speedboats strongly eroded? Why does a syringe have to be filled slowly in order to avoid the formation of a vapour cavity near the piston? Why does a pump for watering the garden not work efficiently if it is placed too high above the ground water level? These questions, and many others taken from day to day experience, refer to situations which apparently have no connection between them, except for the fact that the motion of a liquid in part of the system plays an essential role.

Cavitation science is that part of liquid physics which addresses the motion of liquids near -or beyond- the limit of vaporization. Generally, vaporization occurs if liquid velocities are large, causing pressure to decrease below a critical value at which the liquid continuum is broken at one or several points. Vapor cavities appear there and various unexpected effects follow for the system such as noise, lower performance, vibrations, wall erosion For a long time, it was believed that cavitation phenomena should be avoided entirely because of the generally negative character of their consequences. However, over the years it appeared that such a constraint could be costly, though not necessarily justified on scientific grounds. A limited development of cavitation - if carefully defined and controlled - can be allowed. This promotes the development of high speed hydrodynamics and hydraulics.

The present book is aimed at providing a comprehensive presentation of cavitation phenomena in liquid flows. It is further backed up by the experience, both experimental and theoretical, of the authors whose expertise has been internationally recognized. A special effort is made toplace the various methods of investigation in strong relation with the fundamental physics of cavitation, enabling the reader to treat specific problems independently. Furthermore, it is hoped that a better knowledge of the cavitation phenomenon will allow engineers to create systems using it positively. Examples in the literature show the feasibility of this approach.

The fifth ERCOFfAC workshop 'Direct and Large-Eddy Simulation-5' (DLES-5) was held at the Munich University of Technology, August 27-29, 2003. It is part of a series of workshops that originated at the University of Surrey in 1994 with the intention to provide a forum for presentation and dis cussion of recent developments in the field of direct and large-eddy simula tion. Over the years the DLES-series has grown into a major international venue focussed on all aspects of DNS and LES, but also on hybrid methods like RANSILES coupling and detached-eddy simulation designed to provide reliable answers to technical flow problems at reasonable computational cost. DLES-5 was attended by 111 delegates from 15 countries. Its three-day pro gramme covered ten invited lectures and 63 original contributions partially pre sented in parallel sessions. The workshop was financially supported by the fol lowing companies, institutions and organizations: ANSYS Germany GmbH, AUDI AG, BMW Group, ERCOFfAC, FORTVER (Bavarian Research Asso ciation on Combustion), JM BURGERS CENTRE for Fluid Dynamics. Their help is gratefully acknowledged. The present Proceedings contain the written versions of nine invited lectures and fifty-nine selected and reviewed contributions which are organized in four parts: 1 Issues in LES modelling and numerics 2 Laminar-turbulent transition 3 Turbulent flows involving complex physical phenomena 4 Turbulent flows in complex geometries and in technical applications.

This is an up-to-date review of recent advances in the study of two-phase flows, with focus on gas-liquid flows, liquid-liquid flows, and particle transport in turbulent flows. The book is divided into several chapters, which after introducing basic concepts lead the reader through a more complex treatment of the subjects. The reader will find an extensive review of both the older and the more recent literature, with abundance of formulas, correlations, graphs and tables. A comprehensive (though non exhaustive) list of bibliographic references is provided at the end of each chapter. The volume is especially indicated for researchers who would like to carry out experimental, theoretical or computational work on two-phase flows, as well as for professionals who wish to learn more about this topic.

This Symposium, and these Proceedings, provided a forum for the latest thinking in analytical, computational and experimental modelling of structures interacting with fluid environments. A meaningful and lasting dialogue was facilitated between leading researchers in the different component disciplines. It is intended that, through these dialogues, multidisciplinary linkages will be establishes leading to integrated approaches to modelling the complex, nonlinear interactions between fluids and structures. Examples of classes of interactions that may be addressed in this Symposium include ocean structures, fluid conveying structures, and aerospace structures. The energy transfer processes are inherently nonlinear in all aspects of the behaviour. The important class of vortex-induced oscillations has regions of lock-in, where the structural natural frequencies rather than the fluid velocity govern the shedding, and there exists hysteretic behaviour.
A large body of engineering and engineering science is concerned about fluid-structure interactions. Yet there are many unanswered questions about the underlying physics, so much so that a great deal of empiricism remains. Much of this empiricism can be traced to the relative lack of detailed collaboration between the fluid and structural mechanics communities studying these interactions. Generally, it has been that structural mechanicians would place extensive effort into the structural model, while a simple oscillator represented fluid motions. Conversely, fluid mechanicians placed most of their modelling efforts into the fluid, often considering the structure to be a rigid single degree of freedom oscillator. While such studies havesignificantly increased understanding, it appears that the next breakthroughs in the field need to be modelled at a comparable lever of accuracy.
The real fluid-structure system is one of complex exchanges of forces and energies, resulting in highly nonlinear behaviours. The ability to model, solve and test fully coupled fluid-structure systems portends a rich and profound understanding. In fact, recent research efforts have indeed started to focus on the development of fully coupled models. This Symposium is therefore a response to these new and exciting developments in the field.

This textbook is written for senior undergraduate and graduate students as well as engineers who will develop or use code in the simulation of fluid flows or other physical phenomena. The objective of the book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. It is based on the finite-difference method and simple enough problems that allow also the analytic solutions to be worked out. ODEs as well as hyperbolic, parabolic and elliptic types are treated. The reader also will find a chapter on the techniques of linearization of nonlinear problems. The final chapter applies the material to the equations of gas dynamics. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions.

This volume contains the paper presented at the 13th DGLRlST AB- Symposium held at the Technische Universitat Miinchen, November 12 to 14, 2002. STAB is the German Aerospace Aerodynamics Association, founded towards the end of the 70's, whereas DGLR is the German Society for Aeronautics and Astronautics (Deutsche Gesellschaft fUr Luft- und Raumfahrt - Lilienthal Oberth e.V.). The mission of STAB is to foster development and acceptance of the dis- cipline "Aerodynamics" in Germany. One of its general guidelines is to concentrate resources and know-how in the involved institutions and to avoid duplication in research work as much as possible. Nowadays, this is more necessary than ever. The experience made in the past makes it easier now, to obtain new knowledge for solving today's and tomorrow's prob- lems. STAB unites German scientists and engineers from universities, research- establishments and industry doing research and project work in numerical and experimental fluid mechanics and aerodynamics for aerospace and other applications. This has always been the basis of numerous common research activities sponsored by different funding agencies.

This volume presents selected papers from the IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, convened in Princeton, NJ, USA, September I1-13, 2002. The behavior ofturbulence at high Reynolds number is interesting from a fundamental point of view, in that most theories of turbulence make very specific predictions in the limit of infinite Reynolds number. From a more practical point of view, there exist many applications that involve turbulent flow where the Reynolds numbers are extremely large. For example, large vehicles such as submarines and commercial transports operate at Reynolds 9 numbers based on length ofthe order oft0 , and industrial pipe flows cover a 7 very wide range of Reynolds numbers up to 10 * Many very important applications of high Reynolds number flow pertain to atmospheric and other geophysical flows where extremely high Reynolds numbers are the rule rather than the exception, and the understanding of climate changes and the prediction of destructive weather effects hinges to some extent on our appreciation ofhigh-Reynolds number turbulence behavior. The important effects of Reynolds number on turbulence has received a great deal of recent attention. The objective of the Symposium was to bring together many of the world's experts in this area to appraise the new experimental results, discuss new scaling laws and turbulence models, and to enhance our mutual understanding of turbulence.

"Symposium Transsonicum" was founded by Klaus Oswatitsch four decades ago when there was clearly a need for a systematic treatment of flow problems in the higher speed regime in aeronautics. The first conference in 1962 brought together scientists concerned with fundamental problems involving the sonic flow speed regime. Results of the conference provided an understanding of some basic tran sonic phenomena by proposing mathematical methods that allowed for the de velopment of practical calculations. The "Transonic Controversy" (about shock free flows) was still an open issue after this meeting. In 1975 the second symposium was held, by then there was much understanding in how to avoid shocks in a steady plane flow to be designed, but still very little was known in unsteady phenomena due to a lack of elucidating experiments. A third meeting in 1988 reflected the availability oflarger computers which allowed the numerical analysis of flows with shocks to a reasonable accuracy. Because we are trying to keep Oswatitsch's heritage in science alive especially in Gottingen, we were asked by the aerospace research community to organize another symposium. Much had been achieved already in the knowledge, techno logy and applications in transonics, so IUT AM had to be convinced that a fourth meeting would not just be a reunion of old friends reminiscing some scientific past. The scientific committee greatly supported my efforts to invite scientists ac tively working in transonic problems which still pose substantial difficulties to ae rospace and turbomachinery industry.

The present set of lectures and tutorial reviews deals with various topical aspects related to instabilities of interfacial processes and driven flows from both the theoretical and experimental point of views. New research has been spurred by demands for many applications in material sciences (melting, solidification, electro deposition), biomedical engineering and processing in microgravity environments. This book is intended as both a modern source of reference for researchers in the field as well as an introduction to postgraduate students and non-specialists from related areas.

Thisvolumecontainsacollectionofpapersbyinternationalexpertsingeoph- ical ?uid dynamics, based upon presentations at a colloquium held in memory of Pedro Ripa on the ?rst anniversary of his untimely death. They review or present recent developments in hydrodynamic stability theory, Hamiltonian ?uid mechanics,balanceddynamics, waves,vortices,generaloceanographyand the physical oceanography of the Gulf ofCalifornia; all of them subjects in which Professor Ripamadeimportant contributions. His work, but also his friendly spiritandkindnesswerehighly regardedandappreciatedby colleagues and students alike around the world. This book is a tribute to his scienti?c legacy and constitutes a valuable reference for researchers and graduate s- dents interested in geophysical and general ?uid mechanics. Earlyin his career asa physicaloceanographer,Pedro Ripa made two la- mark contributions to geophysical ?uid dynamics. In 1981, he showed that the conservation of the potential vorticity is related to the invariance of the eq- tions of motion under the symmetry transformationsof the labels that identify the ?uid particles. That is, potential vorticity conservation is a consequence, via Noether's theorem, of the particle re-labelling symmetry. Two years later he published a paper entitled "General stability conditions for zonal ?ows in a one-layer model on the beta-plane or the sphere", where he established nec- sary conditions for stability in the shallow water equations, nowadays known as "Ripa's Theorem. " This is one of the very few Arnol'd-like stability con- tions that goes beyond two-dimensional or quasi-geostrophic ?ow, and stands alongside other famous stability criteria in making the foundations of the ?eld.

The priority research, Analysis, Modelling and Numerical Calculations ofMul tiphase Flows" was running for 6 years (from 1996 to 2002) and financially sup ported by the Deutsche Forschungsgemeinschaft (DFG). The main objective ofthe research programme was to provide a better understanding of the physical basis for multiphase gas-liquid flows as they are found in numerous chemical and bio chemical reactors. The research comprised steady and unsteady multiphase flows in three frequently found reactor configurations, namely bubble columns without interiors, loop reactors, and aerated stirred vessels. For this purpose, new and im proved measurement techniques should be developed. From the resulting knowl edge and data, new and refined models for describing the underlying physical processes should result, which can be used for the establishment and improvement of analytic as well as numerical methods for predicting multiphase reactors. Thereby, the development, lay-out and scale-up ofsuch processes should be pos sible on a more reliable basis. For achieving this objective three research areas were defined: development and improvement of experimental techniques which allow accu rate measurements in steady and unsteady multiphase flows elaboration of new modelling approaches in order to describe the basic trans port processes for mass, momentum, and heat in bubbly flows development of analytical and numerical methods supplemented by the new modelling strategies in order to support optimisation and lay-out of technical multiphase processes."

Large eddy simulation (LES) seeks to simulate the large structures of a turbulent flow. This is the first monograph which considers LES from a mathematical point of view. It concentrates on LES models for which mathematical and numerical analysis is already available and on related LES models. Most of the available analysis is given in detail, the implementation of the LES models into a finite element code is described, the efficient solution of the discrete systems is discussed and numerical studies with the considered LES models are presented.

The 24 papers presented at the international concluding colloquium of the German priority programme (DFG-Verbundschwerpunktprogramm) "Transition," held in April 2002 in Stuttgart.

The unique and successful programme ran six years, starting April 1996, and was sponsored mainly by the Deutsche Forschungsgemeinschaft, DFG, but also by the Deutsches Zentrum f r Luft-und Raumfahrt, DLR, the Physikalisch-Technische Bundesanstalt Braunschweig, PTB, and Airbus Deutschland. The papers summarise the results of the programme and cover transition mechanisms, transition prediction, transition control, natural transition and measurement techniques, transition - turbulence - separation, and visualisation issues. Three invited papers are devoted to mechanisms of turbulence production, to a general framework of stability, receptivity and control, and a forcing model for receptivity analysis. Almost every transition topic arising in subsonic and transonic flow is covered.

As mentioned in the Introduction to Volume I, the present monograph is intended both for mathematicians interested in applications of the theory of linear operators and operator-functions to problems of hydrodynamics, and for researchers of applied hydrodynamic problems, who want to study these problems by means of the most recent achievements in operator theory. The second volume considers nonself-adjoint problems describing motions and normal oscillations of a homogeneous viscous incompressible fluid. These ini tial boundary value problems of mathematical physics include, as a rule, derivatives in time of the unknown functions not only in the equation, but in the boundary conditions, too. Therefore, the spectral problems corresponding to such boundary value problems include the spectral parameter in the equation and in the bound ary conditions, and are nonself-adjoint. In their study, we widely used the theory of nonself-adjoint operators acting in a Hilbert space and also the theory of operator pencils. In particular, the methods of operator pencil factorization and methods of operator theory in a space with indefinite metric find here a wide application. We note also that this volume presents both the now classical problems on oscillations of a homogeneous viscous fluid in an open container (in an ordinary state and in weightlessness) and a new set of problems on oscillations of partially dissipative hydrodynamic systems, and problems on oscillations of a visco-elastic or relaxing fluid. Some of these problems need a more careful additional investigation and are rather complicated."

This volume contains the proceedings of a workshop held in Melbourne, Australia, entitled "Coupling of Fluids, Structures and Waves in Aeronautics". The 22 papers deal with new computational methods for multi-disciplinary design in aeronautics. They are grouped into chapters on fluids, structures, electromagnetics, optimisation, mathematical methods and tools, and aircraft design. Several papers treat coupling of these themes in a multi-physics setting. Included is a 17-page report of a Round Table discussion entitled "Future Tools for Design and Manufacture of Innovative Products in the Aeronautics Industry", together with a summary of important themes and issues. This research promotes the advanced technologies necessary for continued development of efficient and environmentally sustainable transport systems.

This volume contains results of a European project on Large Eddy Simulation (LES) of the flow around an airfoil. The main objective of the LESFOIL project was to assess the suitability of LES for airfoil flow. In conclusion, preliminary work was carried out such as development of numerical methods, and subgrid modelling in geometrically simple flows such as fully developed channel flow and periodic flow in a channel with a curved hill-shaped surface. Accurate LES of wall-bounded flow requires fine cells in the near-wall region in all coordinate directions. In an attempt to release this constraint, a large part of the LESFOIL project was aimed at developing and validating different approximate near-wall treatments. In the second half of the book, several LESs of the flow around the Aerospatiale-A airfoil are presented, using different numerical methods, grids, SGS models and near-wall treatments.

The IUTAM Symposium on Flow in Collapsible Tubes and Past Other Highly Compliant Boundaries was held on 26-30 March, 2001, at the University of Warwick. As this was the first scientific meeting of its kind we considered it important to mark the occasion by producing a book. Accordingly, at the end of the Symposium the Scientific Committee met to discuss the most appropriate format for the book. We wished to avoid the format of the conventional conference book consisting of a large number of short articles of varying quality. It was agreed that instead we should produce a limited number of rigorously refereed and edited articles by selected participants who would aim to sum up the state of the art in their particular research area. The outcome is the present book. Peter W. Ca rpenter, Warwick Timothy J. Pedley, Cambridge May, 2002. VB SCIENTIFIC COMMITTEE Co-Chair: P.W. Carpenter, Engineering, Warwiek, UK Co-Chair: TJ. Pedley, DAMTP, Cambridge, UK V.V. Babenko, Hydromechanics, Kiev, Ukraine R. Bannasch, Bionik & Evolutionstechnik, TU Berlin, Germany C.D. Bertram, Biomedical Engineering, New South Wales, Australia M. Gad-el-Hak, Aerospace & Mechanical Engineering, Notre Dame, USA J.B. Grotberg, Biomedical Engineering, Michigan, USA. R.D. Kamm, Mechanical Engineering, MIT, USA Y. Matsuzaki, Aerospace Engineering, N agoya, Japan P.K. Sen, Applied Mechanics, IIT Delhi, India L. van Wijngaarden, Twente, Netherlands K-S. Yeo, Mechanical Engineering, NU Singapore.