The goal of this book is to present the new trend of Computational Fluid Dynamics (CFD) for the 21 st Century. It consists of papers presented at a symposium honoring Prof. No buyuki Satofuka on the occasion of his 60th birthday. The symposium entitled Computational Fluid Dynamics fOT the 21st Century was held at Kyoto Institute of Technology (KIT) in Kyoto, Japan on July 15-17,2000. The symposium was hosted by KIT as a memorial event celebrating the 100 year anniversary of this establishment. The invited speakers were from Ja pan as weil as from the international community in Asia, Europe and North America. It is a great pleasure to dedicate this book to Prof. Satofuka in appreciation ofhis contributions to this field. During the last 30 years, Prof. Satofuka made many important contributions to CFD ad vancing the numerics and our understanding of flow physics in different regimes. The details of his contributions are discussed in the first chapter. The book contains chapters covering re lated topics with emphasis on new promising directions for the 21 st Century. The chapters of the book reflect the 10 sessions of the symposium on both the numerics and the applications including grid generation and adaptation, new numerical schemes, optimi zation techniques and parallel computations as weil as applications to multi-sc ale and multi physics problems, design and flow control and new topics beyond aeronautics. In the follow ing, the chapters of the book are introduced."

The book focuses on the main physical ideas and mathematical methods of the microscopic theory of fluids, starting with the basic principles of statistical mechanics. The detailed derivation of results is accompanied by explanation of their physical meaning. The same approach refers to several specialized topics of the liquid state, most of which are recent developments, such as: a perturbation approach to the surface tension, an algebraic perturbation theory of polar nonpolarizable fluids and ferrocolloids, a semi-phenomenological theory of the Tolman length and some others. The book addresses researchers as well as graduate students in physics and chemistry with research interests in the statistical physics of fluids.

Computation of Unsteady Internal Flows provides an in-depth understanding of unsteady flow modeling and algorithms. This understanding enables suitable algorithms and approaches for particular fields of application to be selected. In addition, the understanding of the behavior of algorithms gained allows practitioners to use them more safely in existing codes, enabling meaningful results to be produced more economically. Features of Computation of Unsteady Internal Flows: Specialized unsteady flow modeling algorithms, their traits, and practical tips relating to their use are presented. Case studies considering complex, practically significant problems are given. Source code and set-up files are included. Intended to be of a tutorial nature, these enable the reader to reproduce and extend case studies and to further explore algorithm performances. Mathematical derivations are used in a fashion that illuminates understanding of the physical implications of different numerical schemes. Physically intuitive mathematical concepts are used. New material on adaptive time stepping is included. GBP/LISTGBP Audience: Researchers in both the academic and industrial areas who wish to gain in-depth knowledge of unsteady flow modeling will find Computation of Unsteady Internal Flows invaluable. It can also be used as a text in courses centered on computational fluid dynamics.

This is an advanced textbook on the subject of turbulence, and is suitable for engineers, physical scientists and applied mathematicians. The aim of the book is to bridge the gap between the elementary accounts of turbulence found in undergraduate texts, and the more rigorous monographs on the subject. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. Chapters 1 to 5 may be appropriate as background material for an advanced undergraduate or introductory postgraduate course on turbulence, while chapters 6 to 10 may be suitable as background material for an advanced postgraduate course on turbulence, or act as a reference source for professional researchers. This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the Earth

This volume contains the proceedings of the CEAS/DragNet European Drag Reduction Conference 2000. The conference addressed the recent advances in all areas of drag reduction research, development, validation and demonstration including laminar flow technology, adaptive wing concepts, turbulent and induced drag reduction, separation control and supersonic flow aspects. This volume is of particular interest to engineers, scientists and students working in the aeronautics industry, research establishments or academia.

This book offers to students, engineers, CFD modelers, and scientists a detailed synthetic presentation of turbulence physics and modeling with the possibility to find a quick route through the jungle of publications and models. Chapters 1 to 4 show that turbulence models may be derived and analyzed in a physically sound manner with their potential merits and drawbacks. Chapters 5 and 6 review the physics of (inhomogenous) turbulent flows starting from the most simple flow cases and adding more and more complexity. The status and uncertainties of available experimental data and the practical performance of currently available turbulent models are discussed.

This volume contains the papers presented at the IUTAM Symposium on Geometry and Statistics of Turbulence, held in November 1999, at the Shonan International Village Center, Hayama (Kanagawa-ken), Japan. The Symposium was proposed in 1996, aiming at organizing concen trated discussions on current understanding of fluid turbulence with empha sis on the statistics and the underlying geometric structures. The decision of the General Assembly of International Union of Theoretical and Applied Mechanics (IUTAM) to accept the proposal was greeted with enthusiasm. Turbulence is often characterized as having the properties of mixing, inter mittency, non-Gaussian statistics, and so on. Interest is growing recently in how these properties are related to formation and evolution of struc tures. Note that the intermittency is meant for passive scalars as well as for turbulence velocity or rate of dissipation. There were eighty-eight participants in the Symposium. They came from thirteen countries, and fifty-seven papers were presented. The presenta tions comprised a wide variety of fundamental subjects of mathematics, statistical analyses, physical models as well as engineering applications. Among the subjects discussed are (a) Degree of self-similarity in cascade, (b) Fine-scale structures and degree of Markovian property in turbulence, (c) Dynamics of vorticity and rates of strain, (d) Statistics associated with vortex structures, (e) Topology, structures and statistics of passive scalar advection, (f) Partial differential equations governing PDFs of velocity in crements, (g) Thermal turbulences, (h) Channel and pipe flow turbulences, and others.

A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.

This symposium continues a long tradition for IUGGjIUTAM symposia going back to "Fundamental Problems in Thrbulence and their Relation to Geophysics" Marseille, 1961. The five topics that were emphasized were: turbulence modeling, statistics of small scales and coherent structures, con vective turbulence, stratified turbulence, and historical developments. The objective was to consider the ubiquitous nature of turbulence in a variety of geophysical problems and related flows. Some history of the contribu tions of NCAR and its alumni were discussed, including those of Jackson R Herring, who has been a central figure at NCAR since 1972. To the original topics we added rotation, which appeared in many places. This includes rotating stratified turbulence, rotating convective turbulence, horizontal rotation that appears in flows over terrain and the role of small scale vorticity in many flows. These complicated flows have recently begun to be simulated by several groups from around the world and this meeting provided them with an excellent forum for exchanging results, plus inter actions with those doing more fundamental work on rotating stratified and convective flows. New work on double diffusive convection was given in two presentations. The history of Large Eddy Simulations was presented and several new approaches to this field were given. This meeting also spawned some interesting interactions between observational side and how to inter pret the observations with modeling and simulations around the theme of particle dispersion in these flows."

Segregation is a pervasive phenomenon whereby a flowing granular mass consisting of particles with diverse physical properties becomes spatially inhomogeneous. In the industrial sector that deals with the handling and processing of bulk solids, this non-uniformity is highly undesirable since blend homogeneity is generally a stringent requirement of most products. In the arena of geophysical flows, segregation can enhance the destructive capabilities of natural events such as avalanches and landslides. During the last 15 years, these issues have provided motivation and fostered collaborations between the communities of mathematicians, engineers, industrial researchers, and physicists to develop predictive models of segregation by integrating the perspectives and approaches of each. The collection of unique papers brings to light many of the perplexing scientific and technical issues in our current understanding of this complex phenomenon. It addresses advances in experiment, computational modeling and theory. This volume is one of the very few books devoted entirely to problems of segregation of particulate solids.

The origins of turbulent flow and the transition from laminar to turbulent flow are among the most important unsolved problems of fluid mechanics and aerodynamics. Besides being a fundamental question of fluid mechanics, there are many practical applications for information regarding transition location and the details of the subsequent turbulent flow. This proceedings volume contains the papers of two keynote lectures as well as of 104 technical presentations and posters that were presented at the IUTAM Symposium on Laminar-Turbulent Transition in Sedona, Arizona, September 13-17, 1999. The papers published in the present volume document the state of the art in transition research, and therefore, increased emphasis on the various topics covered in this meeting can be expected in the future.

This book describes in detail the current, state-of-the-art numerical treatment and simulation of multiphase flows in porous media. The porous media considered range from ordinary to fractured and deformable media, the models treated from single-phase compressible flow to multiphase multicomponent flow with mass interchange, while the computational algorithms encompass everything from classical iterative solvers to modern multigrid and domain decomposition approaches. Addressing many problems originating from the applied geosciences, the book focuses on their common mathematical and computational aspects. It will serve as an excellent research reference for all geoscientists, mathematicians, physicists, and engineers who work in the mathematical modeling and numerical simulation of multiphase flows in porous media.

The active field of multi-phase flow has undergone fundamental changes in the last decade. Many salient complex interfacial dynamics of such flows are now understood at a basic level with precise mathematical and quantitative characterization. This is quite a departure from the traditional empirical approach. At an IUTAM Symposium at Notre Dame, in 1999, some of the leading researchers in the field gathered to review the progress thus far and to contemplate future directions. Their reports are summarized in this Proceedings. Topics covered include solitary wave dynamics on viscous film flows, sheet formation and drop entrainment in stratified flow, wetting and dewetting dynamics, self-similar drop formation dynamics, waves in bubbly and suspension flow, and bubble dynamics. It is a unique and essential reference for applied mathematicians, physicists, research engineers, and graduate students to keep abreast of the latest theoretical and numerical developments that promise to transform multi-phase flow research.

The aeronautics industry is presently aiming for faster design cycles and shorter time to market of new aircraft. It is looking at the same time for improved aerodynamic performance, for evident competitive reasons. Advanced, computer based design systems, including fast and reliable numerical flow solvers, have been developed in the last decade including new turbulence models. On the experimental side, measurement techniques in general have also been improved significantly, however the data evaluation process remains still very time consuming, and unsteady effects and turbulence are often not being captured with sufficient accuracy and detail. The development of Particle Image Velocimetry (PIV) has helped to improve the analysis of the flow fields. After investigations in laboratory scale wind tunnels, a joint initiative on PIV research, by the European Aerospace Research Establishments, within GARTEUR have enabled a wide breakthrough of this new technology in Europe. Within the Research Framework Program of the European Union, the joint research project EUROPIV aimed to apply PIV technology to problems of industrial interest.

Despite the fact that fluid dynamics and filtration through porous media and mathematics, there are classical research areas in engineering, physics, are still many industrial processes that require the study of new mathemat ical models for flows of particular complexity, due to the peculiar properties of the systems involved. The aim of this book is to provide a number of examples showing how frequently such situations arise in various branches of industrial technology. The selection of the subjects was motivated not only by their industrial rel evance and mathematical interest. What I had in mind was a collection of problems having a really distinctive character, thus bringing some fresh air into one of the oldest and most revered domains of applied mathematics. The incredible richness of nonstandard flow problems in industrial appli cations has always been, and still is, a constant surprise to me. Therefore I tried to offer a very large spectrum of subjects, with special attention devoted to those problems in which the modeling phase is far from being obvious, and the mathematical content is absolutely nontrivial. With such a view to diversity, topics have been selected from a variety of sources (such as glass industry, polymers science, coffee brewing, fuels pipelining), and contributors from different backgrounds (mathematics, physics, chemical engineering) have been included. Consequently, the mathematical nature of the problems formulated spans over a large range, so that their theoret ical investigation and numerical computation require a variety of different techniques."

The practical importance of turbulence led the U.K. Royal Academy of Engineering to launch an Initiative on Turbulence, the most important outcome of which was the definition and agreement of the 1999 Newton Institute Research Programme on Turbulence. The main aim of the- month programme, held at the institute in Cambridge, was to bring together the mathematics and engineering communities involved in the turbulence area to address the many problems and to map out future strategy. As a part of the Research Programme, a Symposium on Direct and Large-Eddy Simulation was jointly organised with ERCOFfAC through their Large-Eddy Simulation Interest Group and took place in May 1999. Two previous ERCOFf AC Workshops had already taken place on these closely related varieties of turbulence simulation, at The University of Surrey in 1994 and at Universite Joseph Fourier, Grenoble in 1996. The Symposium at Cambridge was therefore the third in the ERCOFTAC series, enhanced by the presence of leading figures in the field from Europe and the USA who were resident at INI for that period of the Research Programme. Professors M. Germano, A. Leonard, J. Jimenez, R. Kerr and S. Sarkar gave the invited lectures, text versions of which will be found in this volume. As occurred at the previous two ERCOFT AC workshops, there were almost one hundred participants mostly from Europe but including some from Japan and the USA, including on this occasion resident scientists of the INI Research Programme.

This book describes an engineering approach based on interactive boundary-layer and stability-transition theories, both developed by the author, for calculating aerodynamic flows. The contents include two-dimensional and three-dimensional steady and unsteady flows with and without compressibility effects. The former theory is based on the numerical solutions of the reduced Navier-Stokes equations in which Euler and boundary-layer equations are coupled with an interaction law. The latter theory is based on the linear stability theory and employs the so-called en method. The book details applications of this approach to airfoils, wings and high lift systems. It is intended for undergraduate and graduate students and practicing engineers interested in aerodynamics, hydrodynamics and modern numerical methods and computer programs for solving linear and nonlinear ordinary and parabolic partial differential equations.

This single-volume work gives an introduction to the fields of transition, turbulence, and combustion modeling of compressible flows and provides the physical background for today's modeling approaches in these fields. It presents basic equations and discusses fundamental aspects of hydrodynamical instability.

Rapid advances in Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of turbulence provide opportunities for improved prediction of incompressible and compressible turbulent flows. The book includes five invited and thirty-eight contributed papers presented at the Second AFOSR International Conference on DNS and LES held at Rutgers - The State University of New Jersey, on June 7-9, 1999. A broad range of topics in DNS and LES are presented, including new developments in LES modeling, numerical algorithms for LES and DNS, DNS and LES of reacting flows, and DNS and LES for supersonic and hypersonic boundary layers. The book provides a extensive view of the state of the art in DNS and LES.

This book is designed to fulfill a dual role. On the one hand it provides a description of the rheological behavior of molten poly mers. On the other, it presents the role of rheology in melt processing operations. The account of rheology emphasises the underlying principles and presents results, but not detailed deriva tions of equations. The processing operations are described qualita tively, and wherever possible the role of rheology is discussed quantitatively. Little emphasis is given to non-rheological aspects of processes, for example, the design of machinery. The audience for which the book is intended is also dual in nature. It includes scientists and engineers whose work in the plastics industry requires some knowledge of aspects of rheology. Examples are the polymer synthetic chemist who is concerned with how a change in molecular weight will affect the melt viscosity and the extrusion engineer who needs to know the effects of a change in molecular weight distribution that might result from thermal degra dation. The audience also includes post-graduate students in polymer science and engineering who wish to acquire a more extensive background in rheology and perhaps become specialists in this area. Especially for the latter audience, references are given to more detailed accounts of specialized topics, such as constitutive relations and process simulations. Thus, the book could serve as a textbook for a graduate level course in polymer rheology, and it has been used for this purpose."

This monograph aims to fill the gap between the mathematical literature which significantly contributed during the last decade to the understanding of the collapse phenomenon, and applications to domains like plasma physics and nonlinear optics where this process provides a fundamental mechanism for small scale formation and wave dissipation. This results in a localized heating of the medium and in the case of propagation in a dielectric to possible degradation of the material. For this purpose, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal asymptotic expansions and numerical simulations.

Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics, ' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely."

1. Objective and Scope Bubbles, drops and rigid particles occur everywhere in life, from valuable industrial operations like gas-liquid contracting, fluidized beds and extraction to such vital natural processes as fermentation, evaporation, and sedimentation. As we become increasingly aware of their fundamental role in industrial and biological systems, we are driven to know more about these fascinating particles. It is no surprise, therefore, that their practical and theoretical implications have aroused great interest among the scientific community and have inspired a growing number of studies and publications. Over the past ten years advances in the field of small Reynolds numbers flows and their technological and biological applications have given rise to several definitive monographs and textbooks in the area. In addition, the past three decades have witnessed enormous progress in describing quantitatively the behaviour of these particles. However, to the best of our knowledge, there are still no available books that reflect such achievements in the areas of bubble and drop deformation, hydrodynamic interactions of deformable fluid particles at low and moderate Reynolds numbers and hydrodynamic interactions of particles in oscillatory flows. Indeed, only one more book is dedicated entirely to the behaviour of bubbles, drops and rigid particles ["Bubbles, Drops and Particles" by Clift et al. (1978)] and the authors state its limitations clearly in the preface: "We treat only phenomena in which particle-particle interactions are of negligible importance. Hence, direct application of the book is limited to single-particle systems of dilute suspensions.

TUrbulence modeling encounters mixed evaluation concerning its impor tance. In engineering flow, the Reynolds number is often very high, and the direct numerical simulation (DNS) based on the resolution of all spatial scales in a flow is beyond the capability of a computer available at present and in the foreseeable near future. The spatial scale of energetic parts of a turbulent flow is much larger than the energy dissipative counterpart, and they have large influence on the transport processes of momentum, heat, matters, etc. The primary subject of turbulence modeling is the proper es timate of these transport processes on the basis of a bold approximation to the energy-dissipation one. In the engineering community, the turbulence modeling is highly evaluated as a mathematical tool indispensable for the analysis of real-world turbulent flow. In the physics community, attention is paid to the study of small-scale components of turbulent flow linked with the energy-dissipation process, and much less interest is shown in the foregoing transport processes in real-world flow. This research tendency is closely related to the general belief that universal properties of turbulence can be found in small-scale phenomena. Such a study has really contributed much to the construction of statistical theoretical approaches to turbulence. The estrangement between the physics community and the turbulence modeling is further enhanced by the fact that the latter is founded on a weak theoretical basis, compared with the study of small-scale turbulence."

Recent advances in boundary-layer theory have shown how modern analytical and computational techniques can and should be combined to deepen the understanding of high Reynolds number flows and to design effective calculation strategies. This is the unifying theme of the present volume which addresses laminar as well as turbulent flows.