Hyposonic fluid flows, characterized by a low Mach number, are mainly linked with geophysical and environmental fluid flows. In addition they are relevant to engineers because of their connection with aerodynamics. The books brings together insights derived from mathematically rigorous results and combines them with a number of realistic fluid flow situations. Asymptotic analytic solutions for the low-Mach number cases are developed to provide both insights into the underlying physics as well as benchmarks for numerical computations.

This volume contains contributions to the First Kazakh-German Advanced Research Workshop on Computational Science and High Performance Computing presented in September 2005 at Almaty, Kazakhstan. The workshop was organized by the High Performance Computing Center Stuttgart (Stuttgart, Germany), al-Farabi Kazakh National University (Almaty, Kazakhstan) and the Institute of Computational Technologies SB RAS (Novosibirsk, Russia) in the framework of activities of the German-Russian Center for Computational Technologies and High Performance

The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.

This textbook discusses the fundamental principles of sediment transport in the geophysical context of rivers and is intended as both a course textbook and as a guide for the practical engineer. We begin by describing phenomena such as bed load and suspension transport from a classical perspective by applying the mean wall shear stress approach while additionally incorporating a statistical description of the inherent wall shear stress fluctuations. Concepts from turbulent flow regime are introduced to address the limitations of the classical approach to various aspects of sediment transport, such as for example, the Newtonian description of dense suspensions, or the description of the self-organization processes for developing bed forms, or the prediction of transport in very rough bed conditions. In this context coherent structures and flow separation mechanisms are developed as important new elements, which allow using topological rules for the formulation of transport especially for developing bed forms. Since the most up-to-date research findings in the field are presented, this book serves as both a support in the formulation of academic research programs, and as a practical text for engineers seeking to simulate complex problems or special aspects of sediment transport. This book will therefore be of interest and of use to both students and to the professional scientist.

This text is a brief introduction to fundamental concepts of transport p- nomena within a ?uid, namely momentum, heat and mass transfer. The - phasis of the text is placed upon a basic, systematic approach from the ?uid mechanics point of view, in conjunction with a uni?ed treatment of transport phenomena. In order to make the book useful for students, there are numerous - amples. Each chapter presents a collection of proposed problems, whose so- tions can be found in the Problem Solutions Appendix. Also the Self Eva- ation chapter gathers exercises from exams, so readers and students can test their understanding of the subject. Most of the content can be taught in a course of 45 hours and has been employed in the course Transport Phenomena in Chemical Engineering at the Centro Polit ecnico Superior of the University of Zaragoza. The text is aimedatbeginnersinthesubjectoftransportphenomenaand?uidmechanics, emphasizing the foundations of the subject. Thetextisdividedintofourparts: Fundamentals, ConservationPrinciples, DimensionalAnalysis;TheoryandApplications, andTransportPhenomenaat Interfaces. In the ?rst part, Fundamentals, basic notions on the subject are int- duced: de?nition of a ?uid, preliminary hypothesis for its mathematical tre- ment, elementary kinematics, ?uid forces, especially the concept of pressure, and ?uid statics. In the Conservation Principles part, the conservation equations that g- ern transport phenomena are presented and explained, both in integral and di?erentialform.Emphasisisplacedonpracticalapplicationsofintegraleq- tions. Also, constitutive equations for transport by di?usion are contained in this part.

First concise textbook on Large-Eddy Simulation, a very important method in scientific computing and engineering

From the foreword to the third edition written by Charles Meneveau: ..". this meticulously assembled and significantly enlarged description of the many aspects of LES will be a most welcome addition to the bookshelves of scientists and engineers in fluid mechanics, LES practitioners, and students of turbulence in general."

Elementary vortices those tubular swirling vortical structures with concentrated vorticity commonly observed in various kinds of turbulent flows play key roles in turbulence dynamics (e.g. enhancement of mixing, diffusion and resistance) and characterize turbulence statistics (e.g. intermittency). Because of their dynamical importance, manipulation of elementary vortices is expected to be effective and useful in turbulence control as well as in construction of turbulence modeling. The most advanced research works on elementary vortices and related problems were presented and discussed at the IUTAM Symposium in Kyoto, Japan, 26-28 October 2004. This book contains 40 contributions presented there, the subjects of which cover vortex dynamics, coherent structures, chaotic advection and mixing, statistical properties of turbulence, rotating and stratified turbulence, instability and transition, dynamics of thin vortices, finite-time singularity, and superfluid turbulence. The book should be useful for readers of graduate and advanced levels in the field of fluid turbulence. "

These proceedings are a continuation of the series of International Conferences in Germany entitled "Mechanics of Unsaturated Soils." The primary objective is to discuss and understand unsaturated soil behaviour such that engineered activities are made better with times in terms of judgment and quality. The proceedings contain recent research by leading experts in Mechanics of Unsaturated Soils.

Ideals are simple and able to be easily understood, but never exist in reality. In this book a theory based on the second law of thermodynamics and its applications are described. In thermodynamics there is a concept of an ideal gas which satisfies a mathematical formula PV = RT. This formula can appro- mately be applied to the real gas, so far as the gas has not an especially high pressure and low temperature. In connection with the second law of thermo- namics there is also a concept of reversible and irreversible processes. The reversible process is a phenomenon proceeding at an infinitely low velocity, while the irreversible process is that proceeding with a finite velocity. Such a process with an infinitely slow velocity can really never take place, and all processes observed are always irreversible, therefore, the reversible process is an ideal process, while the irreversible process is a real process. According to the first law of thermodynamics the energy increase dU of the thermodynamic system is a sum of the heat dQ added to the system and work dW done in the system. Practically, however, the mathematical formula of the law is often expressed by the equation , or some similar equations derived from this formula, is applied to many phenomena. Such formulae are, however, th- retically only applicable to phenomena proceeding at an infinitely low velocity, that is, reversible processes or ideal processes.

Stefanescu here attempts to describe solidification theory through the complex mathematical apparatus required for a fundamental treatment of the problem. The mathematics is however restricted to the elements essential to attain a working knowledge in the field. This is in line with the main goal of the book, which is to educate the reader in the fast moving area of computational modeling of solidification of castings. A special effort has been made to introduce the reader to the latest developments in solidification theory including, in this second edition, a new chapter on semi-solid casting.

Fluid Mechanics, as a scientific discipline in a modern sense, was established between the last third of the 17th century and the first half of the 18th century. This book analyses its genesis from two lines: resistance and discharge. This approach highlights the existence of a remarkable experimental aspect in the aforementioned research lines, together with their link with problems of a practical nature, such as ballistics, hydraulics, fluid-using machines or naval theory.

Combustion systems are confined fields of compressible fluids where exothermic processes of combustion take place, subject to boundary conditions imposed at its borders. The subject of Dynamics of Combustion Systems is presented in three parts:

Part 1. Exothermicity considering the thermodynamic effects due to evolution of exothermic energy in a combustion system

Chapter 1. Thermodynamic Aspects
Chapter 2. Evolutionary Aspects
Chapter 3. Heat Transfer Aspects
Chapter 4. Chemical Kinetic Aspects

Part 2. Field exposing the dynamic properties of flow fields where the exothermic energy is deposited

Chapter 5. Aerodynamic Aspects
Chapter 6. Random Vortex Method
Chapter 7. Gasdynamic Aspects
Chapter 8. Gasdynamic Fronts

Part 3. Explosions revealing the dynamic features of fields and fronts due to rapid deposition of exothermic energy

Chapter 9. Blast Wave Theory
Chapter 10. Self-Similar Solution
Chapter 11. Phase Space Method
Chapter 12. Detonation

The nuclear thermal hydraulic is the science providing knowledge about the physical processes occurring during the transferring the fission heat released in structural materials due to nuclear reactions into its environment. Along its way to the environment the thermal energy is organized to provide useful mechanical work or useful heat or both. Chapter 1 contains introductory information about the heat release in the re- tor core, the thermal power and thermal power density in the fuel, structures and moderator, the influence of the thermal power density on the coolant temperature, the spatial distribution of the thermal power density. Finally some measures are introduced for equalizing of the spatial distribution of the thermal power density. Chapter 2 gives the methods for describing of the steady and of the transient temperature fields in the fuel elements. Some information is provided regarding influence of the cladding oxidation, hydrogen diffusion and of the corrosion pr- uct deposition on the temperature fields. Didactically the nuclear thermal hydraulic needs introductions at different level of complexity by introducing step by step the new features after the previous are clearly presented. The followed two Chapters serve this purpose. Chapter 3 describes mathematically the "simple" steady boiling flow in a pipe. The steady mass-, momentum- and energy conservation equations are solved at different level of complexity by removing one after the other simplifying assu- tions. First the idea of mechanical and thermodynamic equilibrium is introduced.

This book contains lecture notes and invited contributions presented at the NATO Advanced Study Institute and EPS Liquid State Conference on PHYSICOCHEMICAL HYDRODYNAMICS-PCH: INTERFACIAL PHENOMENA that were held July 1-15, 1986, in LA RABIDA (Huelva) SPAIN. Although we are aware of the difficulty in organizing the contents due to the broad and multidisciplinary aspects of PCH-Interfacial Phenomena, we have tried to accomodate papers by topics and have not followed the order in the presentation at the meetings. There is also no distinction between the ASI notes and Conference papers. We have done our best to offer a coverage as complete as possible of the field. However, we had difficulties coming from the fact that some authors were so busy that either did not find time to submit their contribution or did not have time to write a comprehensive paper. We also had to cope with very late arrivals, postdeadline valuable contributions that we felt had to be included here. Our gratitude goes to the NATO Scientific Affairs Division for its economic support and to the EPS Liquid State Committee for its sponsorship. Financial support also came from Asociacion Industrias Quimicas-Huelva (Spain), Caycit-Ministerio De Educacion Y Ciencia (Spain), Canon-Espana (Spain), Citibank-Espana (Spain), CNLS-Los Alamos Nat. Lab. (U. S. A. ), CSIC (Spain), EPS, ERT (Spain), ESA, Fotonica (Spain), IBM-Espana (Spain), Junta De Andalucia (Spain), NATO, NSF (U. S. A. ), ONR-London (U. S. A.

These two volumes contain the proceedings of the workshop on the Institute for Computer Instability and Transition, sponsored by Applications in Science and Engineering (ICASE) and the Langley Research Center (LaRC), during May 15 to June 9, 1989. The work shop coincided with the initiation of a new, focused research pro gram on instability and transition at LaRC. The objectives of the workshop were to (i) expose the academic community to current technologically important issues of instability and transition in shear flows over the entire speed range, (ii) acquaint the academic com munity with the unique combination of theoretical, computational and experimental capabilities at LaRC and foster interaction with these facilities, (iii) review current state-of-the-art and propose fu ture directions for instability and transition research, (iv) accelerate progress in elucidating basic understanding of transition phenomena and in transferring this knowledge into improved design methodolo gies through improved transition modeling, and (v) establish mech anisms for continued interaction. The objectives (i) to (iii) were of course immediately met. It is still premature to assess whether ob jectives (iv) and (v) are achieved. The workshop program consisted of tutorials, research presenta tions, panel discussions, experimental and computational demonstra tions, and collaborative projects.

This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer.

Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail.

A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media.

Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.

The Summer School has been dedicated to one of the proponents and ?rst Chairman of the Strategy Board of MACSI-net, the late Jacques Louis Lions (see the dedication by Roland Glowinski). MACSI-net is a European Network of Excellence, where both enterprises and university institutions co-operate to solve challenging problems to their mutual bene?t. In particular the network focuses on strategies to enhance interactions between industry and academia. The aim is to help industry (in particular SMEs) alert academia about industrial needs in terms of advanced mathematical and computational methods and tools. The network is mul- disciplinary oriented, combining the power of applied mathematics, scienti?c computing and engineering, for modeling and simulation. It was set up by a joint e?ort of ECCOMAS and ECMI European associations. Thisparticularevent,occurredduringMarch17-22,2003,wasajointe?ort ofthe TrainingCommittee (chairedby VC)andIndustrialRelationsComm- tee (chairedby JP)to alert both Academia and Industry about the increasing role of Multidisciplinary Methods and Tools for the design of complex pr- uctsinvariousareasofindustrialinterest.Thisincreasingcomplexityisdriven by societal constraints to be satis? ed in a simultaneous and a?ordable way. The mastering of complexity implies the sharing of di?erent tools by di?erent actors which require much higher level of communication between culturally di?erent people. The school o?ered to young researchers the opportunity to be exposed to the presentation of real industrial and societal problems and the relevant innovative methods used; the need of further contributions from mathematics to improve or provide better solutions had also been considered.

This volume is published as the proceedings of the third Russian-German - vanced Research Workshop on Computational Science and High Performance Computing in Novosibirsk, Russia, in July 2007. The contributions of these proceedings were provided and edited by the - thors, chosen after a careful selection and reviewing. The workshop was organized by the High Performance Computing Center Stuttgart(Stuttgart,Germany)andtheInstituteofComputationalTechnologies SBRAS(Novosibirsk,Russia)intheframeworkofactivitiesoftheGerman-Russian CenterforComputationalTechnologiesandHighPerformanceComputing. Thee event is held biannually and has already become a good tradition for German and Russian scientists. The ?rst Workshop took place in September 2003 in Novosibirskand the second Workshopwas hosted by Stuttgart in March 2005. Both workshops gave the possibility of sharing and discussing the latest results and developing further scienti?c contacts in the ?eld of computational science and high performance computing. The topics of the current workshop include software and hardware for high performancecomputation,numericalmodellingingeophysicsandcomputational ?uid dynamics, mathematical modelling of tsunami waves, simulation of fuel cellsandmodern? breopticsdevices,numericalmodellingincryptographypr- lems andaeroacoustics,interval analysis,toolsfor Gridapplications,researchon service-oriented architecture (SOA) and telemedicine technologies. Theparticipationofrepresentativesofmajorresearchorganizationsengagedin the solution of the most complex problems of mathematical modelling, devel- ment of new algorithms,programsandkey elementsof informationtechnologies, elaboration and implementation of software and hardware for high performance computing systems,provideda highlevelof competenceofthe workshop. Among the German participants were the heads and leading specialists of the HighPerformanceComputingCenterStuttgart(HLRS)(UniversityofStuttgart), NECHighPerformanceComputingEuropeGmbH,SectionofAppliedMathem- ics(UniversityofFreiburgi.Br.),InstituteofAerodynamics(RWTHAachen),- gionalComputingCenterErlangen(RRZE(UniversityofErlangen-Nuremberg), Center for High Performance Computing (ZHR) (Dresden University of Technology).

The monograph is devoted to modern mathematical models and numerical methods for solving gas- and ?uid-dynamic problems based on them. Two interconnected mathematical models generalizing the Navier-Stokes system are presented; they differ from the Navier-Stokes system by additional dissipative terms with a small parameter as a coef?cient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective ?nite-difference algorithms for calculating viscous nonstationary ?ows are constructed and examples of numerical computations are presented. The universality, the ef?ciency, and the exactness of the algorithms constructed are ensured by the ful?llment of integral conservation laws and the theorem on entropy balance for them. The book is a course of lectures and is intended for scientists and engineers who deal with constructing numerical algorithms and performing practical calculations of gas and ?uid ?ows and also for students and postgraduate students who specialize in numerical gas and ?uid dynamics.

HYDRODYNAMIC PROPULSION AND ITS OPTIMIZATION ANALYTIC THEORY Hydrodynamic propulsion has been of major interest ever since craft took to the water. In the course of time, many attempts have been made to invent, develop, or to improve hydrodynamic propulsion devices. Remarkable achievements in this field were made essentially by experienced individuals, who were in need of reliable propulsion units such as paddle wheels, sculling devices, screw propellers, and of course, sails. The problem of minimizing the amount of input energy for a prescribed effective output was first investigated seriously at the beginning of this century. In 1919, BETZ presented a paper on air-screw propellers with minimum consumption of energy which could be applied to ship-screw propellers also. Next, attempts were made to optimize hydrodynamic propulsion units. Ensuing investigations concerned the optimization of the hydrodynamic system: ship-propeller. The first simple theory of ship propulsion which was presented considered more or less only thrust augmentation, wake processing and modification of propeller characteristics when operating behind the ships hull. This theory has been little improved meanwhile and is still useful, particularly with regard to practical ship design and for evaluating results of ship model tests. However, this theory is not adequate for optimization procedures necessary for high-technology propulsion, particularly for ship propellers utilizing propulsion improving devices such as tip end plates or tip fins at the propeller blades, spoilers in front of the propeller, asymmetrical stern etc.

Drag Reduction of Turbulent Flows by Additives is the first treatment of the subject in book form. The treatment is extremely broad, ranging from physicochemical to hydromechanical aspects. The book shows how fibres, polymer molecules or surfactants at very dilute concentrations can reduce the drag of turbulent flow, leading to energy savings. The dilute solutions are considered in terms of the physical chemistry and rheology, and the properties of turbulent flows are presented in sufficient detail to explain the various interaction mechanisms. Audience: Those active in fundamental research on turbulence and those seeking to apply the effects described. Fluid mechanical engineers, rheologists, those interested in energy saving methods, or in any other application in which the flow rate in turbulent flow should be increased.

This volume contains selected presentations of the "EUROMECH Colloquium 412 on LES of complex transitional and turbulent flows" held at the Munich University of Technology from 4 to 6 October 2000.

The articles focus on new developments in the field of large-eddy simulation of complex flows and are related to the topics: modelling and analysis of subgrid scales, numerical issues in LES cartesian grids for complex geometries, curvilinear and non-structured grids for complex geometries. DES and RANS-LES coupling, aircraft wake vortices, combustion and magnetohydrodynamics.

Progress has been made not only in understanding and modelling the dynamics of unresolved scales, but also in designing means that prevent the contamination of LES predictions by discretization errors. Progress is reported as well on the use of cartesian and curvilinear coordinates to compute flow in and around complex geometries and in the field of LES with unstructured grids. A chapter is dedicated to the detached-eddy simulation technique and its recent achievements and to the promising technique of coupling RANS and LES solutions in order to push the resolution-based Reynolds number limit of wall-resolving LES to higher values.

Complexity due to physical mechanisms links the last two chapters. It is shown that LES constitutes the tool to analyse the physics of aircraft wake vortices during landing and takeoff. Its thorough understanding is a prerequisite for reliable predictions of the distance between consecutive landing airplanes. Subgrid combustion modelling for LES of single and two-phase reacting flows is demonstrated to have the potential to deal with finite-rate kinetics in high Reynolds number flows of full-scale gas turbine engines. Fluctuating magnetic fields are more reliably predicted by LES when tensor-diffusivity rather than gradient-diffusion models are used. An encouraging result in the context of turbulence control by magnetic fields.

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.

Knowledge of added body masses that interact with fluid is necessary in various research and applied tasks of hydro- and aeromechanics: steady and unsteady motion of rigid bodies, total vibration of bodies in fluid, local vibration of the external plating of different structures. This reference book contains data on added masses of ships and various ship and marine engineering structures. Also theoretical and experimental methods for determining added masses of these objects are described. A major part of the material is presented in the format of final formulas and plots which are ready for practical use.

The book summarises all key material that was published in both Russian and English-language literature.

This volume is intended for technical specialists of shipbuilding and related industries.

The author is one of the leading Russian experts in the area of ship hydrodynamics.

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.