The book covers selected problems in free surface flows. The topics range from linear and nonlinear gravity and capillary waves, thin film dynamics, equilibrium shape, stability, and dynamics of capillary surfaces to thermal Marangoni effects in several geometries. The fluid dynamical problems are supplemented by a review Eulerian based computational methods.

Nuclear Thermal-Hydraulic Systems provides a comprehensive approach to nuclear reactor thermal-hydraulics, reflecting the latest technologies, reactor designs, and safety considerations. The text makes extensive use of color images, internet links, computer graphics, and other innovative techniques to explore nuclear power plant design and operation. Key fluid mechanics, heat transfer, and nuclear engineering concepts are carefully explained, and supported with worked examples, tables, and graphics. Intended for use in one or two semester courses, the text is suitable for both undergraduate and graduate students. A complete Solutions Manual is available for professors adopting the text.

Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.

This volume contributes to one of the most important topics of Fluid Mechanics in future and presents recent research results on control theory and applied control methods. Understanding and handling of control methods of nonlinear systems, typical of Fluid Mechanics, is the key to reduce losses and to improve the efficiency and safety of technical processes.

Numerical large-eddy simulation techniques are booming at present and will have a decisive impact on industrial modeling and flow control. The book represents the general framework in physical and spectral space. It also gives the recent subgrid-scale models. Topics treated include compressible turbulence research, turbulent combustion, acoustic predictions, vortex dynamics in non-trivial geometries, flows in nuclear reactors and problems in atmospheric and geophysical sciences. The book addresses numerical analysts, physicists, and engineers.

These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.

This well-known 2-volume textbook provides senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques in the various branches of computational fluid dynamics. In Volume 2 specific techniques are described for inviscid, compressible, boundary layer and separating flow. Grid generation and the use of generalized coordinates for complex geometric domains are dealt with in detail. The most modern methods (including many computer programs) are described in connection with real problems in the field of fluid dynamics. For the the second edition the author also compiled a separately available manual of solutions to the many exercises to be found in the main text.

Prof. Newman is considered one of the great chemical engineers of his time. His reputation derives from his mastery of all phases of the subject matter, his clarity of thought, and his ability to reduce complex problems to their essential core elements. He is a member of the National Academy of Engineering, Washington, DC, USA, and has won numerous national awards including every award offered by the Electrochemical Society, USA. His motto, as known by his colleagues, is "do it right the first time." He has been teaching undergraduate and graduate core subject courses at the University of California, Berkeley (UC Berkeley), USA, since joining the faculty in 1966. His method is to write out, in long form, everything he expects to convey to his class on a subject on any given day. He has maintained and updated his lecture notes from notepad to computer throughout his career. This book is an exact reproduction of those notes. This book shows a clean and concise way on how to use different analytical techniques to solve equations of multiple forms that one is likely to encounter in most engineering fields, especially chemical engineering. It provides the framework for formulating and solving problems in mass transport, fluid dynamics, reaction kinetics, and thermodynamics through ordinary and partial differential equations. It includes topics such as Laplace transforms, Legendre's equation, vector calculus, Fourier transforms, similarity transforms, coordinate transforms, conformal mapping, variational calculus, superposition integrals, and hyperbolic equations. The simplicity of the presentation instils confidence in the readers that they can solve any problem they come across either analytically or computationally.

Modern Methods in Analytical Acoustics considers topics fundamental to the understanding of noise, vibration and fluid mechanisms. The series of lectures on which this material is based began by some twenty five years ago and has been developed and expanded ever since. Acknowledged experts in the field have given this course many times in Europe and the USA. Although the scope of the course has widened considerably, the primary aim of teaching analytical techniques of acoustics alongside specific areas of wave motion and unsteady fluid mechanisms remains. The distinguished authors of this volume are drawn from Departments of Acoustics, Engineering of Applied Mathematics in Berlin, Cambridge and London. Their intention is to reach a wider audience of all those concerned with acoustic analysis than has been able to attend the course.

Das Buch fuhrt in die CAE-Methoden ein und behandelt die spezifischen Fragestellungen von CAE-Methoden in der Fahrzeugtechnik. Zunachst werden Grundlagen zur Modellbildung und zu Diskretisierungsverfahren fur partielle Differentialgleichungen dargestellt. Die anschliessenden Kapitel beschreiben die Inhalte Temperaturausgleich, Mehrkorpersimulationen sowie Statik und Dynamik elastischer Korper. Es folgt ein Kapitel uber Finite-Elemente. Anschliessend werden die fahrzeugspezifischen Themen Crash- und Insassensimulation, Akustik, Statik und Dynamik von Rohkarosserien, Mehrkorpersimulationen und Lebensdauer, Stromungssimulation und Reifen-Fahrbahn-Wechselwirkungen behandelt. Erganzt werden die Inhalte durch Kapitel uber nichtlineare Phanomene und Optimierungsverfahren."

This volume contains contributions to the BRI-TE/EURAM, Area 5, Pilot phase programme on the validation of computational fluid dynamics (CFD) codes, EUROVAL. Two- and three-dimensional flows are investigated with particular emphasis on precise comparison against measurements, with special attention paid to the validation of turbulence models investigated by the 16 project partners. The main part of this volume is designated to the validation of turbulence models on a boundary layer and Navier-Stokes basis, presented in an application-oriented structure for single- and two-element aerofoils, internal flow over bumps, wind-tunnel-interference problems and a vortex breakdown study.

This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use."

Modern continuum mechanics is the topic of this book. After its introduction it will be applied to a few typical systems arising in the environmental sciences and in geophysics. In large lake/ocean dynamics peculiar effects of the rotation of the Earth will be analyzed in linear/nonlinear processes of a homogenous and inhomogenous water body. Strong thermomechanical coupling paired with nonlinear rheology affects the flow of large ice sheets (such as Antarctica and Greenland) and ice shelves. Its response to the climatic forcing in an environmental of greenhouse warming may significantly affect the life of future generations. The mechanical behavior of granular materials under quasistatic loadings requires non-classical mixture concepts and encounters generally complicated elastic-plastic-type constitutive behavior. Creeping flow of soils, consolidation processes and ground water flow are described by such theories. Rapid shearing flow of granular materials lead to constitutive relations for the stresses which incorporate rate independent behavior of Mohr-Coulomb type together with dispersive stress contributions due to particle collisions. Rockfalls, sturzstroms, snow and ice avalanches, but also debris flow and sea ice drifting can be described with such formulations.

Supercomputer technologies have evolved rapidly since the first commercial-based supercomputer, CRAY-1 was introduced in 1976. In early 1980's three Japanese super computers appeared, and Cray Research delivered the X-MP series. These machines including the later-announced CRAY-2 and NEC SX series created one generation of supercomputers, and the market was spread dramatically. The peak performance was higher than 1 GFLOPS and the compiler improvement was remarkable. There appeared many articles and books that described their architecture and their performance on The late 1980's saw a new generation of supercomputers. several benchmark problems. Following CRAY Y-MP and Hitachi S-820 delivered in 1988, NEC announced SX-3 and Fujitsu announced the VP2000 series in 1990. In addition, Cray Research announced the Y-MP C-90 late in 1991. The peak performance of these machines reached several to a few ten's GFLOPS. The hardware characteristics of these machines are known, but their practical performance has not been well documented so far. Computational Fluid Dynamics (CFD) is one of the important research fields that have been progressing with the growth of supercomputers. Today's fluid dynamic re search cannot be discussed without supercomputers and since CFD is one of the im portant users of supercomputers, future development of supercomputers has to take the requirements of CFD into account. There are many benchmark reports available today. However, they mostly use so called kernels. For fluid dynamics researchers, benchmark test on real fluid dynamic codes are necessary."

This volume contains 37 contributions in which the research work is summarized which has been carried out between 1984 and 1990 in the Priority Research Program "Physik abgeloster Stromungen" of the Deutsche Forschungsgemeinschaft (DFG, German Research Society). The aim of the Priority Research Program was the inten sive research of the whole range of phenomena associated with separated flows. Physi cal models as well as prediction methods had to be developed based on detailed experi mental investigations. It was in accordance with the main concept of the research program that scientists working on problems of separated flows in different technical areas of application participated in this program. The following fields have been represented in the program: aerodynamics of wings and bodies, aerodynamics of auto mobiles, turbomachinery, ship hydrodynamics, hydraulics, internal flows, heat exchan gers, bio-fluid-dynamics, aerodynamics of buildings and structures. In order to concentrate on problems common in all those areas the emphasis of the program was on basic research dealing with generic geometric configurations showing the fundamental physical phenomena of separated flows. The engagement and enthusiasm of all participating scientists are highly appreciated. The program was organized such that all researchers met once a year to report on the progress of their work. Special thanks ought to go to Prof. E. A. Muller (Gottingen), Prof. H. Oertel jun. (Braunschweig), Dr. W. Schmidt (Dornier), Dr. H. -W. Stock (Dornier) and Dr. B. Wagner (Dornier), who had the functions of referees on those annual meetings."

The aim of the 1989 GAMM Workshop on 3D-Computation of Incompressible Internal Flows was the simulation of a realistic incompressible flow field in an important industrial application. In view of the difficulties involved in formulating such a test case, requiring the availability of an experimental data base, extreme care had to be taken in the selection of the proper one. Professor I. L. Ryhming's proposal, that the flow through a Francis turbine configuration or parts thereof would be feasible as a test case, because of the numerical challenges as well as the possibility to produce an experimental data base by using the experimental facilities of the Hydraulic Machines and Fluid Mechanics Institute (IMHEF) at the Swiss Federal Institute of Technology in Lausanne (EPFL), was accepted by the GAMM Committee in April 1987. A scientific committee, formed under the chairmanship of Professor I. L. Ryhming, met a few times to decide on the Francis turbine configuration, the test case specifications, etc. , whereby the design input came from the water turbine experts. This committee decided to restrict the studies to the three following typical applications for the best operating point of the turbine: * simulation of the 3D flow in a Francis runner in rotation * simulation of the 3D flow in the distributor (stay and guide vane rings) of this turbine * simulation of the 3D flow in an elbow draft tube The simultaneous computation of two or three of these geometries was encouraged.

11 The GAMM Committee for Efficient Numerical Methods for Partial 11 Differential Equations organises workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various types of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such workshops was continued in 1991, January 25- 27, with the 7th Kiel-Seminar on the special topic 11 11 Numerical techniques for boundary element methods at the Christian-Albrechts-University of Kiel. The seminar was attended by 57 scientists from 8 countries. The list of topics contained applications of the boundary element method (BEM) to various problems of practical interest, algo rithmic aspects of the BEM (coupling with finite element method, parallelisation), convergence analysis, and in particular the treatment of the numerical integration. In six contributions the quadrature of weakly singular, Cauchy singular, and hypersingular integrals is analysed. 11 11 The editor thanks the DFG-Schwerpunkt Randelementmethoden for its support. He also likes to express his gratitude to all persons involved in the organisation of the seminar."

V.A. Solonnikov, A. Tani: Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid.- W. Borchers, T. Miyakawa: On some coercive estimates for the Stokes problem in unbounded domains.- R. Farwig, H. Sohr: An approach to resolvent estimates for the Stokes equations in L(q)-spaces.- R. Rannacher: On Chorin's projection method for the incompressible Navier-Stokes equations.- E. S}li, A. Ware: Analysis of the spectral Lagrange-Galerkin method for the Navier-Stokes equations.- G. Grubb: Initial value problems for the Navier-Stokes equations with Neumann conditions.- B.J. Schmitt, W. v.Wahl: Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations.- O. Walsh: Eddy solutions of the Navier-Stokesequations.- W. Xie: On a three-norm inequality for the Stokes operator in nonsmooth domains.

The volume presents a comprehensive overview of rotation effects on fluid behavior, emphasizing non-linear processes. The subject is introduced by giving a range of examples of rotating fluids encountered in geophysics and engineering. This is then followed by a discussion of the relevant scales and parameters of rotating flow, and an introduction to geostrophic balance and vorticity concepts. There are few books on rotating fluids and this volume is, therefore, a welcome addition. It is the first volume which contains a unified view of turbulence in rotating fluids, instability and vortex dynamics. Some aspects of wave motions covered here are not found elsewhere.

Replacing the Traditional Physical Model Approach Computational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change and evolve. Modeling Shallow Water Flows Using the Discontinuous Galerkin Method examines a technique that focuses on hyperbolic conservation laws and includes one-dimensional and two-dimensional shallow water flows and pollutant transports. Combines the Advantages of Finite Volume and Finite Element Methods This book explores the discontinuous Galerkin (DG) method, also known as the discontinuous finite element method, in depth. It introduces the DG method and its application to shallow water flows, as well as background information for implementing and applying this method for natural rivers. It considers dam-break problems, shock wave problems, and flows in different regimes (subcritical, supercritical, and transcritical). Readily Adaptable to the Real World While the DG method has been widely used in the fields of science and engineering, its use for hydraulics has so far been limited to simple cases. The book compares numerical results with laboratory experiments and field data, and includes a set of tests that can be used for a wide range of applications. Provides step-by-step implementation details Presents the different forms in which the shallow water flow equations can be written Places emphasis on the details and modifications required to apply the scheme to real-world flow problems This text enables readers to readily understand and develop an efficient computer simulation model that can be used to model flow, contaminant transport, and other aspects in rivers and coastal environments. It is an ideal resource for practicing environmental engineers and researchers in the area of computational hydraulics and fluid dynamics, and graduate students in computational hydraulics.

This valuable volume provides a broad understanding of the main computational techniques used for processing reclamation of fluid and solid mechanics. The aim of these computational techniques is to reduce and eliminate the risks of mechanical systems failure in hydraulic machines. Using many computational methods for mechanical engineering problems, the book presents not only a platform for solving problems but also provides a wealth of information to address various technical aspects of troubleshooting of mechanical system failure. The focus of the book is on practical and realistic fluids engineering experiences. Many photographs and figures are included, especially to illustrate new design applications and new instruments.

This monograph is the result of my PhD thesis work in Computational Fluid Dynamics at the Massachusettes Institute of Technology under the supervision of Professor Earll Murman. A new finite element al gorithm is presented for solving the steady Euler equations describing the flow of an inviscid, compressible, ideal gas. This algorithm uses a finite element spatial discretization coupled with a Runge-Kutta time integration to relax to steady state. It is shown that other algorithms, such as finite difference and finite volume methods, can be derived using finite element principles. A higher-order biquadratic approximation is introduced. Several test problems are computed to verify the algorithms. Adaptive gridding in two and three dimensions using quadrilateral and hexahedral elements is developed and verified. Adaptation is shown to provide CPU savings of a factor of 2 to 16, and biquadratic elements are shown to provide potential savings of a factor of 2 to 6. An analysis of the dispersive properties of several discretization methods for the Euler equations is presented, and results allowing the prediction of dispersive errors are obtained. The adaptive algorithm is applied to the solution of several flows in scramjet inlets in two and three dimensions, demonstrat ing some of the varied physics associated with these flows. Some issues in the design and implementation of adaptive finite element algorithms on vector and parallel computers are discussed."

The numerical simulation of the Euler equations of Fluid Dynamics has been these past few years a challenging problem both for research scientists and aerospace engineers. The increasing interest of more realistic models such as the Euler equations originates in Aerodynamics and also Aerothermics where aerospace applications such as military aircrafts and also space vehicles require accurate and efficient Euler solvers (which can be extended to more complicated modelisations including non-equilibrium chemistry) for su personic and hypersonic flows at high angles of attack and Mach number regimes involving strong shocks and vorticity. This book contains the proceedings of the GAMM Workshop on the Numerical Simu lation of Compressible Euler Flows. that W: LS held at INRIA, Rocquencourt (France), on June 10-13, 1986. The purpose of this event was to compare in terms of accuracy and efficiency several codes for solving compressible inviscid, mainly steady, Euler flows. This workshop was a sequel of the GAMM workshop held in 1979 in Stockholm; this time, though, because of the present strong activity in numerical methods for the Euler equat.ions, the full-potential approach was not included. Since 1979, other Eulpr workshops have been organised, sev eral of them focussed on airfoil calculations; however, many recently derived methods were not presented at these workshops, because, among other reasons, the methods were not far enough developed, or had not been applied to flow problems of sufficient complexity. In fact, the 1986 GAMM workshop scored very high as regards to the novelty of methods."