In developing this book, we decided to emphasize applications and to provide methods for solving problems. As a result, we limited the mathematical devel opments and we tried as far as possible to get insight into the behavior of numerical methods by considering simple mathematical models. The text contains three sections. The first is intended to give the fundamen tals of most types of numerical approaches employed to solve fluid-mechanics problems. The topics of finite differences, finite elements, and spectral meth ods are included, as well as a number of special techniques. The second section is devoted to the solution of incompressible flows by the various numerical approaches. We have included solutions of laminar and turbulent-flow prob lems using finite difference, finite element, and spectral methods. The third section of the book is concerned with compressible flows. We divided this last section into inviscid and viscous flows and attempted to outline the methods for each area and give examples.
This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow, in clear and elementary terms. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.
This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow, in clear and elementary terms. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.
In developing this book, we decided to emphasize applications and to provide methods for solving problems. As a result, we limited the mathematical devel opments and we tried as far as possible to get insight into the behavior of numerical methods by considering simple mathematical models. The text contains three sections. The first is intended to give the fundamen tals of most types of numerical approaches employed to solve fluid-mechanics problems. The topics of finite differences, finite elements, and spectral meth ods are included, as well as a number of special techniques. The second section is devoted to the solution of incompressible flows by the various numerical approaches. We have included solutions of laminar and turbulent-flow prob lems using finite difference, finite element, and spectral methods. The third section of the book is concerned with compressible flows. We divided this last section into inviscid and viscous flows and attempted to outline the methods for each area and give examples.
This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow, in clear and elementary terms. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.
Navier-Stokes Equations: Theory and Numerical Analysis focuses on the processes, methodologies, principles, and approaches involved in Navier-Stokes equations, computational fluid dynamics (CFD), and mathematical analysis to which CFD is grounded. The publication first takes a look at steady-state Stokes equations and steady-state Navier-Stokes equations. Topics include bifurcation theory and non-uniqueness results, discrete inequalities and compactness theorems, existence and uniqueness theorems, discretization of Stokes equations, existence and uniqueness for the Stokes equations, and function spaces. The text then examines the evolution of Navier-Stokes equations, including linear case, compactness theorems, alternate proof of existence by semi-discretization, and discretization of the Navier-Stokes equations. The book ponders on the approximation of the Navier-Stokes equations by the projection and compressibility methods; properties of the curl operator and application to the steady-state Navier-Stokes equations; and implementation of non-conforming linear finite elements. The publication is a valuable reference for researchers interested in the theory and numerical analysis of Navier-Stokes equations.
The only film critic to win the Pulitzer Prize, Roger Ebert collects his reviews from the last 30 months in Roger Ebert's Movie Yearbook 2012. Forbes Magazine described Ebert as the "most powerful pundit in America." In January 2011, he and his wife, Chaz, launched Ebert Presents at the Movies, a weekly public television program in the tradition that he and Gene Siskel began 35 years earlier. Since 1986, each edition of Roger Ebert's Movie Yearbook has presented full-length movie reviews, with interviews, essays, tributes, journal entries, and "Questions for the Movie Answer Man," and new entries in his popular Movie Glossary. Inside Roger Ebert's Movie Yearbook 2012, readers can expect to find every movie review Ebert has written from January 2009 to July 2011, including The Social Network, Waiting for Superman, Inception, The King's Speech, My Dog Tulip, The Human Centipede, and more. Also included in the Yearbook are: * In-depth interviews with newsmakers and celebrities, such as John Waters and Justin Timberlake. * Memorial tributes to those in the film industry who have passed away, such as Blake Edwards, Tony Curtis, and Arthur Penn. * Essays on the Oscars and reports from the Cannes and Toronto Film Festivals.
Atmospheric chemistry is central to understanding global changes ? ozone depletion, appearance of the polar ozone holes, and compositional changes which worsen the greenhouse effect. Because of its importance, work is progressing on many fronts.This volume emphasizes the troposhere and stratosphere and has chapters on gas phase, condensed phase, and heterogeneous chemistry. Present progress is emphasized, and important future directions are also described.This book fills a need not satisfied by any others and will be popular for some years to come. It informs students and newcomers to the field of the many facets of atmospheric chemistry and can be used as a text for advanced students. It is also a valuable desk reference summarizing activities by quite a number of the most active research groups.Chapter 18 by Kolb et al. on heterogeneous chemistry is especially noteworthy because it represents a unique joint effort by several groups working on a very timely subject; they describe a conceptual framework and establish conventions which will be standard in future papers on this subject.
Roger Ebert’s “criticism shows a nearly unequaled grasp of film history and technique, and formidable intellectual range. . . .” —New York Times Pulitzer Prize–winning film critic Roger Ebert presents more than 600 full-length critical movie reviews, along with interviews, tributes, and journal entries inside Roger Ebert’s Movie Yearbook 2013. It includes every movie review Ebert has written from January 2010 to July 2012. Also included in the Yearbook: In-depth interviews with newsmakers and celebrities Tributes to those in the film industry who have passed away recently Essays on the Oscars, reports from the Toronto Film Festival, and entries into Ebert's Little Movie Glossary
This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds. Inertial manifolds were first introduced under this name in 1985 and, since then, have been systematically studied for partial differential equations of the Navier-Stokes type. Inertial manifolds are a global version of central manifolds. When they exist they encompass the complete dynamics of a system, reducing the dynamics of an infinite system to that of a smooth, finite-dimensional one called the inertial system. Although the theory of inertial manifolds for Navier-Stokes equations is not complete at this time, there is already a very interesting and significant set of results which deserves to be known, in the hope that it will stimulate further research in this area. These results are reported in this edition.
Born in 1916, Henri Dutilleux is one of France‘s leading composers, enjoying an international reputation for his beautifully crafted works. This is the first translation into English of a series of interviews between Dutilleux and the French writer and journalist Claude Glayman which took place in 1996. Dutilleux discusses aspects of his life including his early training at the Paris Conservatoire, the German occupation of France and the time that he spent in the United States. The interviews reveal much about his music and his approach to composition, as well as the influences on his musical style. Originally published by Actes Sud in 1997, this English edition is the work of translator Roger Nichols, one of the UK‘s leading specialists on French music.
With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.
Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases. This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.
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