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This book details a systematic characteristics-based finite element procedure to investigate incompressible, free-surface and compressible flows. Several sections derive the Fluid Dynamics equations from thermo-mechanics principles and develop this multi-dimensional and infinite-directional upstream procedure by combining a finite element discretization with an implicit non-linearly stable Runge-Kutta time integration for the numerical solution of the Euler and Navier Stokes equations. Based on the mathematics and physics of multi-dimensional characteristics, convection as well as acoustics, and inducing by design a controllable multi-dimensional upwind bias that can be locally optimized, the procedure crisply captures contact discontinuities, normal as well as oblique shocks, and generates essentially non-oscillatory solutions for incompressible, subsonic, transonic, supersonic, and hypersonic inviscid and viscous flows with chemical reactions and work, heat and mass transfer.

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This volume collects the contributions of a conference held in June 2005, at the laboratoire Paul Painlevé (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in fluid dynamics, with the objective to foster exchanges of theoretical and numerical viewpoints.

The content of the volume can be split into three categories:

A first set of contributions is devoted to the description of the connection between different models of fluid dynamics. An important part of these papers relies on the discussion of the modeling issues, the identification of the relevant dimensionless coefficients, and on the physical interpretation of the models.

A second set of contributions considers the question of the stability of particular structures in fluid mechanics equations.

The third set of contributions is concerned with numerical issues; it is indeed a crucial challenge to design numerical schemes that are able to capture the complex features generated by fluid flows.

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The monograph is devoted to modern mathematical models and numerical methods for solving gas- and fluid-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 coefficient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective finite-difference algorithms for calculating viscous non-stationary flows are constructed and examples of numerical computations are presented. The universality, the efficiency, and the exactness of the algorithms constructed are ensured by the fulfillment 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 fluid flows and also for students and post-graduated students who specialize in numerical gas and liquid dynamics

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This book has grown out of the author's lecture notes for aninterdisciplinary graduate-level course on nonlinear dynamics. Theauthor describes in a clear and coherent way the basic concepts,language and results of nonlinear dynamical systems. In order to allowfor an interdisciplinary readership, an informal style has beenadopted and the mathematical formalism kept to a minimum.
The book starts with a discussion of nonlinear differential equations,bifurcation theory and Hamiltonian dynamics. It then embarks on asystematic discussion of the traditional topics of modern nonlineardynamics - integrable systems, Poincaré maps, chaos,fractals and strange attractors. Baker's transformation, the logisticmap and the Lorenz system are discussed in detail. Finally, there aresystematic discussions of the application of fractals to turbulence influids, and the Painlevé property of nonlinear differentialequations. Exercises are given at the end of each chapter.
This book is accessible to first-year graduate students in appliedmathematics, physics and engineering, and is useful to anytheoretically inclined researcher in physical sciences andengineering. Among the unique features of this book are:

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Fluid mechanics is the study of how fluids move and the forces that develop as a result. Fluids include liquids and gases and fluid flow can be either laminar or turbulent. This book presents a level set based methodology that will avoid problems in potential flow models with moving boundaries. A review of the state-of-the-art population balance modelling techniques that have been adopted to describe the nature of dispersed phase in multiphase problems is presented as well. Recent works that are aimed at putting forward the main ideas behind a new theoretical approach to turbulent wall-bounded flows are examined, including a state-of-the-art review on single-phase incompressible fluid flow. ... Read more

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This book considers the main hydrodynamic aspects of thedynamics of bubbles, drops and rigid particles with a special emphasison the deformations and hydrodynamic interactions between fluidparticles in uniform or shear flows and hydrodynamic interactionsbetween rigid spherical particles in an oscillatory flow. There is noother published book to date which reveals these topics in thedescribed manner.
Readers should have a basic understanding of introductory fluidmechanics, real analysis and numerical methods. The book provides thebasis for quantitative description of the phenomena that occur in thedynamics of bubbles, drops and rigid particles.
The book is intended to serve both as a graduate textbook for studentsin chemical engineering, physics and applied mathematics, and as areference monograph for academic and industrial researchers. ... Read more

Customer Reviews (1)

Perfect!
I've used this book as a basic of my Ph. D. work. It's written in very intelligiblestyle but also has a very good scientific value! I'm recommending the book to those who has been interested in fluid dynamics! ... Read more

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Volume 1 - Engineering science is presently contributing enormously to the improvement of quality of health and patient care, and physicians, clinical engineers and paramedics are increasingly dependent on high-tech apparatus for diagnosis, therapy or research. This technical revolution has encouraged the use of fluid dynamic principles for solving flow and fluid problems within the cardiovascular system, in extracorporeal circulation and artificial organs. Featuring a collection of expert reviews in lecture note format, Intra and Extracorporeal Cardiovascular Fluid Dynamics: General Principles in Application contains contributions from active members of international biomedical engineering organisations such as the IFMBE, the ISAO, the ESEM, the ESAO and the INFA. A comprehensive introduction for students, it also provides a state-of-the-art guide for investigators working in this fascinating and complex field. Volume 2 - This book contains a collection of expert reviews of new computational techniques to simulate blood-wall interaction in the cardiovascular system. It is the result of two three-day courses organised within the COMETT (Community Action Programme for Education and Training for Technology) programme of the European Community and many of the contributors are active members of international biomedical organisations such as the IFMBE, the ESEM, the ESAO, the INFA, and the ESB. Featuring a collection of expert reviews in lecture note format, the text provides both a comprehensive introduction for students, and a state-of-the-art guide for investigators working in the fascinating and complex field of computational cardiovascular mechanics. ... Read more

Customer Reviews (1)

could be better
Good contents, but graphics and pagination could be better (it has a fashion of cut&paste) compared with the price. All figures of ch.3 are missing. ... Read more

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The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time, having won the Boltzmann Medal (1986), the Dirac Medal (1992), Dannie Heinemann Prize for Mathematical Physics (1989), Nemmers Prize (2002), and the Wolf Prize in Mathematics (1997).  He is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields, and this book should be of interest to researchers from all fields of the physical sciences.This volume follows Volume I.

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This text offers a systematic and practical introduction to the discontinuous finite element method. It moves from a brief review of the fundamental laws and equations governing thermal and fluid systems, through a discussion of different approaches to the formulation of discontinuous finite element solutions for boundary and initial value problems, to their applicaton in a variety of thermal-system and fluid-related problems. Mesh generation and adaptivity, parellelization algorithms and error analysis are also introduced and explained.

Each chapter features worked examples and exercises illustrating situations ranging from simple benchmarks to practical engineering questions.

The book forms a foundation of senior undergraduate and graduate learning and also provides scientists, applied mathematicians and research engineers with a thorough treatment of basic concepts, specific techniques and methods for the use of discontinuous Galerkin methods in fluid dynamics and heat transfer applications.

Customer Reviews (1)

Indispensable reference
This is a good starting point for the reader interested in rheology or polymer dynamics. Many definitions and concepts widely used in the field of rheology of complex fluids can be found in this work. One of the introductory chapters is dedicated to qualitatively explain the most counter intuitive phenomena found in polymeric liquids. The rest of the book is primarily devoted to describe a variety of models, frequently illustrated with experimental data. The models are provided in a self-contained fashion, facilitating their use nad understanding.
Vol. I is a detailed introduction to rheology, with plenty of exercises. Explains in a clear way a variety of concepts such as material functions, and many classical models. Contains useful tables and appendices.
Vol. II also has good appendices and tables. It goes in detail through several microscopic models of polymers, starting from the simplest ones. Chapters are of increasing difficulty, getting more and more technical through the book, a good idea is to work the problems and exercises in detail. After this process is likely that the reader will be able to understand many polymer rheology papers. ... Read more

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This symposium brought together mechanicians, physicists and applied mathematicians to discuss the interdisciplinary topic of nonlinear wave motion, which displays effects that give rise to a multitude of unanswered questions. Nonlinear waves in fluids in particular display all the prominent nonlinear phenomena such as chaos, turbulence and pattern formation. Amongst the topics emphasized in these proceedings are: travelling fronts, solitary waves and periodic waves (dissipative and conservative); temporal and spatial asymptotics of perturbations of waves; bifurcations, stability and local dynamics of waves; interaction between different waves, and between waves and the mean flow; wave breaking, nonlinear effects on focusing and diffraction; modulation and envelope equations (their derivation and validity); and numerical and experimental results. ... Read more