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Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.
Non-Newtonian flows and their numerical simulations have generated an abundant literature, as well as many publications and references to which can be found in this volume's articles. This abundance of publications can be explained by the fact that non-Newtonian fluids occur in many real life situations: the food industry, oil & gas industry, chemical, civil and mechanical engineering, the bio-Sciences, to name just a few. Mathematical and numerical analysis of non-Newtonian fluid flow models provide challenging problems to partial differential equations specialists and applied computational mathematicians alike. This volume offers investigations. Results and conclusions that will no doubt be useful to engineers and computational and applied mathematicians who are focused on various aspects of non-Newtonian Fluid Mechanics. - New review of well-known computational methods for the simulation viscoelastic and viscoplastic types - Discusses new numerical methods that have proven to be more efficient and more accurate than traditional methods - Articles that discuss the numerical simulation of particulate flow for viscoelastic fluids
These Proceedings contain a selection of the lectures given at the conference BAIL 2008: Boundary and Interior Layers – Computational and Asymptotic Methods, which was held from 28th July to 1st August 2008 at the University of Limerick, Ireland. The ?rst three BAIL conferences (1980, 1982, 1984) were organised by Professor John Miller in Trinity College Dublin, Ireland. The next seven were held in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth (2002),Toulouse(2004),and Got ̈ tingen(2006).With BAIL 2008the series returned to Ireland. BAIL 2010 is planned for Zaragoza. The BAIL conferences strive to bring together mathematicians and engineers whose research involves layer phenomena,as these two groups often pursue largely independent paths. BAIL 2008, at which both communities were well represented, succeeded in this regard. The lectures given were evenly divided between app- cations and theory, exposing all conference participants to a broad spectrum of research into problems exhibiting solutions with layers. The Proceedings give a good overview of current research into the theory, app- cation and solution (by both numerical and asymptotic methods) of problems that involve boundaryand interior layers. In addition to invited and contributed lectures, the conference included four mini-symposia devoted to stabilized ?nite element methods, asymptotic scaling of wall-bounded ?ows, systems of singularly p- turbed differential equations, and problems with industrial applications (supported by MACSI, the Mathematics Applications Consortium for Science and Industry). These titles exemplify the mix of interests among the participants.
Rheology is a component of Encyclopedia of Chemical Sciences, Engineering and Technology Resources in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty Encyclopedias. Rheology is the study of the flow of matter. It is classified as a physics discipline and focuses on substances that do not maintain a constant viscosity or state of flow. That can involve liquids, soft solids and solids that are under conditions that cause them to flow. It applies to substances which have a complex molecular structure, such as muds, sludges, suspensions, polymers and other glass formers, as well as many foods and additives, bodily fluids and other biological materials. The theme on Rheology focuses on five main areas, namely, basic concepts of rheology; rheometry; rheological materials, rheological processes and theoretical rheology. Of course, many of the chapters contain material from more than one general area. Rheology is an interdisciplinary subject which embraces many aspects of mathematics, physics, chemistry, engineering and biology. These two volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.
Filling a gap in the literature and all set to become the standard in this field, this monograph begins with a look at computational viscoelastic fluid mechanics and studies of turbulent flows of dilute polymer solutions. It then goes on discuss simulations of nanocomposites, polymerization kinetics, computational approaches for polymers and modeling polyelectrolytes. Further sections deal with tire optimization, irreversible phenomena in polymers, the hydrodynamics of artificial and bacterial flagella as well as modeling and simulation in liquid crystals. The result is invaluable reading for polymer and theoretical chemists, chemists in industry, materials scientists and plastics technologists.
This book presents recent advances in computational methods for polymers. It covers multiscale modeling of polymers, polymerization reactions, and polymerization processes as well as control, monitoring, and estimation methods applied to polymerization processes. It presents theoretical insights gained from multiscale modeling validated with exprimental measurements. The book consolidates new computational tools and methods developed by academic researchers in this area and presents them systematically. The book is useful for graduate students, researchers, and process engineers and managers.
The areas of suspension mechanics, stability and computational rheology have exploded in scope and substance in the last decade. The present book is one of the first of a comprehensive nature to treat these topics in detail. The aim of the authors has been to highlight the major discoveries and to present a number of them in sufficient breadth and depth so that the novice can learn from the examples chosen, and the expert can use them as a reference when necessary.The first two chapters, grouped under the category General Principles, deal with the kinematics of continuous media and the balance laws of mechanics, including the existence of the stress tensor and extensions of the laws of vector analysis to domains bounded by fractal curves or surfaces. The third and fourth chapters, under the heading Constitutive Modelling, present the tools necessary to formulate constitutive equations from the continuum or the microstructural approach. The last three chapters, under the caption Analytical and Numerical Techniques, contain most of the important results in the domain of the fluid mechanics of viscoelasticity, and form the core of the book.A number of topics of interest have not yet been developed to a theoretical level from which applications can be made in a routine manner. However, the authors have included these topics to make the reader aware of the state of affairs so that research into these matters can be carried out. For example, the sections which deal with domains bounded by fractal curves or surfaces show that the existence of a stress tensor in such regions is still open to question. Similarly, the constitutive modelling of suspensions, especially at high volume concentrations, with the corresponding particle migration from high to low shear regions is still very sketchy.
This book consists of two strongly interweaved parts: the mathematical theory of stochastic processes and its applications to molecular theories of polymeric fluids. The comprehensive mathematical background provided in the first section will be equally useful in many other branches of engineering and the natural sciences. The second part provides readers with a more direct understanding of polymer dynamics, allowing them to identify exactly solvable models more easily, and to develop efficient computer simulation algorithms in a straightforward manner. In view of the examples and applications to problems taken from the front line of science, this volume may be used both as a basic textbook or as a reference book. Program examples written in FORTRAN are available via ftp from ftp.springer.de/pub/chemistry/polysim/.
Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the range of the larger scales. Challenging multiscale problems are very common and are found in e.g. materials science, fluid mechanics, electrical and mechanical engineering. Homogenization, subgrid modelling, heterogeneous multiscale methods, multigrid, multipole, and adaptive algorithms are examples of methods to tackle these problems. This volume is an overview of current mathematical and computational methods for problems with multiple scales with applications in chemistry, physics and engineering.