Mathematical Analysis of Viscoelastic Flows PDF Download

Author: Michael Renardy
Publisher: SIAM
ISBN: 9780898719413
Category : Mathematics
Languages : en
Pages : 113

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Book Description
This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.

Author: Michael Renardy
Publisher: SIAM
ISBN: 0898714575
Category : Mathematics
Languages : en
Pages : 110

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Book Description
This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.

Author: Arthur S. Lodge
Publisher: Academic Press
ISBN: 1483263355
Category : Technology & Engineering
Languages : en
Pages : 456

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Book Description
Viscoelasticity and Rheology covers the proceedings of a symposium by the same title, conducted by the Mathematics Research Center held at the University of Wisconsin-Madison on October 16-18, 1984. The contributions to the symposium are divided into four broad categories, namely, experimental results, constitutive theories, mathematical analysis, and computation. This 16-chapter work begins with experimental topics, including the motion of bubbles in viscoelastic fluids, wave propagation in viscoelastic solids, flows through contractions, and cold-drawing of polymers. The next chapters covering constitutive theories explore the molecular theories for polymer solutions and melts based on statistical mechanics, the use and limitations of approximate constitutive theories, a comparison of constitutive laws based on various molecular theories, network theories and some of their advantages in relation to experiments, and models for viscoplasticity. These topics are followed by discussions of the existence, regularity, and development of singularities, change of type, interface problems in viscoelasticity, existence for initial value problems and steady flows, and propagation and development of singularities. The remaining chapters deal with the numerical simulation of flow between eccentric cylinders, flow around spheres and bubbles, the hole pressure problem, and a review of computational problems related to various constitutive laws. This book will prove useful to chemical engineers, researchers, and students.

Author: Mauro Fabrizio
Publisher: SIAM
ISBN: 0898712661
Category : Science
Languages : en
Pages : 210

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Book Description
Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.

Author: Jose Francisco Rodrigues
Publisher: CRC Press
ISBN: 1000115232
Category : Mathematics
Languages : en
Pages : 280

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Book Description
This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.

Author: Michel Deville
Publisher: Springer Science & Business Media
ISBN: 364225294X
Category : Mathematics
Languages : en
Pages : 278

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Book Description
Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics. In doing so it supplies the means to design mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non-Newtonian fluids such as those required in food processing and polymeric flows. The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian, viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory, especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomial representations and accounting for non-inertial and curvature effects. Ranging from fundamental concepts to practical methodology, and including discussion of emerging technologies, this book is ideal for those requiring a single-source assessment of current practice in this intricate yet vital field.

Author: Patrick Le Tallec
Publisher:
ISBN: 9783540524502
Category : Mathematical physics
Languages : en
Pages : 136

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Book Description
The problem of computing the deformations of viscoelastic, viscoplastic or elastoplastic bodies is of great relevance to practical problems e.g. in the numerical modelling of viscoelastic structures of hot metal forming or of polymer melt flows. This book shows how such practical engineering problems may be written as standard problems of functional analysis and how this mathematical framework is used for their analysis and numerical solution. The author looks at the mechanical and the mathematical problem in a unified context, especially for the case of nonlinear Maxwell problems, and gives a mixed discrete formulation for viscoelastic flow problems. Some classical numerical strategies are described as extensions of the mathematical theory. The treatment is restricted to small strain situations (with an introduction to the large strain problem at the end) and to constitute laws of differential type, and will be of interest to researchers and graduate students in mechanical engineering, computer science and applied mathematics.

Author: Giovanni P. Galdi
Publisher: Springer Science & Business Media
ISBN: 3764378069
Category : Medical
Languages : en
Pages : 512

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Book Description
This book surveys research results on the physical and mathematical modeling, as well as the numerical simulation of complex fluid and structural mechanical processes occurring in the human blood circulation system. Topics treated include continuum mechanical description; choice of suitable liquid and wall models; mathematical analysis of coupled models; numerical methods for flow simulation; parameter identification and model calibration; fluid-solid interaction; mathematical analysis of piping systems; particle transport in channels and pipes; artificial boundary conditions, and many more. The book was developed from lectures presented by the authors at the Oberwolfach Research Institute (MFO), in Oberwolfach-Walke, Germany, November, 2005.

Author: Philippe G. Ciarlet
Publisher: Elsevier
ISBN: 0444530479
Category : Mathematics
Languages : en
Pages : 827

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Book Description
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.

Author: Amr Guaily
Publisher: LAP Lambert Academic Publishing
ISBN: 9783846521007
Category :
Languages : en
Pages : 156

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Book Description
Although viscoelastic flows are characterized by a very low Mach number regime, it involves a weakly compressible liquid phase, which requires a special treatment. This work is devoted to the mathematical modeling and numerical simulation for viscoelastic fluids. It follows directly a previous publication, PhD dissertation of the author. A Unified purely hyperbolic mathematical model for compressible and incompressible viscoelastic fluids is presented. To complete the mathematical model, a complete chapter is devoted to describe a new procedure to determine the correct type and number of boundary conditions for hyperbolic systems. Then a new model describing the non-isothermal viscoelastic flows is introduced while keeping the hyperbolic nature of the system. The main advantage of the proposed model over the existing ones is its hyperbolic nature, which overcomes some of the drawbacks of the available models. The proposed model is then solved numerically using a hybrid finite element/finite difference scheme.