Energy Methods for Free Boundary Problems
Energy Methods for Free Boundary Problems

Author: S.N. Antontsev

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 338

ISBN-13: 1461200911

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For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.

Free Boundary Problems
Free Boundary Problems

Author: Ioannis Athanasopoulos

Publisher: CRC Press

Published: 1999-06-25

Total Pages: 372

ISBN-13: 9781584880189

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Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.

Computational Fluid Dynamics with Moving Boundaries
Computational Fluid Dynamics with Moving Boundaries

Author: Wei Shyy

Publisher: Courier Corporation

Published: 2012-08-21

Total Pages: 306

ISBN-13: 0486135551

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This text describes several computational techniques that can be applied to a variety of problems in thermo-fluid physics, multi-phase flow, and applied mechanics involving moving flow boundaries. Step-by-step discussions of numerical procedures include multiple examples that employ algorithms in problem-solving. In addition to its survey of contemporary numerical techniques, this volume discusses formulation and computation strategies as well as applications in many fields. Researchers and professionals in aerospace, chemical, mechanical, and materials engineering will find it a valuable resource. It is also an appropriate textbook for advanced courses in fluid dynamics, computation fluid dynamics, heat transfer, and numerical methods.

Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer
Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer

Author: Ben Q. Li

Publisher: Springer Science & Business Media

Published: 2006-06-29

Total Pages: 587

ISBN-13: 1846282055

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Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer. Certain unique features of the method have made it attractive as an alternative for other popular methods such as finite volume and finite elements in thermal fluids engineering analyses. This book is written as an introductory textbook on the discontinuous finite element method for senior undergraduate and graduate students in the area of thermal science and fluid dynamics. It also can be used as a reference book for researchers and engineers who intend to use the method for research in computational fluid dynamics and heat transfer. A good portion of this book has been used in a course for computational fluid dynamics and heat transfer for senior undergraduate and first year graduate students. It also has been used by some graduate students for self-study of the basics of discontinuous finite elements. This monograph assumes that readers have a basic understanding of thermodynamics, fluid mechanics and heat transfer and some background in numerical analysis. Knowledge of continuous finite elements is not necessary but will be helpful. The book covers the application of the method for the simulation of both macroscopic and micro/nanoscale fluid flow and heat transfer phenomena.

Free Boundaries in Rock Mechanics
Free Boundaries in Rock Mechanics

Author: Anvarbek Meirmanov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2017-09-11

Total Pages: 276

ISBN-13: 3110545047

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This monograph is concerned with free-boundary problems of partial differential equations arising in the physical sciences and in engineering. The existence and uniqueness of solutions to the Hele-Shaw problem are derived and techniques to deal with the Muskat problem are discussed. Based on these, mathematical models for the dynamics of cracks in underground rocks and in-situ leaching are developed. Contents Introduction The Hele–Shaw problem A joint motion of two immiscible viscous fluids Mathematical models of in-situ leaching Dynamics of cracks in rocks Elements of continuum mechanics

Numerical Methods in Fluid Dynamics
Numerical Methods in Fluid Dynamics

Author: Gary A. Sod

Publisher: Cambridge University Press

Published: 1985-10-31

Total Pages: 464

ISBN-13: 9780521259248

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Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.

Free Boundary Problems in Fluid Flow with Applications
Free Boundary Problems in Fluid Flow with Applications

Author: J M Chadam

Publisher: CRC Press

Published: 1993-02-22

Total Pages: 278

ISBN-13: 9780582215672

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This is the third of three volumes containing the proceedings of the International Colloquium 'Free Boundary problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main part of this volume studies the flow of fluids, an area which has led to many of the classical free boundary problems. The first two sections contain the papers on various problems in fluid mechanics. The types of problems vary fromthe collision of two jets to the growth of a sand wave. In the next two sections porous flow is considered. This has important practical applications in fields such as petroleum engineering and groundwater pollution. Some new and interesting free boundary problems in geology and engineering are treated in the final section.

The Stefan Problem
The Stefan Problem

Author: A.M. Meirmanov

Publisher: Walter de Gruyter

Published: 2011-05-03

Total Pages: 257

ISBN-13: 3110846721

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures

Author: Gui-Qiang G Chen

Publisher: Princeton University Press

Published: 2018-02-27

Total Pages: 832

ISBN-13: 0691160554

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This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.