Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems


Book Description

Harmonic and biharmonic boundary value problems (BVP) arising in physical situations in fluid mechanics are, in general, intractable by analytic techniques. In the last decade there has been a rapid increase in the application of integral equation techniques for the numerical solution of such problems [1,2,3]. One such method is the boundary integral equation method (BIE) which is based on Green's Formula [4] and enables one to reformulate certain BVP as integral equations. The reformulation has the effect of reducing the dimension of the problem by one. Because discretisation occurs only on the boundary in the BIE the system of equations generated by a BIE is considerably smaller than that generated by an equivalent finite difference (FD) or finite element (FE) approximation [5]. Application of the BIE in the field of fluid mechanics has in the past been limited almost entirely to the solution of harmonic problems concerning potential flows around selected geometries [3,6,7]. Little work seems to have been done on direct integral equation solution of viscous flow problems. Coleman [8] solves the biharmonic equation describing slow flow between two semi infinite parallel plates using a complex variable approach but does not consider the effects of singularities arising in the solution domain. Since the vorticity at any singularity becomes unbounded then the methods presented in [8] cannot achieve accurate results throughout the entire flow field.













Finite Rotations in Structural Mechanics


Book Description

The deformation near a material particle of the classical continuum is produced by successive superposition of a rigid-body translation, a pure stretch along principal directions of strain and a rigid-body ro tation of those directions. The rotational part of deformation is par ticularly important in the non-linear analysis of thin-walled solid structures such as ~eams, thin-walled bars, plates and shells, since in this case finite rotations may appear even if the strains are infinite simal. It seems that the research concerning the application of finite ro tations is carried out independently in different fields of structural mechanics. Theoretical and numerical methods developed and the results obtained for a particular type of the structure or for a particular ma terial behaviour not always are used to analyse similar problems for other types of structures or for another material behaviour. Since the research in this field had been growing rapidly, it was decided to organize an informal international meeting, under the auspi ces of the European Mechanics Co~mittee, entitled: Euromech Colloquium 197 "Finite Rotations in Structural Mechanics". The meeting was held on 17 - 20 September 1985 in Jablonna, a small suburbian area of Warsaw.




Numerical Simulation of Fluid Flow and Heat/Mass Transfer Processes


Book Description

Computational fluid flow is not an easy subject. Not only is the mathematical representation of physico-chemical hydrodynamics complex, but the accurate numerical solution of the resulting equations has challenged many numerate scientists and engineers over the past two decades. The modelling of physical phenomena and testing of new numerical schemes has been aided in the last 10 years or so by a number of basic fluid flow programs (MAC, TEACH, 2-E-FIX, GENMIX, etc). However, in 1981 a program (perhaps more precisely, a software product) called PHOENICS was released that was then (and still remains) arguably, the most powerful computational tool in the whole area of endeavour surrounding fluid dynamics. The aim of PHOENICS is to provide a framework for the modelling of complex processes involving fluid flow, heat transfer and chemical reactions. PHOENICS has now been is use for four years by a wide range of users across the world. It was thus perceived as useful to provide a forum for PHOENICS users to share their experiences in trying to address a wide range of problems. So it was that the First International PHOENICS Users Conference was conceived and planned for September 1985. The location, at the Dartford Campus of Thames Polytechnic, in the event, proved to be an ideal site, encouraging substantial interaction between the participants.




The Boundary Element Method


Book Description

The Boundary Element Method, or BEM, is a powerful numerical analysis tool with particular advantages over other analytical methods. With research in this area increasing rapidly and more uses for the method appearing, this timely book provides a full chronological review of all techniques that have been proposed so far, covering not only the fundamentals of the BEM but also a wealth of information on related computational analysis techniques and formulations, and their applications in engineering, physics and mathematics. An indispensable handbook and source of inspiration for researchers and professionals in these fields, this book is also an ideal textbook for graduate engineering students.




Emerging Technologies and Techniques in Porous Media


Book Description

Heat and fluid flow in fluid-saturated porous media has become increas ingly more attractive to researchers and thus it has become a very pro ductive field for many researchers and practical engineers in very diverse range of fields. The great interest in the topic stems from its widespread number of different practical applications in modern industries and in many environmental issues, such as nuclear waste management, build ing thermal insulators, geothermal power plants, grain storage, etc. In building sciences and thermal insulation engineering, an appreciable in sulating effect has been derived by placing porous material in the gap between the cavity walls and multishield structures of nuclear reactors between the pressure vessel and the reactor. Geophysical applications include modeling of the spread of pollutants (e. g. radioactive mater ial), water movements in geothermal reservoirs, enhanced recovery of petroleum reservoirs, etc. These, and many other, important practical applications have resulted in a rapid expansion of research in the general area of porous media and thus generated a vast amount of both theor etical and experimental research work. It has attracted the attention of industrialists, engineers and scientists from many varying disciplines, such as applied mathematics, chemical, civil, environmental, mechanical and nuclear engineering, geothermal physics, food science, medicine, etc. This book contains some of the contributions to the NATO Advanced Study Institute on Emerging Technologies and Techniques in Porous Media that was held in Neptun-Olimp, Constanta, Black Sea, Romania on 9-20 June, 2003.




Numerical Methods for Problems in Infinite Domains


Book Description

This volume reviews and discusses the main numerical methods used today for solving problems in infinite domains. It also presents in detail one very effective method in this class, namely the Dirichlet-to-Neumann (DtN) finite element method. The book is intended to provide the researcher or engineer with the state-of-the-art in numerical solution methods for infinite domain problems, such as the problems encountered in acoustics and structural acoustics, fluid dynamics, meteorology, and many other fields of application. The emphasis is on the fundamentals of the various methods, and on reporting recent progress and forecasting future directions. An appendix at the end of the book provides an introduction to the essentials of the finite element method, and suggests a short list of texts on the subject which are categorized by their level of mathematics.




Handbook of Differential Equations


Book Description

This book compiles the most widely applicable methods for solving and approximating differential equations. as well as numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations. For nearly every technique, the book provides: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs