**1979**

*Banerjee, P.K. and Butterfield, R. (Eds) *

**Developments in Boundary Element Methods - 1**

1979

Elsevier Applied Science Publishers

Barking

292 pp

ISBN: 0 85334 845 6

The book is intended to demonstrate the versatility and power of BEM.

It covers the applications to a wide range of complex practical

problems. Many subjects are covered in ten chapters, including new

concepts of BEM, non-linear problems of potential flow, implementation

of BEM for 2-D and 3-D elastostatics, 2-D and 3-D problems of

elastoplasticity, 2-D and 3-D problems of fracture mechanics, analysis

of wave problems, BEM in thermoelasticity, analysis of plates and

shells, applications in electrical engineering, and coupling with other

numerical methods. List of contributors, with addresses, and Index

complete the book.

*Brebbia, C.A. (Ed.) *

**Progress in Boundary Element Methods**

1981

**Vol 1**

Pentech Press

Oxford

315 pp

ISBN: 0 7273 1610 9

The book presents the fundamentals of the BEM, and applications to

different areas of engineering. Nine chapters of the book present the

following topics: basis of boundary elements, fundamental solutions,

potential theory, elastostatics, plasticity, time-dependent potential

problems, elastodynamics, combined boundary element and finite element

methods, and mathematical aspects on asymptotic accuracy and

convergence. A list of contributors and Index complete the book.

*Banerjee, P.K. and Shaw, R.P. (Eds) *

**Developments in Boundary Element Methods - 2**

1982

Elsevier Applied Science Publishers

Barking

288 pp

ISBN: 0 85334 112 5

The book aims to demonstrate the versatility and power of the BEM. It

covers the applications to a wide range of complex practical problems.

Many subjects are covered in nine chapters. This volume has been

restricted to time-dependent problems in engineering. Topics included

are: BE formulation for melting and solidification, transient flow

through porous elastic media, applications to water wave problems,

general viscous flow, time-dependent inelastic deformation of metals,

determination of eigenvalues, transient stress analysis of tunnels and

caverns, analysis of hydrodynamic loads, and acoustic emissions from

submerged structures. List of contributors, with addresses, and Index

complete the book.

*Brebbia, C.A. (Ed.) *

**Progress in Boundary Element Methods**

1983

**Vol 2**

Pentech Press

Plymouth

217 pp

ISBN: 0 7273 1611 7

The book presents the recent developments in BEM. This volume contains

eight chapters representing new developments on the subject or reviews

of recent literature in a particular area. Subjects covered are as

follows: inhomogeneous heat conduction problems, pressure waves in

liquid sodium in a pressure vessel, fracture mechanics and bibliography

review, 2-D and 3-D body force loading problems, BEM application to 2-D

contact problems with and without friction, bending of thin plates,

fluid-shell interaction and fluid-solid impact problems, viscosity and

creep problems.

*Banerjee, P.K. and Mukherjee, S. (Eds) *

**Developments in Boundary Element Methods - 3**

1984

Elsevier

Barking

313 pp

ISBN: 0 85334 253 9

The book aims to demonstrate the versatility and power of the BEM. It

covers applications to a wide range of complex practical problems. This

volume is designed to describe the developments in non-linear problems

of solid and fluid mechanics. Subjects covered in ten chapters are as

follows: application of BEM for 3-D problems of elastoplasticity and

viscoplasticity, formulations for large strain - large deformation

problems of plasticity and viscoplasticity elastoplastic analysis by

indirect methods, non-linear problems of fracture mechanics, large

deflection analysis of thin elastic plates, time-dependent

Navier-Stokes flow, non-linear water wave problems, non-linear sloshing

problems, integration schemes for 2-D and 3-D non-linear analysis, and

linear and non-linear problems in aero- and hydrodynamics. List of

contributors, with addresses, and Index complete the book.

*Brebbia, C.A. (Ed.) *

**Progress in Engineering Series**

1984

**Vol V**

Computational Mechanics Publications

Southampton

100 pp

ISBN: 0 905451 27 9

The book contains a series of papers on boundary elements published in

the Engineering Analysis, Applied Ocean Research and Advances in

Engineeering Software journals. The papers are extracted and edited

versions of those published in the journals. They deal with fluid flow

applications, thermoelastic problems, hydrodynamics, seepage,

structural vibrations and microcomputer applications.

*Brebbia, C.A. (Ed.) *

**Topics in Boundary Element Research**

1984

**Vol 1 - Basic Principles and Applications**

Springer-Verlag

Berlin

260 pp

ISBN: 0 387 13097 7

The book is aimed at the state-of-the-art in current research activity

in the boundary element method. Chapters included in the book cover:

review of formulations of BEM, transient heat conduction problems,

thermoelastic fracture mechanics, fluid mechanics problems, water wave

analysis, interelement continuity in BEM, applications in geomechanics,

applications to mining problems, combined BEM/FEM methods, and finite

deflection of plates.

*Brebbia, C.A. (Ed.) *

**Topics in Boundary Element Research**

1985

**Vol 2 - Time-Dependent and Vibration Problems**

Springer-Verlag

Berlin

260 pp

ISBN: 0 387 13993 1

The book is aimed at the state-of-the-art in the solution of

time-dependent and vibration problems. Chapters included in the book

cover: boundary integral equation methods in elastodynamics, elastic

potentials in BIE formulations, time-dependent non-linear potential

problems, transient scalar waves, boundary integral formulation of mass

matrices for dynamic analysis, and asymptotic accuracy and convergence

for point collocation methods.

*Banerjee, P.K. and Watson, J.O. (Eds) *

**Development in Boundary Element Methods - 4**

1986

Elsevier Science Publishers

Barking

346 pp

ISBN: 0 85334 376 4

The book aims to demonstrate the versatility and power of the BEM. It

covers the applications to a wide range of complex practical problems.

Different subjects not covered in previous volumes are presented in eight

chapters, namely: Hermitian cubic boundary elements, 3-D transient

(hyperbolic) dynamic analysis, stress analysis of axisymmetric bodies

subjected to asymmetric loading, new plate bending formulation,

non-linear deformation analysis of sandwich plates and shallow shells,

transient non-linear heat transfer analysis, non-linear analysis of

geomechanics problems (BEM/FEM), review of modelling of fluid flow

problems in the aircraft industry. List of contributors, with

addresses, and Index complete the book

*Beskos, D.E. (Ed.) *

**Boundary Element Methods in Mechanics**

1987

**Computational Methods in Mechanics - Vol 3**

Computational Mechanics Publications

Southampton

598 pp

ISBN: 0 444 87990 0

The book presents a collection of 12 chapters on different BEM topics

written by some of the best researchers. It contains the following

chapters: introduction, potential theory, elastostatics, two chapters

on elastodynamics, non-linear problems, fracture mechanics, fluid

mechanics, acoustics, heat conduction problems and thermoelasticity,

dynamics of soil-structure interaction and fluid-structure interaction.

*Brebbia, C.A. (Ed.) *

**Applications in Geomechanics**

1987

**Topics in Boundary Element Research - Vol 4**

Springer-Verlag

Berlin

172 pp

ISBN: 0 387 17497 4

This volume studies the applications of the method to a wide variety of

geomechanics problems, most of which are ideally suited for boundary

elements. The eight chapters in this volume bring together a series of

recent advances made in the applications of BEM for soil mechanics,

soil-structure interaction, consolidation, foundations, saltwater

intrusion and groundwater flow problems.

*Brebbia, C.A. (Ed.) *

**Computational Aspects**

1987

*Topics in Boundary Element Research - Vol 3*

Springer-Verlag

Berlin

288 pp

ISBN: 0 387 16113 9

This book deals with the computational aspects of boundary elements and

includes fully operational codes for potential and elastostatics. It

consists of nine chapters: numerical convergence for transient heat

conduction, viscoelastic problems, numerical integration, computational

aspects of boundary elements, the Edge Function method, multigrid

methods, complex variable boundary elements, software for potential

problems and software for elastostatics. A subject index completes the

book.

*Mackerle, J. and Brebbia, C.A. (Eds) *

**The Boundary Element Reference Book**

1988

Computational Mechanics Publications

Southampton

382 pp

ISBN:0 905451 74 0

This handbook is intended to provide boundary element practitioners

with a reference book dealing with the most important boundary element

publications and the most up to date codes. The book is divided into

four sections: development of the BEM, the BE books written up to now

with a brief description of their contents, BE codes description

(general purpose and special purpose programs), and Who's Who of

Boundary Elements with details of the best known practitioners in

industry and academia.

*Stein, E. and Wendland, W.L. (Eds) *

**Finite Element and Boundary Element Techniques from Mathematical and
Engineering Point of View**

1988

No 301

CISM International Centre for Mechanical Sciences

Courses and Lecture

Springer-Verlag

Berlin

333 pp

ISBN: 3 211 82103 1

Traditional FEM and the more recent BEM are underlying many engineering

computational methods and corresponding software. Both methods have

their merits and their restrictions. Therefore, the combination of both

methods will provide an improved numerical tool in the future.

The aim of this book is to present significant basic formulations

of FEM and BEM and to show their common practical and mathematical

foundations, their differences as well as possibilities for their

combination. These include variational foundations, FEM and BEM for

linear and nonlinear elasticity and potential problems, the combination

of FEM-BEM asymptotic error analysis, modifications due to corner and

crack singularities and corresponding improvement of convergence,

plastic analysis, numerical algorithms and engineering applications.

*Brebbia, C.A. (Ed.)*

**Viscous Flow Applications**

1989

**Topics in Boundary Element Research - Vol 5**

Springer-Verlag

Berlin

181 pp

ISBN: 0 387 50609 8

This book presents the state-of-the-arts on the solution of viscous

flow using boundary elements and discusses different current approaches

which have been validated by numerical experiments.

Chapter 1 of the book presents a brief review of previous work on

viscous flow simulation and in particular gives an up-to-date list of

the most important BEM references in the field. Chapter 2 reviews the

governing equations for general viscous flow, including

compressibility. The authors present a comprehensive treatment of the

different cases and their formulation in terms of boundary integral

equations. This work has been the result of collaboration between

Computational Mechanics Institute and Massachusetts Institute of

Technology researchers. Chapter 3 describes the generalized formulation

for unsteady viscous flow problems developed over many years at Georgia

Institute of Technology. This formulation has been extensively applied

to solve aerodynamic problems. The approach followed in Chapter 4 is

the velocity-vorticity formulation plus the inclusion of special

integral expressions for the energy equation and the computation of

pressure fields. The approach has been validated by numerical

experiments and represents the work carried out at Computational

Mechanics Institute, University of Maribor and University of Nuremberg.

The procedure proposed in Chapter 5 for the solution of steady state

Navier-Stokes type problems is different from that in Chapters 2 and 3

as it is based on a pseudo-body force formulation employing the penalty

function approach. This technique has been developed at Toshiba in

collaboration with Computational Mechanics Institute.

Chapter 6 discusses how the boundary layer effect can be introduced in

potential flow. It deals with the coupling of FDM and BEM. The authors

at DFVLR Gottingen proposed solving the boundary layer flow using

infinite difference and then combining that solution with boundary

elements for the outer flow.

Chapter 7 is based on the research carried out at Western Australia

University for the solution of non-Newtonian fluid also using a concept

of `pseudo forces' related to that described in Chapter 4. The last

chapter of the book deals with the solution of Stokes flow as a

particular type of viscous fluid.

*Brebbia, C.A. (Ed.) *

**Electromagnetic Applications**

1989

**Topics in Boundary Element Research - Vol 6**

Springer-Verlag

Berlin

234 pp

ISBN: 0 387 50607 1

Chapter 1 of this volume reviews the different formulations of

Maxwell's equations used in electrical engineering and the resulting

boundary integral statements. It discusses indirect as well as direct

approaches and applies them to a series of interesting practical cases.

Chapter 2 concentrates on the boundary element solution of three

dimensional electromagnetic fields in terms of the magnetic flux or the

vector potential. The next contribution - Chapter 3 - discusses the case

of magnetic fields of power devices under constant voltage sources. A

new approach is proposed which can take into account the external power

source voltage as input data and permits a direct rather than iterative

analysis to be carried out. Chapter 4 analyses eddy current problems

with particular reference to three dimensional cases.

In some cases it is more advantageous to couple boundary elements

with classical finite elements. The author of Chapter 5 recommends the

use of finite elements for saturation phenomena and boundary elements

for the nonsaturable region. The technique is applied to the case of

electric motors and electromagnetics. Chapter 6 also studies the

coupling of the two methods for electromagnetic problems reviewing the

advantages of both techniques and their field of applications.

Examples are presented for electrostatics, magnetostatics and field

analysis, including the non-linear case. The last contribution

- Chapter 7 - deals with applications of boundary elements for the

analysis and design of electrical machines considering two and three

dimensional cases.

*Ciskowski, R.D. and Brebbia, C.A. (Eds) *

**Boundary Element Methods in Acoustics**

1991

Computational Mechanics Publications

Southampton

292 pp

ISBN: 1 85312 104 5

ISBN: 0 945824 87 4 (US, Canada, Mexico)

This book is the first to focus on research and applications involving

the use of boundary elements in acoustics. Acoustics is an ideal

application area for the boundary element method (BEM) because of the

presence in many cases of infinite domains extending to infinity, the

need to obtain accurate solutions and as a BEM requires only the

discretization of the boundary.

Chapter 2 provides an historical perspective of BEM in acoustics

with a valuable list of key references. Chapter 2 addresses basic

formulations and fundamental concepts. Chapter 3 deals with radiation

and scattering from elastic solids and shells. Chapter 4 provides

formulations to determine the sensitivity of the acoustic field to

material or shape parameters and frequency. Chapter 6 discusses the use

of BEM for acoustic modeling coupled to FEM for structural modeling.

Chapter 7 addresses boundary element applications in automobile

interior and exterior acoustics. Chapter 8 presents applications in

biological and biomedical engineering, and bioacoustics. Chapter 9

introduces the use of the BEM for the study and prediction of noise in

the environment.

The intended audience for this book consists of engineers and

scientists in research and practice, and postgraduate students who want

to understand the BEM and its many applications in acoustics.

*Beskos, D.E. (Ed.) *

**Boundary Element Analysis of Plates and Shells**

1992

Computational Mechanics Publications

Southampton

VIII+368 pp

ISBN: 3 540 54464 X

hardcover

This is the first book to deal specifically with the analysis of plates

and shells by the BEM and to cover all aspects of their behaviour, and

combines tutorial and state-of-the-art articles on the BEM as applied

to plates and shells.

**Aliabadi, M.H. and Brebbia, C.A. (Eds) **

Computational Methods in Contact Mechanics

1993

Computational Mechanics Publications

Southampton

ISBN: 1 85312 184 3

ISBN: 1 56252 113 6 (US, Canada, Mexico)

Modern engineering design leads to the realization of the importance of

contact problems in many technological fields. Contact problems are

complex and inherently non-linear due to their moving boundaries and

the existence of friction along contact surfaces. Until a few years ago,

researchers were engaged only in the fundamental concepts of contact

problems. Today, due to the great improvement in computer technology

and computational methods, it is possible to solve many complex

practical contact problems accurately and efficiently.

This book is the first which presents a comprehensive review of the

contact mechanics with particular emphasis on computational methods.

Much attention is devoted to the physical interpretation of the contact

properties as well as the numerical methodologies necessary to solve

complex engineering problems. As such, the book covers formulations

based on load incremental and mathematical programming approaches

using both finite and boundary element methods. The mathematical

modelling techniques described include the constraint method, the

flexibility approach, the penalty method and the Lagrange multiplier

technique.

In Chapter One, the applications of boundary element method to

frictional contact problems are presented using a fully load incremental

technique together with a constraint approach. Its application to fracture

mechanics is also described. Chapter Two deals with the boundary

element flexibility formulation for the analysis of frictionless and

frictional contact problems. The formulation is described in detail and

several examples are presented to demonstrate the accuracy of the

method.

In Chapter Three, the Lagrange multiplier formulation for the finite

element method is presented. General algorithms are described for the

detection of overlapping meshes and the evaluation of contact forces.

An example problem of contact stress analysis in an orthopaedic knee

is presented.

Chapters Four and Five concentrate on the application of the penalty

method in contact problems using the finite and boundary element

methods respectively. Particular attention is paid to the numerical

implementation of the method and several examples are presented to

demonstrate the accuracy of the methods.

In Chapter Six, the application of the boundary element method to

three-dimensional contact problem is described. The authors present a

detailed formulation of the problem before proceeding to solve some

classical problems.

The remaining three chapters of the book deal with mathematical

programming approaches. Chapter Seven presents a formulation to deal

with both small and large displacement contact problems. The chapter

provides a review of the mathematical programming methods as well

as giving recommendations for future development of the method. In

Chapter Eight, a general solution method for three dimensional quasistatic

contact problems is presented. The formulation is based on the boundary

element method and mathematical programming approaches.

Finally, in Chapter Nine, the application of the finite element method

to elastic-plastic contact problems is presented employing a parametric

quadratic programming approach. The authors describe the numerical

implementation of the method in detail and present several examples to

demonstrate the accuracy of their technique.

*Aliabadi, M.H. and Brebbia, C.A. (Eds) *

**Advances in Boundary Element Methods for Fracture Mechanics**

1993

Computational Mechanics Publications

Southampton

ISBN: 1 85312102 9

ISBN: 1 94582 485 8 (US, Canada, Mexico)

The boundary element method (BEM) has emerged over the past few years

as the most powerful numerical technique for the solution of linear

elastic crack problems in fracture mechanics. While much progress has

been made, there are still many new frontiers to be explored with this

method. The aim of this book is to present the state-of-the-art in

applications of the boundary element method to crack problems. As such,

it includes chapters written by some of the leading researchers in the

field describing the recent advances of the method, as well as

presenting new ideas for further development.

It is well-known that the straightforward application of BEM to

crack problems leads to a mathematical degeneration in the numerical

formulation, if the two cracks are co-planar. The first two chapters of

the book deal with methods of removing this difficulty. In Chapter 1, a

dual boundary element formulation is presented where the displacement

integral equation and the traction equation are used independently on

crack surfaces. In Chapter 2, a boundary element displacement

discontinuity method is presented for elastodynamic problems.

Formulation for bodies containing interior, surface breaking and near

surface cracks are presented. Also discussed are problems associated

with interface cracks for which multidomain analysis is used.

In Chapter 3, the applications of BEM to analyse delamination

of composite laminates is described. The numerical treatment of

delaminated structures is carried out by using special crack-tip

elements and the energy method. In Chapter 4, an indirect boundary

element formulation known as the body force method is described.

The remaining chapters of the book concentrate on the

application of BEM to three-dimensional crack problems. Chapter 5

describes different crack-front elements, including the quarter-point

element which can be used to model the displacement and stress fields

in the vicinity of the crack front. Chapter 6 presents an application

of BEM to the analysis of three-dimensional stress intensity factor

weight functions. A weight function formulation based on the notion of

fundamental fields is derived. The fundamental displacements and stress

fields for rectilinear and penny-shaped crack fronts are given.

The final chapter describes the application of the boundary

element method to anisotropic crack problems. A detailed discussion

on the numerical implementation of the anisotropic fundamental solution

is described.

*Aliabadi, M.H. and Brebbia, C.A. (Eds) *

**Advanced Formulations in Boundary Element Methods**

1993

Computational Mechanics Publications

Southampton

ISBN: 1 85312 182 7

ISBN: 1 56252 111 X (US, Canada, Mexico)

The boundary element method is now being increasingly applied to new

topics in engineering. This has led researchers to investigate and

develop new formulations of the method which lend themselves better to

problems such as fracture mechanics, coupling with finite elements,

moving boundary applications and nonlinear problems. This book

presents new boundary element formulations which are now emerging as

viable alternatives for a wide range of complex problems.

In Chapter 1, a new formulation entitled dual boundary element

method (DBEM) is presented for crack problems in fracture mechanics.

This new formulation removes the difficulties associated with the

modelling of co-planar crack surface using the standard boundary

element method. Chapters 2 and 3 address the problem of domain

integrals which can occur in the boundary element method for problems

involving body forces or nonlinearities. In Chapter 2, the dual

reciprocity method (DRM) is presented to solve these difficulties for a

wide range of problems such as time dependent convection diffusion and

elastodynamics. In Chapter 3, the so-called multiple reciprocity method

(MRM) is presented for applications involving body forces as well as

transient heat conduction problems.

A new hybrid boundary element formulation is presented in Chapter

4, which enables the simple coupling with finite elements. The authors

also briefly describe the hybrid-stress formulation before proceeding

with the detailed description of the hybrid-displacement approach.

Several examples are presented to demonstrate the accuracy of the

method. Chapter 5, concentrates on a new formulation for obtaining

higher-order interelement continuity using B-splines. Chapter 6, deals

with the hypersingular approach (HIBEM) for two-dimensional potential

problems. The formulation is presented in detail and several examples

are included to demonstrate its accuracy. In Chapter 7, the

non-singular computation of field derivatives is described. It is

demonstrated that by using the proposed formulation the field

derivatives such as temperature gradients can be evaluated more

accurately than has been possible using conventional approaches.

Finally, the application of the complex variable boundary element

method (CVBEM) to heat conduction problems is presented in Chapter 8.

Formulations are presented for simply and multiply connected domains

and several examples are given to demonstrate the versatility of the

method for two-dimensional problems.

*Brebbia, C.A. and Aliabadi, M.H. (Eds) *

Adaptive Finite and Boundary Element Methods

1993

Computational Mechanics Publications

Southampton

ISBN: 1 85312 185 1

ISBN: 1 56252 114 4 (US, Canada, Mexico)

In recent years increasing attention has been paid to adaptive meshing

and analysis techniques in order to improve the reliability of numerical

analysis techniques such as the finite and boundary element method.

This book presents a comprehensive review of adaptive analysis in

engineering computation. As such the topics are wide ranging and

include algorithms for automatic meshing, adaptive improvements,

error analysis and adaptive solution procedures.

In Chapter 1, adaptive analysis methods such as h, p and h-p versions

are described in detail for the finite and boundary element methods. A

detailed description of a posteriori error estimates and subsequent mesh

refinements are presented. Chapter 2, deals with adaptive finite element

techniques for three-dimensional Navier Stokes equations and other

transient problems. A technique is described to control the mesh grading

by the estimate of errors. Several examples are presented for problems

involving viscous flow simulation and phase transitions. In Chapter 3,

adaptivity through mesh movements is considered rather than the usual

localized mesh refinement techniques. Application to aeronautical

problems such as inviscid flow around an aerofoil are presented to

demonstrate the versatility of the proposed method. Chapter 4, deals

with adaptive finite element method for transient compressible flow

problems. In this chapter the capability of an adaptive unstructured

mesh approach is described in which the mesh is automatically adapted

to account for the motion of the boundaries. The application of adaptive

finite element method for phase change problems is described in

Chapter 5. Here, an error estimation technique for adaptive finite

element analysis of heat conduction problems is presented. Two

examples of solidification of an aluminium casting with change of

phase are presented. In Chapter 6, adaptive solution strategies for

nonlinear finite element analysis are presented. Particular attention has

been paid to computationally intensive operations such as updating the

stiffness matrices, decomposition, bisection and line search algorithms.

Parallel computation and solution procedures for linear elliptic partial

differential systems are presented in Chapter 7, using the finite element

method based on automatically unstructured grids. Finally, the application

of boundary and finite element methods to three-dimensional problems

of acoustic scattering is presented in Chapter 8. This chapter concentrates

mainly on computational aspects such as geometric modelling,

hp-adaptivity and a posteriori error estimates.

*Kane, J.H., Maier, G., Tosaka, N. and Atluri, S.N. (Eds) *

**Advances in Boundary Element Techniques**

1993

Springer-Verlag

Berlin

ISBN: 3 540 55921 3

ISBN: 0 387 55921 3

The book contains a collection of papers written by leading experts in

the field providing an overview of the state-of-the-art of boundary

element analysis.

With treatments of mechanical, thermal, fluid, and electromagnetic

phenomena, this book will be of great value to graduate students,

practitioners, and researchers in engineering, mathematics and the

physical sciences wishing to obtain a broader perspective or remain

current in these important areas of computational simulation. The

topics include mathematical, numerical, and computational aspects,

basic formulations, potential, thermal, fluid mechanics and

aerodynamics applications, elasticity and elastoplasticity,

elastodynamics, electromagnetics, and acoustics, and coupled problems.

Throughout this volume, many different boundary approaches are

described including the indirect and direct singular and hypersingular

collocation and symmetric Galerkin formulations.

*Manolis, G.D. and Davies, T.G. (Eds) *

**Boundary Element Techniques in Geomechanics**

1993

Computational Mechanics Publications

Southampton

*Wrobel, L.C. and Brebbia, C.A. (Eds) *

**Computational Methods for Free and Moving Boundary Problems
in Heat Transfer and Fluid Flow**

1993

Computational Mechanics

Southampton

ISBN: 1 85312 221 1

ISBN:1 56252 145 4 (US, Canada, Mexico)

The mathematical modelling of free and moving boundary problems is

characterized by the presence of one or more surfaces which are

initially unknown or move throughout the analysis. The determination of

the location of these surfaces is an important part of the solution

procedure, generally involving the use of iterative or time-marching

algorithms. Examples of practical engineering problems are numerous,

e.g. nonlinear wave motion, cavitating flows, solidification and

melting, metal casting, to name but a few. The present volume

concentrates on computational methods of solution of such problems with

emphasis on boundary and finite elements.

Chapter 1 discusses direct iteration and optimization

techniques used in conjunction with the boundary element method (BEM)

for solution of gravity and pressure-driven free surface flow problems.

Chapter 2 uses Baiocchi's integral transformation in a fixed domain

method for free surface flow in porous media. Chapters 3 and 4 deal

with nonlinear wave motion. The former describes a wave model based on

the fully nonlinear potential flow equation to study wave motion in

shallow water, including wave overturning induced by the ocean bottom

or by coastal engineering structures.

The flow about submerged partially or supercavitating

axisymmetric bodies both at zero and non-zero angle of attack is

considered in Chapter 5. Chapter 6 discuss two implementations of the

BEM to solve the slow viscous flow of a fluid moving between two

parallel plates which are in relative motion. The situations in which

petroleum reservoir models generate shocks are considered in Chapter 7.

When rain runs down a window pane in a stream, it normally

meanders instead of going straight. This interesting problem is

analysed in Chapter 8, which presents the condition of stable

meandering of water rivulets on an inclined smooth plate, derived by the

bend theory including the effect of surface tension. A series of heat

flow problems are considered in Chapters 9 to 11. Chapter 9, on

solidification problems, presents a macroscopic model for the treatment

of the macrosegregation process in a binary material, and a microscopic

model for the freezing processes in foodstuffs. Modelling of the

mathematical behaviour of an aluminium electrolytic cell is presented

in Chapter 11. This model predicts and assesses fundamental variables

in cell operation: form and thickness of the frozen bath, heat flows,

position of isotherms, electric potentials, etc. Chapter 12 presents a

resume of work involving the Isotherm Migration Method. Applications

include implicit moving boundaries (oxygen diffusion through absorbing

tissues) and melting ranges (mushy problems). The modelling of the

filling stage of casting processes is the subject of Chapter 13 where a

two-dimensional FEM to treat non-steady flows of Newtonian fluids,

coupled with heat transfer and turbulence is described.

Chapter 14 discusses the steady state, irrotational, ideal

fluid flow produced by a submerged source, or sink, from a region

containing three homogeneous layers of fluids at different densities

with gravity as the restoring force. In Chapter 15, the motion and

deformation of viscous drops and gas bubbles which occur in many

industrial and biological systems, are studied through a completed

double layer boundary integral equation method. Finally Chapter 16

reviews the historical development and state-of-the-art in Green's

function structured discrete approximation methods for modelling

microscopic and macroscopic transport phenomena in solid-liquid

phase-change systems.

*Power, H. (Ed.)*

**BE Applications in Fluid Mechanics**

1994

**Advances in Fluid Mechanics - Vol 4**

Computational Mechanics Publications

Southampton

ISBN: 1 85312288 2

ISBN: 1 56252 212 4 (US, Canada, Mexico)

ISSN: 1353 808X

The boundary element method (BEM) is now a well established numerical

technique for the analysis of engineering problems, particularly those

involving linear analysis. One of its main advantages is the

considerable reduction in data preparation in relation to domain

methods, as only surface elements are necessary. The basis of the

method is that a fundamental solution is used to take some or all of

the terms in the governing equation to the boundary.

In the past, further increases in the number of applications of

BEM were hampered by the need to operate with relatively complex

fundamental solutions or the difficulties encountered when trying to

extend the BEM to non-linear and time dependent problems. Recent

developments in the boundary element method have been very successful

in dealing with those complex problems.

Fluid dynamics is traditionally one of the most challenging areas

of computational mechanics; the simulation of fluid motion is always a

serious test for any numerical method. The book is a compilation of

some advanced topics on the application of BEM in fluid mechanics. The

eleven chapters in the book have been contributed by leading authors in

the field. This book accordingly provides an important addition to the

literature in fluid mechanics.

*Nowak, A.J. and Neves, A.C. (Eds)*

**The Multiple Reciprocity Boundary Element Method**

1994

Computational Mechanics Publications

Southampton

ISBN: 1 85312277 7

ISBN: 1 56252 201 9 (US, Canada, Mexico)

The boundary element method (BEM) is a numerical technique which is now

emerging as a viable alternative to finite difference and finite

element methods for solving a wide range of engineering problems. The

main advantage of the BEM over domain-type methods is its unique

ability to confine the dependence of the problem solution to the

boundary values only. This reduces the data preparation effort and

saves computer time since the system of equations to be solved is

smaller than those resulting from domain techniques. However, the main

drawback of the BEM occurs in problems such as those with body forces,

time-dependent effects or non-linearities. In these cases, the domain

integrals that appear in the integral equation are usually evaluated by

using cell integration. Although this technique is effective and

general, it affects the overall efficiency of the BEM and detracts from

its elegance due to the additional internal discretization.

In an effort to avoid the internal discretization, many different

approaches have been developed. The most recent one is the multiple

reciprocity method (MRM) which is the main subject of this book. The

basic idea behind the MRM is to employ a sequence of higher order

fundamental solutions which permit the application of the reciprocity

theorem recurrently. The success of the method is reflected in the

works carried out by several active groups around the world and

presented here in the chapters of the book.