Finite Element Methods for Flow Problems / Edition 1

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Overview

In recent years there have been significant developments in the development of stable and accurate finite element procedures for the numerical approximation of a wide range of fluid mechanics problems. Taking an engineering rather than a mathematical bias, this valuable reference resource details the fundamentals of stabilised finite element methods for the analysis of steady and time-dependent fluid dynamics problems. Organised into six chapters, this text combines theoretical aspects and practical applications and offers coverage of the latest research in several areas of computational fluid dynamics.
* Coverage includes new and advanced topics unavailable elsewhere in book form
* Collection in one volume of the widely dispersed literature reporting recent progress in this field
* Addresses the key problems and offers modern, practical solutions Due to the balance between the concise explanation of the theory and the detailed description of modern practical applications, this text is suitable for a wide audience including academics, research centres and government agencies in aerospace, automotive and environmental engineering.

"The objective [of this book] is to present the fundamentals of stabilized finite element methods for the analysis of steady and time-dependent convection-diffusion and fluid dynamics problems with an engineering rather than a mathematical bias." -- p. xi.

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Editorial Reviews

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“…essential reading for graduate students and researchers in engineering and applied sciences..” (CAB Abstracts)
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Product Details

  • ISBN-13: 9780471496663
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 6/9/2003
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 362
  • Product dimensions: 6.28 (w) x 9.49 (h) x 1.04 (d)

Table of Contents

Preface
1 Introduction and preliminaries 1
1.1 Finite elements in fluid dynamics 1
1.2 Subjects covered 2
1.3 Kinematical descriptions of the flow field 4
1.4 The basic conservation equations 13
1.5 Basic ingredients of the finite element method 19
2 Steady transport problems 33
2.1 Problem statement 33
2.2 Galerkin approximation 36
2.3 Early Petrov-Galerkin methods 50
2.4 Stabilization techniques 59
2.5 Other stabilization techniques and new trends 65
2.6 Applications and solved exercises 70
3 Unsteady convective transport 79
3.1 Introduction 79
3.2 Problem statement 81
3.3 The method of characteristics 82
3.4 Classical time and space discretization techniques 91
3.5 Stability and accuracy analysis 98
3.6 Taylor-Galerkin Methods 107
3.7 An introduction to monotonicity-preserving schemes 117
3.8 Least-squares-based spatial discretization 120
3.9 The discontinuous Galerkin method 124
3.10 Space-time formulations 126
3.11 Applications and solved exercises 129
4 Compressible Flow Problems 147
4.1 Introduction 147
4.2 Nonlinear hyperbolic equations 149
4.3 The Euler equations 159
4.4 Spatial discretization techniques 166
4.5 Numerical treatment of shocks 176
4.6 Nearly incompressible flows 186
4.7 Fluid-structure interaction 187
4.8 Solved exercises 199
5 Unsteady convection-diffusion problems 209
5.1 Introduction 209
5.2 Problem statement 210
5.3 Time discretization procedures 211
5.4 Spatial discretization procedures 222
5.5 Stabilized space-time formulations 241
5.6 Solved exercises 243
App Least-squares in transient/relaxation problems 254
6 Viscous incompressible flows 265
6.1 Introduction 265
6.2 Basic concepts 267
6.3 Main issues in incompressible flow problems 272
6.4 Trial solutions and weighting functions 273
6.5 Stationary Stokes problem 275
6.6 Steady Navier-Stokes problem 293
6.7 Unsteady Navier-Stokes equations 294
6.8 Applications and solved exercices 306
References 323
Index 345
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