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The Finite Element Method for Fluid Dynamics

The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary o… Read more

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Description

The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations.

The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves. Updated throughout, this new edition includes new chapters on:

  • Fluid-structure interaction, including discussion of one-dimensional and multidimensional problems
  • Biofluid dynamics, covering flow throughout the human arterial system

Focusing on the core knowledge, mathematical and analytical tools needed for successful computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics is the authoritative introduction of choice for graduate level students, researchers and professional engineers.

Key features

  • A proven keystone reference in the library of any engineer needing to understand and apply the finite element method to fluid mechanics
  • Founded by an influential pioneer in the field and updated in this seventh edition by leading academics who worked closely with Olgierd C. Zienkiewicz
  • Features new chapters on fluid-structure interaction and biofluid dynamics, including coverage of one-dimensional flow in flexible pipes and challenges in modeling systemic arterial circulation

Readership

Mechanical, Aerospace, Automotive, Marine, Biomedical, Environmental and Civil Engineers, applied mathematicians and computer aided engineering software developers

Table of contents

Chapter 1. Introduction to the Equations of Fluid Dynamics and the Finite Element Approximation

Abstract

1.1 General Remarks and Classification of Fluid Dynamics Problems Discussed in this Book

1.2 The Governing Equations of Fluid Dynamics

1.3 Inviscid, Incompressible Flow

1.4 Incompressible (or Nearly Incompressible) Flows

1.5 Numerical Solutions: Weak Forms, Weighted Residual, and Finite Element Approximation

1.6 Concluding Remarks

References

Chapter 2. Convection-Dominated Problems: Finite Element Approximations to the Convection-Diffusion-Reaction Equation

Abstract

2.1 Introduction

2.2 The steady-state problem in one dimension

2.3 The steady-state problem in two (or three) dimensions

2.4 Steady state: Concluding remarks

2.5 Transients: Introductory remarks

2.6 Characteristic-based methods

2.7 Taylor-Galerkin procedures for scalar variables

2.8 Steady-state condition

2.9 Nonlinear waves and shocks

2.10 Treatment of pure convection

2.11 Boundary conditions for convection-diffusion

2.12 Summary and concluding remarks

References

Chapter 3. The Characteristic-Based Split (CBS) Algorithm: A General Procedure for Compressible and Incompressible Flow

Abstract

3.1 Introduction

3.2 Nondimensional form of the Governing Equations

3.3 Characteristic-Based Split (CBS) Algorithm

3.4 Explicit, Semi-Implicit, and Nearly Implicit Forms

3.5 Artificial Compressibility and Dual Time Stepping

3.6 “Circumvention” of the Babuška-Brezzi (BB) Restrictions

3.7 A Single-Step Version

3.8 Splitting Error

3.9 Boundary Conditions

3.10 The Performance of Two- and Single-Step Algorithms on an Inviscid Problem

3.11 Performance of Dual Time Stepping to Remove Pressure Error

3.12 Concluding Remarks

References

Chapter 4. Incompressible Newtonian Laminar Flows

Abstract

4.1 Introduction and The Basic Equations

4.2 Use of The CBS Algorithm for Incompressible Flows

4.3 Adaptive Mesh Refinement

4.4 Adaptive Mesh Generation for Transient Problems

4.5 Slow Flows: Mixed and Penalty Formulations

4.6 Concluding Remarks

References

Chapter 5. Incompressible Non-Newtonian Flows

Abstract

5.1 Introduction

5.2 Non-Newtonian Flows: Metal and Polymer Forming

5.3 Viscoelastic Flows

5.4 Direct Displacement Approach To Transient Metal Forming

5.5 Concluding Remarks

References

Chapter 6. Free Surface and Buoyancy Driven Flows

Abstract

6.1 Introduction

6.2 Free surface flows

6.3 Buoyancy driven flows

6.4 Concluding remarks

References

Chapter 7. Compressible High-Speed Gas Flow

Abstract

7.1 Introduction

7.2 The Governing Equations

7.3 Boundary Conditions: Subsonic and Supersonic Flow

7.4 Numerical Approximations and the CBS Algorithm

7.5 Shock Capture

7.6 Variable Smoothing

7.7 Some Preliminary Examples for the Euler Equation

7.8 Adaptive Refinement and Shock Capture in Euler Problems

7.9 Three-Dimensional Inviscid Examples in Steady State

7.10 Transient Two- and Three-Dimensional Problems

7.11 Viscous Problems in Two Dimensions

7.12 Three-Dimensional Viscous Problems

7.13 Boundary Layer: Inviscid Euler Solution Coupling

7.14 Concluding Remarks

References

Chapter 8. Turbulent Flows

Abstract

8.1 Introduction

8.2 Treatment of incompressible turbulent flows

8.3 Treatment of compressible flows

8.4 Large eddy simulation (LES)

8.5 Detached eddy simulation (DES) and monotonically integrated LES (MILES)

8.6 Direct numerical simulation (DNS)

8.7 Concluding remarks

References

Chapter 9. Generalized Flow and Heat Transfer in Porous Media

Abstract

9.1 Introduction

9.2 A generalized porous medium flow approach

9.3 Discretization procedure

9.4 Forced convection

9.5 Natural convection

9.6 Concluding remarks

References

Chapter 10. Shallow-Water Problems

Abstract

10.1 Introduction

10.2 The basis of the shallow-water equations

10.3 Numerical approximation

10.4 Examples of application

10.5 Drying areas

10.6 Shallow-water transport

10.7 Concluding remarks

References

Chapter 11. Long and Medium Waves

Abstract

11.1 Introduction and Equations

11.2 Waves in Closed Domains: Finite Element Models

11.3 Difficulties in Modeling Surface Waves

11.4 Bed Friction and other Effects

11.5 The Short-Wave Problem

11.6 Waves in Unbounded Domains (Exterior Surface Wave Problems)

11.7 Unbounded Problems

11.8 Local NonReflecting Boundary Conditions (NRBCs)

11.9 Infinite Elements

11.10 Convection and Wave Refraction

11.11 Transient Problems

11.12 Linking to Exterior Solutions (or DtN Mapping)

11.13 Three-Dimensional Effects in Surface Waves

11.14 Concluding Remarks

References

Chapter 12. Short Waves

Abstract

12.1 Introduction

12.2 Background

12.3 Errors in Wave Modeling

12.4 Recent Developments in Short-Wave Modeling

12.5 Transient Solution of Electromagnetic Scattering Problems

12.6 Finite Elements Incorporating Wave Shapes

12.7 Refraction

12.8 Spectral Finite Elements for Waves

12.9 Discontinuous Galerkin Finite Elements (DGFE)

12.10 Concluding Remarks

References

Chapter 13. Fluid–Structure Interaction

Abstract

13.1 Introduction

13.2 One-dimensional fluid–structure interaction

13.3 Multidimensional problems

13.4 Concluding remarks

References

Chapter 14. Biofluid Dynamics

Abstract

14.1 Introduction

14.2 Flow in Human Arterial System

14.3 Image-Based Subject-Specific Flow Modeling

14.4 Concluding Remarks

References

Chapter 15. Computer Implementation of the CBS Algorithm

Abstract

15.1 Introduction

15.2 The Data Input Module

15.3 Solution Module

15.4 Output Module

References

Appendix A. Self-Adjoint Differential Equations

Appendix B. Nonconservative Form of Navier-Stokes Equations

Appendix C. Computing the Drag Force and Stream Function

C.1 Drag calculation

C.2 Stream function

Appendix D. Convection-Diffusion Equations: Vector-Valued Variables

D.1 The Taylor-Galerkin method used for vector-valued variables

D.2 Two-step predictor-corrector methods: Two-step Taylor-Galerkin operation

References

Appendix E. Integration Formulae

E.1 Linear triangles

E.2 Linear tetrahedron

Appendix F. Edge-Based Finite Element Formulation

Appendix G. Boundary Layer–Inviscid Flow Coupling

Appendix H. Multigrid Method

References

Appendix I. Mass-Weighted Averaged Turbulence Transport Equations

I.1 Turbulence models

Review quotes

Reviews from the previous edition: "...this is a book that you simply cannot afford to be without."—INTERNATIONAL JOURNAL OF NUMERICAL METHODS IN ENGINEERING

Product details

About the authors

OZ

O. C. Zienkiewicz

Professor O.C. Zienkiewicz, CBE, FRS, FREng died on 2 January 2009. Prior to his death he was Professor Emeritus at the Civil and Computational Engineering Centre, University of Wales Swansea and previously was Director of the Institute for Numerical Methods in Engineering at the University of Wales Swansea, UK. He also held the UNESCO Chair of Numerical Methods in Engineering at the Technical University of Catalunya, Barcelona, Spain. He was the head of the Civil Engineering Department at the University of Wales Swansea between 1961 and 1989. During this period he established that department as one of the primary centres of finite element research. In 1968 he became the Founder Editor of the International Journal for Numerical Methods in Engineering which still remains today the major journal in this field. The recipient of 27 honorary degrees and many medals, Professor Zienkiewicz was a member of five academies – an honour he received for his many contributions to the fundamental developments of the finite element method. In 1978, he became a Fellow of the Royal Society and the Royal Academy of Engineering. This was followed by his election as a foreign member to the US National Academy of Engineering (1981), the Polish Academy of Science (1985), the Chinese Academy of Sciences (1998), and the National Academy of Science, Italy (Academia dei Lincei) (1999). He published the first edition of this book in 1967 and it remained the only book on the subject until 1971.
Affiliations and expertise
Swansea University, Swansea, Wales

RT

R. L. Taylor

Professor R.L. Taylor has more than 60 years of experience in the modelling and simulation of structures and solid continua including eighteen years in industry. He is Professor of the Graduate School and the Emeritus T.Y. and Margaret Lin Professor of Engineering at the University of California, Berkeley and also Corporate Fellow at Dassault Systèmes Americas Corp. in Johnston, Rhode Island. In 1991 he was elected to membership in the US National Academy of Engineering in recognition of his educational and research contributions to the field of computational mechanics. Professor Taylor is a Fellow of the US Association for Computational Mechanics – USACM (1996) and a Fellow of the International Association of Computational Mechanics – IACM (1998). He has received numerous awards including the Berkeley Citation, the highest honour awarded by the University of California, Berkeley, the USACM John von Neumann Medal, the IACM Gauss–Newton Congress Medal and a Dr.-Ingenieur ehrenhalber awarded by the Technical University of Hannover, Germany. Professor Taylor has written several computer programs for finite element analysis of structural and non-structural systems, one of which, FEAP, is used world-wide in education and research environments. A personal version, FEAPpv, available on GitHub, is incorporated into this book.
Affiliations and expertise
Emeritus Professor of Engineering, University of California, Berkeley, USA

PN

P. Nithiarasu

P. Nithiarasu is Professor at Zienkiewicz Institute for Modelling, Data and AI and Associate Dean for Research, Innovation and Impact, Faculty of Science and Engineering, Swansea University. Previously he has served as the Head of Zienkiewicz Centre for Computational Engineering, Deputy Head of College of Engineering and Dean of Academic Leadership. He was awarded the Zienkiewicz silver medal from the ICE London in 2002, the ECCOMAS Young Investigator award in 2004, and the prestigious EPSRC Advanced Fellowship in 2006.

Affiliations and expertise
Professor, Zienkiewicz Institute for Modelling, Data and AI and Associate Dean for Research, Innovation and Impact, Faculty of Science and Engineering, Swansea University

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