The Intermediate Finite Element Method: Fluid Flow And Heat Transfer Applications

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9781560323099 | 1560323094
Cover: Hardcover
Copyright: 3/1/1999

Rent

(Recommended)

$215.53

Term

Due

Price

Semester

Dec 12

$239.48

Quarter

Sep 7

$227.51

Short Term

Aug 13

$215.53

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
Buy New

Usually Ships in 3-5 Business Days

$306.59
eBook

Available Instantly

Online: 180 Days

Downloadable: 180 Days

*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

$151.80*

This book is a follow-up to the introductory text written by the same authors. The primary emphasis on this book is linear and nonlinear partial differential equations with particular concentration on the equations of viscous fluid motion. Each chapter describes a particular application of the finite element method and illustrates the concepts through example problems. A comprehensive appendix lists computer codes for 2-D fluid flow and two 3-D transient codes.

Foreword

(2)

Preface

xvii

(4)

Disclaimer

xxi

1 INTRODUCTION

(10)

1.1 Overview

(2)

1.2 Short History of the Finite Element Method

(2)

1.3 Finite Element Concept

(1)

1.4 Present Text

(1)

1.5 Closure

(1)

References

(3)

2 BASIC EQUATIONS OF FLUID DYNAMICS

(10)

2.1 Overview

(1)

2.2 Substantial Derivative

(1)

2.3 Mass Conservation Equation

(1)

2.4 Navier-Stokes Equations

(2)

2.5 Equation of Energy Conservation

(1)

2.6 Mass Transport

(1)

2.7 Wave Equation

(1)

2.8 Boundary Conditions

(1)

2.9 Closure

(1)

References

(2)

3 FUNDAMENTAL CONCEPTS

(88)

3.1 Overview

(1)

3.2 Linear Heat Conduction

(4)

3.3 Linear Operators and Linear Function Spaces

(3)

3.4 Weighted Residuals Formulation

(9)

3.5 Galerkin Method

(9)

3.5.1 Galerkin Method in One Dimension

(1)

3.5.1.1 Approximation 1

(3)

3.5.1.2 Approximation 2

(2)

3.5.2 Galerkin Method in Two Dimensions

(1)

3.6 Finite Element Method in One Dimension

(27)

3.6.1 Basic Piecewise Linear Spaces

(8)

3.6.2 Heat Conduction in One Dimension

(5)

3.6.3 Error in the Finite Element Approximation

(3)

3.6.4 Boundary Fluxes

(4)

3.6.5 Interelement Conditions

(7)

3.7 Finite Element Method in Two Dimensions

(22)

3.7.1 Basic Piecewise Bilinear Space

(4)

3.7.2 Heat Conduction in Two Dimensions

(10)

3.7.3 Error in Two-dimensional Approximation

(1)

3.7.4 Interelement Conditions

(7)

3.8 Finite Element Method in Three Dimensions

(2)

3.8.1 Trilinear Element

(1)

3.8.2 Heat Conduction in Three Dimensions

(1)

3.9 Closure

(1)

References

(1)

Exercises

(10)

4 HIGHER ORDER ELEMENTS

109

(66)

4.1 Overview

109

(1)

4.2 One-Dimensional Elements

110

(6)

4.3 Two-Dimensional Elements

116

(14)

4.3.1 Triangular Elements

117

(7)

4.3.2 Rectangular Elements

124

(3)

4.3.3 Error Bounds for Two-dimensional Elements

127

(3)

4.4 Isoparametric Elements

130

(17)

4.4.1 Difficulty 1

130

(2)

4.4.2 Difficulty 2

132

(15)

4.5 Blending Function Interpolation

147

(16)

4.6 Three-Dimensional Elements

163

(2)

4.7 Closure

165

(1)

References

166

(3)

Exercises

169

(6)

5 NUMERICAL INTEGRATION

175

(34)

5.1 Overview

175

(1)

5.2 Quadrature Formulae

175

(7)

5.2.1 Newton-Cotes Formulae

178

(2)

5.2.2 Gaussian Quadrature

180

(2)

5.3 Multiple Integrals

182

(2)

5.4 Minimum and Optimal Order of Integration

184

(10)

5.5 Reduced Integration, Evaluating Gradients

194

(10)

5.5.1 Reduced and Selective Integration

194

(2)

5.5.2 Evaluating Gradients

196

(8)

5.6 Closure

204

(1)

References

204

(1)

Exercises

205

(4)

6 NONLINEARITY

209

(48)

6.1 Overview

209

(1)

6.2 Basic Methods for Nonlinear Equations

210

(15)

6.2.1 The Newton-Raphson Method

210

(10)

6.2.2 Direct Iteration Methods

220

(5)

6.3 Nonlinear Examples

225

(24)

6.3.1 Heat Transfer with Temperature-Dependent Conductivity

225

(3)

6.3.2 Stationary Navier-Stokes Equations

228

(15)

6.3.3 Steady State Natural Convection

243

(6)

6.4 Closure

249

(1)

References

250

(1)

Exercises

251

(6)

7 TIME DEPENDENCE

257

(56)

7.1 Overview

257

(1)

7.2 Diffusion Equations

257

(18)

7.2.1 Semidiscrete Galerkin Method

258

(2)

7.2.2 The Theta Method

260

(5)

7.2.3 Accuracy and Stability of the Theta Method

265

(3)

7.2.4 Mass Lumping

268

(7)

7.3 Runge-Kutta Methods

275

(8)

7.4 Generalized Newmark Algorithms

283

(22)

7.4.1 Newmark Method for Second-Order Hyperbolic Equations

284

(13)

7.4.2 Generalized Newmark Method for Parabolic Equations

297

(8)

7.5 Closure

305

(1)

References

305

(2)

Exercises

307

(6)

8 STEADY STATE CONVECTIVE TRANSPORT

313

(44)

8.1 Overview

313

(1)

8.2 One-Dimensional Convection-Diffusion

314

(7)

8.3 Petrov-Galerkin Method

321

(10)

8.4 Petrov-Galerkin Method in Two Dimensions

331

(9)

8.5 Petrov-Galerkin Method in Three Dimensions

340

(2)

8.6 Nonlinear Equations

342

(4)

8.7 Closure

346

(1)

References

347

(3)

Exercises

350

(7)

9 TIME-DEPENDENT CONVECTION-DIFFUSION

357

(46)

9.1 Overview

357

(1)

9.2 Time-Dependent Convection

357

(13)

9.2.1 Numerical Damping

361

(7)

9.2.2 Phase Error

368

(2)

9.3 Petrov-Galerkin Method for Time-Dependent Convection-Diffusion

370

(14)

9.3.1 Quadratic in Time, Linear in Space Weights

371

(6)

9.3.2 Stability Analysis

377

(7)

9.4 Multidimensional Time-Dependent Convection-Diffusion

384

(11)

9.5 Closure

395

(1)

References

395

(2)

Exercises

397

(6)

10 VISCOUS INCOMPRESSIBLE FLUID FLOW

403

(62)

10.1 Overview

403

(1)

10.2 Basic Form of the Navier-Stokes Equations

404

(5)

10.3 Constant-Density Flows in Two Dimensions

409

(25)

10.3.1 Mixed Formulation

409

(13)

10.3.2 Fractional Step Method

422

(2)

10.3.3 Penalty Function Formulation

424

(10)

10.4 Stratified Flows

434

(18)

10.4.1 Finite Element Approximations

436

(10)

10.4.2 Calculation of the Pressure

446

(2)

10.4.3 Open Boundaries

448

(4)

10.5 Free Surface Flows

452

(4)

10.6 Closure

456

(2)

References

458

(3)

Exercises

461

(4)

11 MESH GENERATION

465

(70)

11.1 Overview

465

(1)

11.2 Introduction

466

(8)

11.2.1 Types of Meshes

466

(4)

11.2.2 Popular Mesh Generation Schemes

470

(1)

11.2.2.1 Manual Generation

470

(1)

11.2.2.2 Semi-Automatic Generation

470

(1)

11.2.2.3 Transport Mapping

471

(1)

11.2.2.4 Explicit Solution of PDEs

471

(1)

11.2.2.5 Overlapping and Deformation

472

(1)

11.2.2.6 Advancing-front Method

473

(1)

11.2.2.7 Combination

473

(1)

11.3 Mesh Generation Techniques

474

(21)

11.3.1 Structured Meshes

475

(1)

11.3.1.1 One Dimension

475

(1)

11.3.1.2 Two Dimensions

476

(1)

11.3.1.3 Three Dimensions

476

(1)

11.3.1.4 Boundary Fitted Coordinates

477

(7)

11.3.2 Unstructured Meshes

484

(1)

11.3.2.1 General Types of Elements

485

(1)

11.3.2.2 One-dimensional Elements

485

(1)

11.3.2.3 Two-dimensional Elements

486

(2)

11.3.2.4 Three-dimensional Elements

488

(2)

11.3.3 Mesh Generation Guidelines

490

(5)

11.4 Bandwidth

495

(13)

11.4.1 Nodal Renumbering Schemes

498

(1)

11.4.1.1 Gibbs Method

499

(1)

11.4.1.2 Groom's Method

500

(1)

11.4.1.3 Lipton-Tajan Method

500

(1)

11.4.1.4 Akhras and Dhatt Method

500

(1)

11.4.1.5 Frontal Method

501

(1)

11.4.1.6 Element Colorization Method

501

(1)

11.4.1.7 Nested Dissection Method

501

(1)

11.4.2 Simple Bandwidth Reduction Algorithm

501

(4)

11.4.3 Delaunay Triangulation

505

(3)

11.5 Adaptation

508

(19)

11.5.1 Types of Adaptation

508

(3)

11.5.2 Error Estimates and Adaptation Criteria

511

(6)

11.5.3 Simple h-adaptive Technique

517

(1)

11.5.3.1 Mesh Regeneration

517

(3)

11.5.3.2 Element Subdivision

520

(1)

11.5.3.3 Adaptation Parameters

521

(3)

11.5.3.4 Adaptation Rules

524

(1)

11.5.4 Mesh Adaptation Example

525

(2)

11.6 Closure

527

(2)

References

529

(4)

Exercises

533

(2)

12 FURTHER APPLICATIONS

535

(36)

12.1 Overview

535

(1)

12.2 Time-Dependent Flows and Flows in Rotating Systems

535

(12)

12.2.1 Isothermal Flow Past a Circular Cylinder

540

(2)

12.2.2 Natural Convection in a Horizontal Circular Cylinder

542

(3)

12.2.3 Lubricant Flow in a Microgap

545

(2)

12.3 Turbulent Flow

547

(5)

12.4 Compressible Flow

552

(12)

12.4.1 Supersonic Flow Impinging on a Cylinder

558

(2)

12.4.2 Chemically Reacting Supersonic Flow

560

(4)

12.5 Three-dimensional Flow

564

(4)

12.5.1 Natural Convection Within a Sphere

564

(2)

12.5.2 Transonic Flow Through a Rectangular Nozzle

566

(2)

12.6 Closure

568

(1)

References

568

(3)

APPENDIX A: LINEAR OPERATIONS

571

(6)

A.1 Linear Vector Spaces

571

(4)

A.2 Linear Operators

575

(2)

APPENDIX B: UNITS

577

(2)

APPENDIX C: NOMENCLATURE

579

(6)

INDEX

585

Please wait while the item is added to your bag...

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

The Intermediate Finite Element Method: Fluid Flow And Heat Transfer Applications

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

The Intermediate Finite Element Method: Fluid Flow And Heat Transfer Applications

Summary

Table of Contents

Supplemental Materials

Digital License