Applied Computational Fluid... | Buy

Computational fluid dynamics (CFD) is concerned with the efficient numerical solution of the partial differential equations that describe fluid dynamics, and CFD techniques are commonly used in many areas of engineering where fluid behavior is a factor. This book covers the range of topics required for a thorough study and understanding of CFD.

Acknowledgments

ix

Introduction

1

(8)

Introduction and General Considerations

1

(3)

The CFD Code

4

(2)

Porting Research Codes to an Industrial Context

6

(1)

Scope of the Book

6

(3)

References

7

(2)

Data Structures and Algorithms

9

(28)

Representation of a Grid

9

(2)

Derived Data Structures for Static Data

11

(10)

Derived Data Structures for Dynamic Data

21

(2)

Sorting and Searching

23

(4)

Proximity in Space

27

(5)

Nearest Neighbors and Graphs

32

(1)

Distance to Wall

33

(4)

References

36

(1)

Grid Generation

37

(68)

Description of the Domain to be Gridded

39

(1)

Variation of Element Size and Shape

40

(10)

Element Type

50

(2)

Automatic Grid-Generation Methods

52

(1)

Other Grid-Generation Methods

53

(2)

The Advancing Front Technique

55

(8)

Delaunay Triangulation

63

(8)

Grid Improvement

71

(4)

Navier-Stokes Gridding Techniques

75

(15)

Applications

90

(15)

References

99

(6)

Approximation Theory

105

(14)

The Basic Problem

105

(4)

Choice of Trial-Functions

109

(7)

General Properties of Shape-Functions

116

(1)

Weighted Residual Methods with Local Functions

117

(1)

Accuracy and Effort

117

(2)

Approximation of Operators

119

(14)

Taxonomy of Methods

119

(2)

The Poisson Operator

121

(7)

Recovery of Derivatives

128

(5)

References

131

(2)

Discretization in Time

133

(4)

Explicit Schemes

133

(1)

Implicit Schemes

134

(2)

A Word of Caution

136

(1)

References

136

(1)

Solution of Large Systems of Equations

137

(28)

Direct Solvers

137

(4)

Iterative Solvers

141

(15)

Multigrid Methods

156

(9)

References

162

(3)

Simple Euler/Navier-Stokes Solvers

165

(12)

Galerkin Approximation

166

(3)

Lax-Wendroff (Taylor-Galerkin)

169

(3)

Solving for the Consistent Mass-matrix

172

(1)

Artificial Viscosities

172

(3)

Viscous Fluxes

175

(2)

References

176

(1)

Flux-Corrected Transport (FCT) Schemes

177

(14)

FCT Concept

177

(1)

Algorithmic Implementation

178

(2)

Steepening

180

(1)

FCT For Taylor-Galerkin Schemes

181

(1)

Limiting for Systems of Equations

182

(1)

Examples

183

(4)

Summary

187

(4)

References

187

(4)

Edge-Based Compressible Flow Solvers

191

(18)

The Laplacian Operator

192

(2)

First Derivatives: First Form

194

(1)

First Derivatives: Second Form

195

(4)

Edge-Based Schemes for Advection-dominated PDEs

199

(10)

References

206

(3)

Incompressible Flow Solvers

209

(16)

The Advection Operator

210

(2)

The Divergence Operator

212

(3)

Artificial Compressibility

215

(1)

Temporal Discretization: Projection Schemes

215

(2)

Temporal Discretization: Implicit Schemes

217

(1)

Examples

218

(7)

References

222

(3)

Mesh Movement

225

(14)

The ALE Frame of Reference

225

(2)

Geometric Conservation Law

227

(1)

Mesh Movement Algorithms

227

(6)

Region of Moving Elements

233

(1)

Applications

234

(5)

References

236

(3)

Interpolation

239

(22)

Basic Interpolation Algorithm

240

(1)

Fastest 1-Time Algorithm: Brute-Force

241

(1)

Fastest N-Time Algorithm: Octree Search

242

(2)

Fastest known Vicinity Algorithm: Neighbor-to-Neighbor

244

(2)

Fastest Grid-to-Grid Algorithm: Advancing-Front Vicinity

246

(7)

Surface-Grid-to-Surface-Grid Interpolation

253

(2)

Particle-Grid Interpolation

255

(6)

References

258

(3)

Adaptive Mesh Refinement

261

(36)

Optimal Mesh Criteria

262

(2)

Error Indicators and Estimators

264

(6)

Mesh Refinement Strategies

270

(9)

Tutorial: H-refinement with Tetrahedra

279

(6)

Examples

285

(12)

References

291

(6)

Efficient use of Supercomputer Hardware

297

(46)

Reduction of Cache-Misses

298

(15)

Vector-Machines

313

(7)

Parallel Machines: General Considerations

320

(1)

Shared Memory Parallel Machines

321

(7)

SIMD Machines

328

(1)

MIMD Machines

329

(14)

References

339

(4)

Space-marching and Deactivation

343

Space-Marching

343

Deactivation

360

References

361

Index

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