Applied CFD techniques : an introduction based on finite element methods

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	p. ix
1 Introduction	p. 1
1.1 Introduction and General Considerations	p. 1
1.2 The CFD Code	p. 4
1.3 Porting Research Codes to an Industrial Context	p. 6
1.4 Scope of the Book	p. 6
References	p. 7
2 Data Structures and Algorithms	p. 9
2.1 Representation of a Grid	p. 9
2.2 Derived Data Structures for Static Data	p. 11
2.3 Derived Data Structures for Dynamic Data	p. 21
2.4 Sorting and Searching	p. 23
2.5 Proximity in Space	p. 27
2.6 Nearest Neighbors and Graphs	p. 32
2.7 Distance to Wall	p. 33
References	p. 36
3 Grid Generation	p. 37
3.1 Description of the Domain to be Gridded	p. 39
3.2 Variation of Element Size and Shape	p. 40
3.3 Element Type	p. 50
3.4 Automatic Grid-Generation Methods	p. 52
3.5 Other Grid-Generation Methods	p. 53
3.6 The Advancing Front Technique	p. 55
3.7 Delaunay Triangulation	p. 63
3.8 Grid Improvement	p. 71
3.9 Navier-Stokes Gridding Techniques	p. 75
3.10 Applications	p. 90
References	p. 99
4 Approximation Theory	p. 105
4.1 The Basic Problem	p. 105
4.2 Choice of Trial-Functions	p. 109
4.3 General Properties of Shape-Functions	p. 116
4.4 Weighted Residual Methods with Local Functions	p. 117
4.5 Accuracy and Effort	p. 117
5 Approximation of Operators	p. 119
5.1 Taxonomy of Methods	p. 119
5.2 The Poisson Operator	p. 121
5.3 Recovery of Derivatives	p. 128
References	p. 131
6 Discretization in Time	p. 133
6.1 Explicit Schemes	p. 133
6.2 Implicit Schemes	p. 134
6.3 A Word of Caution	p. 136
References	p. 136
7 Solution of Large Systems of Equations	p. 137
7.1 Direct Solvers	p. 137
7.2 Iterative Solvers	p. 141
7.3 Multigrid Methods	p. 156
References	p. 162
8 Simple Euler/Navier-Stokes Solvers	p. 165
8.1 Galerkin Approximation	p. 166
8.2 Lax-Wendroff (Taylor-Galerkin)	p. 169
8.3 Solving for the Consistent Mass-Matrix	p. 172
8.4 Artificial Viscosities	p. 172
8.5 Viscous Fluxes	p. 175
References	p. 176
9 Flux-Corrected Transport (FCT) Schemes	p. 177
9.1 FCT Concept	p. 177
9.2 Algorithmic Implementation	p. 178
9.3 Steepening	p. 180
9.4 FCT For Taylor-Galerkin Schemes	p. 181
9.5 Limiting for Systems of Equations	p. 182
9.6 Examples	p. 183
9.7 Summary	p. 187
References	p. 187
10 Edge-Based Compressible Flow Solvers	p. 191
10.1 The Laplacian Operator	p. 192
10.2 First Derivatives: First Form	p. 194
10.3 First Derivatives: Second Form	p. 195
10.4 Edge-Based Schemes for Advection-dominated PDEs	p. 199
References	p. 206
11 Incompressible Flow Solvers	p. 209
11.1 The Advection Operator	p. 210
11.2 The Divergence Operator	p. 212
11.3 Artificial Compressibility	p. 215
11.4 Temporal Discretization: Projection Schemes	p. 215
11.5 Temporal Discretization: Implicit Schemes	p. 217
11.6 Examples	p. 218
References	p. 222
12 Mesh Movement	p. 225
12.1 The ALE Frame of Reference	p. 225
12.2 Geometric Conservation Law	p. 227
12.3 Mesh Movement Algorithms	p. 227
12.4 Region of Moving Elements	p. 233
12.5 Applications	p. 234
References	p. 236
13 Interpolation	p. 239
13.1 Basic Interpolation Algorithm	p. 240
13.2 Fastest 1-Time Algorithm: Brute-Force	p. 241
13.3 Fastest N-Time Algorithm: Octree Search	p. 242
13.4 Fastest known Vicinity Algorithm: Neighbor-to-Neighbor	p. 244
13.5 Fastest Grid-to-Grid Algorithm: Advancing-Front Vicinity	p. 246
13.6 Surface-Grid-to-Surface-Grid Interpolation	p. 253
13.7 Particle-Grid Interpolation	p. 255
Reference	p. 258
14 Adaptive Mesh Refinement	p. 261
14.1 Optimal Mesh Criteria	p. 262
14.2 Error Indicators and Estimators	p. 264
14.3 Mesh Refinement Strategies	p. 270
14.4 Tutorial: H-refinement with Tetrahedra	p. 279
14.5 Examples	p. 285
References	p. 291
15 Efficient use of Supercomputer Hardware	p. 297
15.1 Reduction of Cache-Misses	p. 298
15.2 Vector-Machines	p. 313
15.3 Parallel Machines: General Considerations	p. 320
15.4 Shared Memory Parallel Machines	p. 321
15.5 SIMD Machines	p. 328
15.6 MIMD Machines	p. 329
References	p. 339
16 Space-marching and Deactivation	p. 343
16.1 Space-Marching	p. 343
16.2 Deactivation	p. 360
References	p. 361
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