Rainald Lohner, Department of Computational and Data Sciences, 4400 University Drive, Fairfax, Virginia 22030, USA? Rainald Lohner gained his PhD from the University of Wales, Swansea. He is now a director of the Computational Fluid Dynamics Center of the Department of Computational and Data Sciences at George Mason University, Virginia, USA. His research interests include Fluid-Structure Interaction, Unstructured Grid Generation, Pre-Processing, and Parallel Computing.? Notable achievements include a Distinguished Professor award 'for his substantive and innovative contributions to the field of computational fluid dynamics' by GMU and being a made a Honorary Professor of the University of Wales at Swansea.

FOREWORD TO THE SECOND EDITION xiv

ACKNOWLEDGEMENTS xvii

1 INTRODUCTION AND GENERAL CONSIDERATIONS 1

1.1 The CFD code 4

1.2 Porting research codes to an industrial context 5

1.3 Scope of the book 5

2 DATA STRUCTURES AND ALGORITHMS 7

2.1 Representation of agrid 7

2.2 Derived data structures for static data 9

2.3 Derived data structures for dynamic data 17

2.4 Sorting and searching 19

2.5 Proximity in space 22

2.6 Nearest-neighbours and graphs 30

2.7 Distance to surface 30

3 GRID GENERATION 35

3.1 Description of the domain to be gridded 37

3.2 Variation of element size andshape 38

3.3 Element type 46

3.4 Automatic grid generation methods 47

3.5 Other grid generation methods 49

3.6 The advancing front technique 51

3.7 Delaunay triangulation 59

3.8 Grid improvement 65

3.9 Optimal space-filling tetrahedra 70

3.10 Grids with uniform cores 72

3.11 Volume-to-surface meshing 73

3.12 Navier-Stokes gridding techniques 75

3.13 Filling space with points/arbitrary objects 90

3.14 Applications 98

4 APPROXIMATION THEORY 109

4.1 The basic problem 109

4.2 Choiceof trial functions 112

4.3 General properties of shape functions 118

4.4 Weighted residual methods with local functions 118

4.5 Accuracy and effort 119

4.6 Grid estimates 121

5 APPROXIMATION OF OPERATORS 123

5.1 Taxonomy of methods 123

5.2 The Poisson operator 124

5.3 Recovery of derivatives 130

6 DISCRETIZATION IN TIME 133

6.1 Explicit schemes 133

6.2 Implicit schemes 135

6.3 A word of caution 136

7 SOLUTION OF LARGE SYSTEMS OF EQUATIONS 137

7.1 Direct solvers 137

7.2 Iterative solvers 140

7.3 Multigrid methods 153

8 SIMPLE EULER/NAVIER-STOKES SOLVERS 161

8.1 Galerkin approximation 162

8.2 Lax-Wendroff (Taylor-Galerkin) 164

8.3 Solvingfor the consistent mass matrix 167

8.4 Artificial viscosities 167

8.5 Boundary conditions 169

8.6 Viscous fluxes 172

9 FLUX-CORRECTED TRANSPORT SCHEMES 175

9.1 Algorithmic implementation 176

9.2 Steepening 178

9.3 FCT for Taylor-Galerkin schemes 179

9.4 Iterative limiting 179

9.5 Limiting for systems of equations 180

9.6 Examples 181

9.7 Summary 183

10 EDGE-BASED COMPRESSIBLE FLOWSOLVERS 187

10.1 TheLaplacianoperator 188

10.2 First derivatives:first form 190

10.3 First derivatives:secondform 191

10.4 Edge-basedschemes foradvection-dominatedPDEs 193

11 INCOMPRESSIBLE FLOWSOLVERS 201

11.1 The advection operator 201

11.2 The divergence operator 203

11.3 Artificial compressibility 206

11.4 Temporal discretization: projection schemes 206

11.5 Temporal discretization: implicit schemes 208

11.6 Temporal discretization of higher order 209

11.7 Acceleration to the steady state 210

11.8 Projective prediction of pressure increments 212

11.9 Examples 213

12 MESH MOVEMENT 227

12.1 The ALE frame of reference 227

12.1.1 Boundary conditions 228

12.2 Geometric conservation law 228

12.3 Mesh movement algorithms 229

12.4 Region of moving elements 235

12.5 PDE-based distance functions 236

12.6 Penalization of deformed elements 238

12.7 Special movement techniques for RANS grids 239

12.8 Rotating parts/domains 240

12.9 Applications 241

13 INTERPOLATION 245

13.1 Basic interpolation algorithm 246

13.2 Fastest 1-time algorithm:brute force 247

13.3 Fastest N-time algorithm:octree search 247

13.4 Fastest known vicinity algorithm: neighbour-to-neighbour 249

13.5 Fastest grid-to-gridalgorithm:advancing-front vicinity 250

13.6 Conservative interpolation 257

13.7 Surface-grid-to-surface-grid interpolation 261

13.8 Particle-grid interpolation 265

14 ADAPTIVE MESH REFINEMENT 269

14.1 Optimal-meshcriteria 270

14.2 Error indicators/estimators 271

14.3 Refinement strategies 278

14.4 Tutorial:h-refinement with tetrahedra 286

14.5 Examples 291

15 EFFICIENT USE OF COMPUTER HARDWARE 299

15.1 Reduction of cache-misses 300

15.2 Vector machines 316

15.3 Parallel machines:general considerations 328

15.4 Shared-memory parallel machines 329

15.5 SIMD machines 334

15.6 MIMD machines 336

15.7 The effect of Moore's law on parallel computing 344

16 SPACE-MARCHING AND DEACTIVATION 351

16.1 Space-marching 351

16.2 Deactivation 365

17 OVERLAPPING GRIDS 371

17.1 Interpolation criteria 372

17.2 External boundaries and domains 373

17.3 Interpolation: initialization 373

17.4 Treatment of domains that are partially outside 375

17.5 Removalof inactive regions 375

17.6 Incremental interpolation 377

17.7 Changes to the flowsolver 377

17.8 Examples 378

18 EMBEDDED AND IMMERSED GRID TECHNIQUES 383

18.1 Kinetic treatmentof embeddedor immersed objects 385

18.2 Kinematic treatment of embedded surfaces 389

18.3 Deactivation of interior regions 395

18.4 Extrapolationof the solution 397

18.5 Adaptive mesh refinement 397

18.6 Load/flux transfer 398

18.7 Treatment of gapsor cracks 399

18.8 Direct link to particles 400

18.9 Examples 401

19 TREATMENT OF FREE SURFACES 419

19.1 Interface fitting methods 419

19.2 Interface capturing methods 429

20 OPTIMAL SHAPE AND PROCESS DESIGN 449

20.1 The general optimization problem 449

20.2 Optimization techniques 451

20.3 Adjoint solvers 462

20.4 Geometric constraints 469

20.5 Approximate gradients 471

20.6 Multipoint optimization 471

20.7 Representation of surface changes 472

20.8 Hierarchical design procedures 472

20.9 Topological optimization via porosities 473

20.10 Examples 474

References 481

Index 515