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.

?This book has a good concept und gives a compact description of applied CFD.? (ZAMM, October 2009)

• FOREWORD TO THE SECOND EDITION xivACKNOWLEDGEMENTS xvii1 INTRODUCTION AND GENERAL CONSIDERATIONS 11.1 The CFD code 41.2 Porting research codes to an industrial context 51.3 Scope of the book 52 DATA STRUCTURES AND ALGORITHMS 72.1 Representation of agrid 72.2 Derived data structures for static data 92.3 Derived data structures for dynamic data 172.4 Sorting and searching 192.5 Proximity in space 222.6 Nearest-neighbours and graphs 302.7 Distance to surface 303 GRID GENERATION 353.1 Description of the domain to be gridded 373.2 Variation of element size andshape 383.3 Element type 463.4 Automatic grid generation methods 473.5 Other grid generation methods 493.6 The advancing front technique 513.7 Delaunay triangulation 593.8 Grid improvement 653.9 Optimal space-filling tetrahedra 703.10 Grids with uniform cores 723.11 Volume-to-surface meshing 733.12 Navier-Stokes gridding techniques 753.13 Filling space with points/arbitrary objects 903.14 Applications 984 APPROXIMATION THEORY 1094.1 The basic problem 1094.2 Choiceof trial functions 1124.3 General properties of shape functions 1184.4 Weighted residual methods with local functions 1184.5 Accuracy and effort 1194.6 Grid estimates 1215 APPROXIMATION OF OPERATORS 1235.1 Taxonomy of methods 1235.2 The Poisson operator 1245.3 Recovery of derivatives 1306 DISCRETIZATION IN TIME 1336.1 Explicit schemes 1336.2 Implicit schemes 1356.3 A word of caution 1367 SOLUTION OF LARGE SYSTEMS OF EQUATIONS 1377.1 Direct solvers 1377.2 Iterative solvers 1407.3 Multigrid methods 1538 SIMPLE EULER/NAVIER-STOKES SOLVERS 1618.1 Galerkin approximation 1628.2 Lax-Wendroff (Taylor-Galerkin) 1648.3 Solvingfor the consistent mass matrix 1678.4 Artificial viscosities 1678.5 Boundary conditions 1698.6 Viscous fluxes 1729 FLUX-CORRECTED TRANSPORT SCHEMES 1759.1 Algorithmic implementation 1769.2 Steepening 1789.3 FCT for Taylor-Galerkin schemes 1799.4 Iterative limiting 1799.5 Limiting for systems of equations 1809.6 Examples 1819.7 Summary 18310 EDGE-BASED COMPRESSIBLE FLOWSOLVERS 18710.1 TheLaplacianoperator 18810.2 First derivatives:first form 19010.3 First derivatives:secondform 19110.4 Edge-basedschemes foradvection-dominatedPDEs 19311 INCOMPRESSIBLE FLOWSOLVERS 20111.1 The advection operator 20111.2 The divergence operator 20311.3 Artificial compressibility 20611.4 Temporal discretization: projection schemes 20611.5 Temporal discretization: implicit schemes 20811.6 Temporal discretization of higher order 20911.7 Acceleration to the steady state 21011.8 Projective prediction of pressure increments 21211.9 Examples 21312 MESH MOVEMENT 22712.1 The ALE frame of reference 22712.1.1 Boundary conditions 22812.2 Geometric conservation law 22812.3 Mesh movement algorithms 22912.4 Region of moving elements 23512.5 PDE-based distance functions 23612.6 Penalization of deformed elements 23812.7 Special movement techniques for RANS grids 23912.8 Rotating parts/domains 24012.9 Applications 24113 INTERPOLATION 24513.1 Basic interpolation algorithm 24613.2 Fastest 1-time algorithm:brute force 24713.3 Fastest N-time algorithm:octree search 24713.4 Fastest known vicinity algorithm: neighbour-to-neighbour 24913.5 Fastest grid-to-gridalgorithm:advancing-front vicinity 25013.6 Conservative interpolation 25713.7 Surface-grid-to-surface-grid interpolation 26113.8 Particle-grid interpolation 26514 ADAPTIVE MESH REFINEMENT 26914.1 Optimal-meshcriteria 27014.2 Error indicators/estimators 27114.3 Refinement strategies 27814.4 Tutorial:h-refinement with tetrahedra 28614.5 Examples 29115 EFFICIENT USE OF COMPUTER HARDWARE 29915.1 Reduction of cache-misses 30015.2 Vector machines 31615.3 Parallel machines:general considerations 32815.4 Shared-memory parallel machines 32915.5 SIMD machines 33415.6 MIMD machines 33615.7 The effect of Moore's law on parallel computing 34416 SPACE-MARCHING AND DEACTIVATION 35116.1 Space-marching 35116.2 Deactivation 36517 OVERLAPPING GRIDS 37117.1 Interpolation criteria 37217.2 External boundaries and domains 37317.3 Interpolation: initialization 37317.4 Treatment of domains that are partially outside 37517.5 Removalof inactive regions 37517.6 Incremental interpolation 37717.7 Changes to the flowsolver 37717.8 Examples 37818 EMBEDDED AND IMMERSED GRID TECHNIQUES 38318.1 Kinetic treatmentof embeddedor immersed objects 38518.2 Kinematic treatment of embedded surfaces 38918.3 Deactivation of interior regions 39518.4 Extrapolationof the solution 39718.5 Adaptive mesh refinement 39718.6 Load/flux transfer 39818.7 Treatment of gapsor cracks 39918.8 Direct link to particles 40018.9 Examples 40119 TREATMENT OF FREE SURFACES 41919.1 Interface fitting methods 41919.2 Interface capturing methods 42920 OPTIMAL SHAPE AND PROCESS DESIGN 44920.1 The general optimization problem 44920.2 Optimization techniques 45120.3 Adjoint solvers 46220.4 Geometric constraints 46920.5 Approximate gradients 47120.6 Multipoint optimization 47120.7 Representation of surface changes 47220.8 Hierarchical design procedures 47220.9 Topological optimization via porosities 47320.10 Examples 474References 481Index 515

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.

?This book has a good concept und gives a compact description of applied CFD.? (ZAMM, October 2009)

• FOREWORD TO THE SECOND EDITION xivACKNOWLEDGEMENTS xvii1 INTRODUCTION AND GENERAL CONSIDERATIONS 11.1 The CFD code 41.2 Porting research codes to an industrial context 51.3 Scope of the book 52 DATA STRUCTURES AND ALGORITHMS 72.1 Representation of agrid 72.2 Derived data structures for static data 92.3 Derived data structures for dynamic data 172.4 Sorting and searching 192.5 Proximity in space 222.6 Nearest-neighbours and graphs 302.7 Distance to surface 303 GRID GENERATION 353.1 Description of the domain to be gridded 373.2 Variation of element size andshape 383.3 Element type 463.4 Automatic grid generation methods 473.5 Other grid generation methods 493.6 The advancing front technique 513.7 Delaunay triangulation 593.8 Grid improvement 653.9 Optimal space-filling tetrahedra 703.10 Grids with uniform cores 723.11 Volume-to-surface meshing 733.12 Navier-Stokes gridding techniques 753.13 Filling space with points/arbitrary objects 903.14 Applications 984 APPROXIMATION THEORY 1094.1 The basic problem 1094.2 Choiceof trial functions 1124.3 General properties of shape functions 1184.4 Weighted residual methods with local functions 1184.5 Accuracy and effort 1194.6 Grid estimates 1215 APPROXIMATION OF OPERATORS 1235.1 Taxonomy of methods 1235.2 The Poisson operator 1245.3 Recovery of derivatives 1306 DISCRETIZATION IN TIME 1336.1 Explicit schemes 1336.2 Implicit schemes 1356.3 A word of caution 1367 SOLUTION OF LARGE SYSTEMS OF EQUATIONS 1377.1 Direct solvers 1377.2 Iterative solvers 1407.3 Multigrid methods 1538 SIMPLE EULER/NAVIER-STOKES SOLVERS 1618.1 Galerkin approximation 1628.2 Lax-Wendroff (Taylor-Galerkin) 1648.3 Solvingfor the consistent mass matrix 1678.4 Artificial viscosities 1678.5 Boundary conditions 1698.6 Viscous fluxes 1729 FLUX-CORRECTED TRANSPORT SCHEMES 1759.1 Algorithmic implementation 1769.2 Steepening 1789.3 FCT for Taylor-Galerkin schemes 1799.4 Iterative limiting 1799.5 Limiting for systems of equations 1809.6 Examples 1819.7 Summary 18310 EDGE-BASED COMPRESSIBLE FLOWSOLVERS 18710.1 TheLaplacianoperator 18810.2 First derivatives:first form 19010.3 First derivatives:secondform 19110.4 Edge-basedschemes foradvection-dominatedPDEs 19311 INCOMPRESSIBLE FLOWSOLVERS 20111.1 The advection operator 20111.2 The divergence operator 20311.3 Artificial compressibility 20611.4 Temporal discretization: projection schemes 20611.5 Temporal discretization: implicit schemes 20811.6 Temporal discretization of higher order 20911.7 Acceleration to the steady state 21011.8 Projective prediction of pressure increments 21211.9 Examples 21312 MESH MOVEMENT 22712.1 The ALE frame of reference 22712.1.1 Boundary conditions 22812.2 Geometric conservation law 22812.3 Mesh movement algorithms 22912.4 Region of moving elements 23512.5 PDE-based distance functions 23612.6 Penalization of deformed elements 23812.7 Special movement techniques for RANS grids 23912.8 Rotating parts/domains 24012.9 Applications 24113 INTERPOLATION 24513.1 Basic interpolation algorithm 24613.2 Fastest 1-time algorithm:brute force 24713.3 Fastest N-time algorithm:octree search 24713.4 Fastest known vicinity algorithm: neighbour-to-neighbour 24913.5 Fastest grid-to-gridalgorithm:advancing-front vicinity 25013.6 Conservative interpolation 25713.7 Surface-grid-to-surface-grid interpolation 26113.8 Particle-grid interpolation 26514 ADAPTIVE MESH REFINEMENT 26914.1 Optimal-meshcriteria 27014.2 Error indicators/estimators 27114.3 Refinement strategies 27814.4 Tutorial:h-refinement with tetrahedra 28614.5 Examples 29115 EFFICIENT USE OF COMPUTER HARDWARE 29915.1 Reduction of cache-misses 30015.2 Vector machines 31615.3 Parallel machines:general considerations 32815.4 Shared-memory parallel machines 32915.5 SIMD machines 33415.6 MIMD machines 33615.7 The effect of Moore's law on parallel computing 34416 SPACE-MARCHING AND DEACTIVATION 35116.1 Space-marching 35116.2 Deactivation 36517 OVERLAPPING GRIDS 37117.1 Interpolation criteria 37217.2 External boundaries and domains 37317.3 Interpolation: initialization 37317.4 Treatment of domains that are partially outside 37517.5 Removalof inactive regions 37517.6 Incremental interpolation 37717.7 Changes to the flowsolver 37717.8 Examples 37818 EMBEDDED AND IMMERSED GRID TECHNIQUES 38318.1 Kinetic treatmentof embeddedor immersed objects 38518.2 Kinematic treatment of embedded surfaces 38918.3 Deactivation of interior regions 39518.4 Extrapolationof the solution 39718.5 Adaptive mesh refinement 39718.6 Load/flux transfer 39818.7 Treatment of gapsor cracks 39918.8 Direct link to particles 40018.9 Examples 40119 TREATMENT OF FREE SURFACES 41919.1 Interface fitting methods 41919.2 Interface capturing methods 42920 OPTIMAL SHAPE AND PROCESS DESIGN 44920.1 The general optimization problem 44920.2 Optimization techniques 45120.3 Adjoint solvers 46220.4 Geometric constraints 46920.5 Approximate gradients 47120.6 Multipoint optimization 47120.7 Representation of surface changes 47220.8 Hierarchical design procedures 47220.9 Topological optimization via porosities 47320.10 Examples 474References 481Index 515

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.

?This book has a good concept und gives a compact description of applied CFD.? (ZAMM, October 2009)

• FOREWORD TO THE SECOND EDITION xivACKNOWLEDGEMENTS xvii1 INTRODUCTION AND GENERAL CONSIDERATIONS 11.1 The CFD code 41.2 Porting research codes to an industrial context 51.3 Scope of the book 52 DATA STRUCTURES AND ALGORITHMS 72.1 Representation of agrid 72.2 Derived data structures for static data 92.3 Derived data structures for dynamic data 172.4 Sorting and searching 192.5 Proximity in space 222.6 Nearest-neighbours and graphs 302.7 Distance to surface 303 GRID GENERATION 353.1 Description of the domain to be gridded 373.2 Variation of element size andshape 383.3 Element type 463.4 Automatic grid generation methods 473.5 Other grid generation methods 493.6 The advancing front technique 513.7 Delaunay triangulation 593.8 Grid improvement 653.9 Optimal space-filling tetrahedra 703.10 Grids with uniform cores 723.11 Volume-to-surface meshing 733.12 Navier-Stokes gridding techniques 753.13 Filling space with points/arbitrary objects 903.14 Applications 984 APPROXIMATION THEORY 1094.1 The basic problem 1094.2 Choiceof trial functions 1124.3 General properties of shape functions 1184.4 Weighted residual methods with local functions 1184.5 Accuracy and effort 1194.6 Grid estimates 1215 APPROXIMATION OF OPERATORS 1235.1 Taxonomy of methods 1235.2 The Poisson operator 1245.3 Recovery of derivatives 1306 DISCRETIZATION IN TIME 1336.1 Explicit schemes 1336.2 Implicit schemes 1356.3 A word of caution 1367 SOLUTION OF LARGE SYSTEMS OF EQUATIONS 1377.1 Direct solvers 1377.2 Iterative solvers 1407.3 Multigrid methods 1538 SIMPLE EULER/NAVIER-STOKES SOLVERS 1618.1 Galerkin approximation 1628.2 Lax-Wendroff (Taylor-Galerkin) 1648.3 Solvingfor the consistent mass matrix 1678.4 Artificial viscosities 1678.5 Boundary conditions 1698.6 Viscous fluxes 1729 FLUX-CORRECTED TRANSPORT SCHEMES 1759.1 Algorithmic implementation 1769.2 Steepening 1789.3 FCT for Taylor-Galerkin schemes 1799.4 Iterative limiting 1799.5 Limiting for systems of equations 1809.6 Examples 1819.7 Summary 18310 EDGE-BASED COMPRESSIBLE FLOWSOLVERS 18710.1 TheLaplacianoperator 18810.2 First derivatives:first form 19010.3 First derivatives:secondform 19110.4 Edge-basedschemes foradvection-dominatedPDEs 19311 INCOMPRESSIBLE FLOWSOLVERS 20111.1 The advection operator 20111.2 The divergence operator 20311.3 Artificial compressibility 20611.4 Temporal discretization: projection schemes 20611.5 Temporal discretization: implicit schemes 20811.6 Temporal discretization of higher order 20911.7 Acceleration to the steady state 21011.8 Projective prediction of pressure increments 21211.9 Examples 21312 MESH MOVEMENT 22712.1 The ALE frame of reference 22712.1.1 Boundary conditions 22812.2 Geometric conservation law 22812.3 Mesh movement algorithms 22912.4 Region of moving elements 23512.5 PDE-based distance functions 23612.6 Penalization of deformed elements 23812.7 Special movement techniques for RANS grids 23912.8 Rotating parts/domains 24012.9 Applications 24113 INTERPOLATION 24513.1 Basic interpolation algorithm 24613.2 Fastest 1-time algorithm:brute force 24713.3 Fastest N-time algorithm:octree search 24713.4 Fastest known vicinity algorithm: neighbour-to-neighbour 24913.5 Fastest grid-to-gridalgorithm:advancing-front vicinity 25013.6 Conservative interpolation 25713.7 Surface-grid-to-surface-grid interpolation 26113.8 Particle-grid interpolation 26514 ADAPTIVE MESH REFINEMENT 26914.1 Optimal-meshcriteria 27014.2 Error indicators/estimators 27114.3 Refinement strategies 27814.4 Tutorial:h-refinement with tetrahedra 28614.5 Examples 29115 EFFICIENT USE OF COMPUTER HARDWARE 29915.1 Reduction of cache-misses 30015.2 Vector machines 31615.3 Parallel machines:general considerations 32815.4 Shared-memory parallel machines 32915.5 SIMD machines 33415.6 MIMD machines 33615.7 The effect of Moore's law on parallel computing 34416 SPACE-MARCHING AND DEACTIVATION 35116.1 Space-marching 35116.2 Deactivation 36517 OVERLAPPING GRIDS 37117.1 Interpolation criteria 37217.2 External boundaries and domains 37317.3 Interpolation: initialization 37317.4 Treatment of domains that are partially outside 37517.5 Removalof inactive regions 37517.6 Incremental interpolation 37717.7 Changes to the flowsolver 37717.8 Examples 37818 EMBEDDED AND IMMERSED GRID TECHNIQUES 38318.1 Kinetic treatmentof embeddedor immersed objects 38518.2 Kinematic treatment of embedded surfaces 38918.3 Deactivation of interior regions 39518.4 Extrapolationof the solution 39718.5 Adaptive mesh refinement 39718.6 Load/flux transfer 39818.7 Treatment of gapsor cracks 39918.8 Direct link to particles 40018.9 Examples 40119 TREATMENT OF FREE SURFACES 41919.1 Interface fitting methods 41919.2 Interface capturing methods 42920 OPTIMAL SHAPE AND PROCESS DESIGN 44920.1 The general optimization problem 44920.2 Optimization techniques 45120.3 Adjoint solvers 46220.4 Geometric constraints 46920.5 Approximate gradients 47120.6 Multipoint optimization 47120.7 Representation of surface changes 47220.8 Hierarchical design procedures 47220.9 Topological optimization via porosities 47320.10 Examples 474References 481Index 515