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CONTENTS FOREWORD TO THE SECOND EDITION ACKNOWLEDGEMENTS 1 INTRODUCTION AND GENERAL CONSIDERATIONS 1.1 The CFD code 1.2 Porting research codes to an industrial context 1.3 Scope of the book 2 DATA STRUCTURES AND ALGORITHMS 2.1 Representation of a grid 2.2 Derived data structures for static data 2.3 Derived data structures for dynamic data 2.4 Sorting and searching 2.5 Proximity ins pace 2.6 Nearest-neighbours and graphs 2.7 Distance to surface 3 GRID GENERATION 3.1 Description of the domain to be gridded 3.2 Variation of element size and shape 3.3 Element type 3.4 Automatic grid generation methods 3.5 Other grid generation methods 3.6 The advancing front technique 3.7 Delaunay triangulation 3.8 Grid improvement 3.9 Optimal space-filling tetrahedra 3.10 Grids with uniform cores 3.11 Volume-to-surface meshing 3.12 Navier–Stokes gridding techniques 3.13 Filling space with points/arbitrary objects 3.14 Applications 4 APPROXIMATION THEORY 4.1 The basic problem 4.2 Choice of trial functions 4.3 General properties of shape functions 4.4 Weighted residual methods with local functions 4.5 Accuracy and effort 4.6 Grid estimates 5 APPROXIMATION OF OPERATORS 5.1 Taxonomy of methods 5.2 The Poisson operator 5.3 Recovery of derivatives 6 DISCRETIZATION IN TIME 6.1 Explicit schemes 6.2 Implicit schemes 6.3 Awordof caution 7 SOLUTION OF LARGE SYSTEMS OF EQUATIONS 7.1 Direct solvers 7.2 Iterative solvers 7.3 Multigrid methods 8 SIMPLE EULER/NAVIER–STOKES SOLVERS 8.1 Galerkin approximation 8.2 Lax–Wendroff (Taylor–Galerkin) 8.3 Solving for the consistent mass matrix 8.4 Artificial viscosities 8.5 Boundary conditions 8.6 Viscous fluxes 9 FLUX-CORRECTED TRANSPORT SCHEMES 9.1 The FCT Concept 9.2 Algorithmic implementation 9.3 Steepening 9.4 FCT for Taylor–Galerkin schemes 9.5 Iterative limiting 9.6 Limiting for systems of equations 9.7 Examples 9.8 Summary 10 EDGE-BASED COMPRESSIBLE FLOWSOLVERS 10.1 The Laplacian operator 10.2 First derivatives: first form 10.3 First derivatives: second form 10.4 Edge-based schemes for advection-dominated PDEs 11 INCOMPRESSIBLE FLOWSOLVERS 11.1 The advection operator 11.2 The divergence operator 11.3 Artificial compressibility 11.4 Temporal discretization:projection schemes 11.5 Temporal discretization: implicit schemes 11.6 Temporal discretization of higher order 11.7 Acceleration to the steady state 11.8 Projective prediction of pressure increments 11.9 Examples 12 MESH MOVEMENT 12.1 The ALE frame of reference 12.2 Geometric conservation law 12.3 Mesh movement algorithms 12.4 Region of moving elements 12.5 PDE-based distance functions 12.6 Penalization of deformed elements 12.7 Special movement techniques for RANS grids 12.8 Rotating parts/domains 12.9 Applications 13 INTERPOLATION 13.1 Basic interpolation algorithm 13.2 Fastest 1-timealgorithm:brute force 13.3 Fastest N-time algorithm: octree search 13.4 Fastest known vicinity algorithm: neighbour-to-neighbour 13.5 Fastest grid-to-grid algorithm: advancing-front vicinity 13.6 Conservative interpolation 13.7 Surface-grid-to-surface-grid interpolation 13.8 Particle–grid interpolation 14 ADAPTIVE MESH REFINEMENT 14.1 Optimal-mesh criteria 14.2 Error indicators/estimators 14.3 Refinement strategies 14.4 Tutorial: h-refinement with tetrahedra 14.5 Examples 15 EFFICIENT USE OF COMPUTER HARDWARE 15.1 Reduction of cache-misses 15.2 Vector machines 15.3 Parallel machines: general considerations 15.4 Shared-memory parallel machines 15.5 SIMD machines 15.6 MIMD machines 15.7 The effect of Moore's law on parallel computing 16 SPACE-MARCHING AND DEACTIVATION 16.1 Space-marching 16.2 Deactivation 17 OVERLAPPING GRIDS 17.1 Interpolation criteria 17.2 External boundaries and domains 17.3 Interpolation: initialization 17.4 Treatment of domains that are partially outside 17.5 Removal of inactive regions 17.6 Incremental interpolation 17.7 Changes to the flow solver 17.8 Examples 18 EMBEDDED AND IMMERSED GRID TECHNIQUES 18.1 Kinetic treatment of embedded or immersed objects 18.2 Kinematic treatment of embedded surfaces 18.3 Deactivation of interior regions 18.4 Extrapolation of the solution 18.5 Adaptive mesh refinement 18.6 Load/flux transfer 18.7 Treatment of gaps or cracks 18.8 Direct link to particles 18.9 Examples 19 TREATMENT OF FREE SURFACES 19.1 Interface fitting methods 19.2 Interface capturing methods 20 OPTIMAL SHAPE AND PROCESS DESIGN 20.1 The general optimization problem 20.2 Optimization techniques 20.3 Adjoint solvers 20.4 Geometric constraints 20.5 Approximate gradients 20.6 Multipoint optimization 20.7 Representation of surface changes 20.8 Hierarchical design procedures 20.9 Topological optimization via porosities 20.10 Examples References