Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods

TABLE OF CONTENTS 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

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