Computational methods for fluid dynamics

Preface......Page 5
Contents......Page 8
Acronyms......Page 15
 1.1 Introduction......Page 17
 1.2 Conservation Principles......Page 19
 1.3 Mass Conservation......Page 20
 1.4 Momentum Conservation......Page 21
 1.5 Conservation of Scalar Quantities......Page 25
 1.6 Dimensionless Form of Equations......Page 27
 1.7 Simplified Mathematical Models......Page 28
  1.7.2 Inviscid (Euler) Flow......Page 29
  1.7.3 Potential Flow......Page 30
  1.7.5 Boussinesq Approximation......Page 31
  1.7.7 Modeling of Complex Flow Phenomena......Page 32
 1.8 Mathematical Classification of Flows......Page 33
  1.8.3 Elliptic Flows......Page 34
 1.9 Plan of This Book......Page 35
 2.1 Approaches to Solving Problems in Fluid Dynamics......Page 38
 2.2 What is CFD?......Page 40
 2.3 Possibilities and Limitations of Numerical Methods......Page 41
  2.4.2 Discretization Method......Page 42
  2.4.4 Numerical Grid......Page 43
  2.4.5 Finite Approximations......Page 48
  2.5.1 Consistency......Page 49
  2.5.2 Stability......Page 50
  2.5.4 Conservation......Page 51
  2.5.7 Accuracy......Page 52
  2.6.2 Finite Volume Method......Page 54
  2.6.3 Finite Element Method......Page 55
 3.1 Introduction......Page 56
 3.2 Basic Concept......Page 57
  3.3.1 Taylor Series Expansion......Page 59
  3.3.2 Polynomial Fitting......Page 61
  3.3.3 Compact Schemes......Page 62
  3.3.4 Non-uniform Grids......Page 64
 3.4 Approximation of the Second Derivative......Page 66
 3.5 Approximation of Mixed Derivatives......Page 69
  3.6.2 Differentiated Terms Near Boundaries......Page 70
  3.7.1 Implementation of Boundary Conditions Using Internal Grid Points......Page 71
  3.7.2 Implementation of Boundary Conditions Using Ghost Points......Page 72
 3.8 The Algebraic Equation System......Page 73
 3.9 Discretization Errors......Page 76
 3.10 Finite-Difference Example......Page 78
 3.11 An Introduction to Spectral Methods......Page 84
  3.11.1 Tools for Analysis......Page 85
  3.11.2 Solution of Differential Equations......Page 88
 4.1 Introduction......Page 95
 4.2 Approximation of Surface Integrals......Page 96
 4.3 Approximation of Volume Integrals......Page 100
  4.4.1 Upwind Interpolation (UDS)......Page 101
  4.4.2 Linear Interpolation (CDS)......Page 102
  4.4.3 Quadratic Upwind Interpolation (QUICK)......Page 103
  4.4.4 Higher-Order Schemes......Page 104
  4.4.5 Other Schemes......Page 106
  4.4.6 A General Strategy, TVD Schemes, and Flux Limiters......Page 107
 4.5 Implementation of Boundary Conditions......Page 111
  4.7.1 Testing the Order of FV-Approximations......Page 112
  4.7.2 Scalar Transport in a Known Velocity Field......Page 117
  4.7.3 Testing the Numerical Diffusion......Page 121
 5.1 Introduction......Page 125
  5.2.1 Gauss Elimination......Page 126
  5.2.2 LU Decomposition......Page 128
  5.2.3 Tridiagonal Systems......Page 129
  5.2.4 Cyclic Reduction......Page 130
  5.3.1 Basic Concept......Page 131
  5.3.2 Convergence......Page 132
  5.3.3 Some Basic Methods......Page 134
  5.3.4 Incomplete LU Decomposition: Stone's Method......Page 135
  5.3.5 ADI and Other Splitting Methods......Page 139
  5.3.6 Krylov Methods......Page 141
  5.3.7 Multigrid Methods......Page 148
  5.3.8 Other Iterative Solvers......Page 152
  5.4.1 Simultaneous Solution......Page 153
  5.4.3 Under-Relaxation......Page 154
  5.5.1 Newton-Like Techniques......Page 156
  5.5.2 Other Techniques......Page 157
 5.6 Deferred-Correction Approaches......Page 158
 5.7 Convergence Criteria and Iteration Errors......Page 160
 5.8 Examples......Page 165
  6.2.1 Two-Level Methods......Page 171
  6.2.2 Predictor-Corrector and Multipoint Methods......Page 174
  6.2.3 Runge–Kutta Methods......Page 177
  6.2.4 Other Methods......Page 179
 6.3 Application to the Generic Transport Equation......Page 181
  6.3.1 Explicit Methods......Page 182
  6.3.2 Implicit Methods......Page 187
 6.4 Examples......Page 192
 7.1 Basics......Page 197
  7.1.1 Discretization of Convection and Viscous Terms......Page 198
  7.1.2 Discretization of Pressure Terms and Body Forces......Page 199
  7.1.3 Conservation Properties......Page 200
  7.1.4 Choice of Variable Arrangement on the Grid......Page 205
  7.1.5 Calculation of the Pressure......Page 207
  7.1.6 Initial and Boundary Conditions for the Navier–Stokes Equations......Page 211
  7.1.7 Illustrative Simple Schemes......Page 215
  7.2.1 Fractional-Step Methods......Page 218
  7.2.2 SIMPLE, SIMPLER, SIMPLEC and PISO......Page 224
  7.2.3 Artificial Compressibility Methods......Page 235
  7.2.4 Streamfunction-Vorticity Methods......Page 238
 8.1 Implicit Iterative Methods on a Staggered Grid......Page 241
  8.1.1 SIMPLE for Staggered Grids......Page 247
  8.1.2 IFSM for Staggered Grids......Page 250
  8.2.1 Treatment of Pressure for Colocated Variables......Page 251
  8.2.2 SIMPLE for Colocated Grids......Page 255
  8.2.3 IFSM for Colocated Grids......Page 257
 8.3 Non-iterative Implicit Methods for Unsteady Flows......Page 258
  8.3.1 Spatial Discretization of the Adams–Bashforth Convection Term......Page 260
  8.3.2 An Alternating-Direction Implicit Scheme......Page 261
  8.3.3 The Poisson Equation for Pressure......Page 262
  8.3.4 Initial and Boundary Conditions......Page 266
  8.3.5 Iterative Versus Non-iterative Schemes......Page 267
 8.4 Examples......Page 269
  8.4.1 Steady Flow in Square Enclosures......Page 270
  8.4.2 Unsteady Flow in Square Enclosures......Page 281
  9.1.1 Stepwise Approximation of Curved Boundaries......Page 289
  9.1.2 Immersed-Boundary Methods......Page 291
  9.1.3 Overlapping Grids......Page 292
 9.2 Grid Generation......Page 294
  9.2.1 Definition of Flow Domain......Page 296
  9.2.2 Generation of a Surface Grid......Page 297
  9.2.3 Generation of a Volume Grid......Page 298
 9.3 The Choice of Velocity Components......Page 302
  9.3.1 Grid-Oriented Velocity Components......Page 303
  9.4.1 Staggered Arrangements......Page 304
  9.4.2 Colocated Arrangement......Page 305
  9.5.1 Methods Based on Coordinate Transformation......Page 306
  9.5.2 Methods Based on Shape Functions......Page 309
 9.6 Finite-Volume Methods......Page 310
  9.6.1 Block-Structured Grids......Page 311
  9.6.2 Unstructured Grids......Page 315
  9.6.3 Grids for Control-Volume-Based Finite-Element Methods......Page 317
  9.6.4 Computation of Grid Parameters......Page 318
  9.7.1 Approximation of Convection Fluxes......Page 321
  9.7.2 Approximation of Diffusion Fluxes......Page 325
  9.7.3 Approximation of Source Terms......Page 328
 9.8 Pressure-Correction Equation......Page 329
 9.9 Axisymmetric Problems......Page 335
 9.10 Higher-Order Finite-Volume Methods......Page 337
  9.11.2 Outlet......Page 338
  9.11.3 Impermeable Walls......Page 340
  9.11.4 Symmetry Planes......Page 342
  9.11.5 Specified Pressure......Page 343
  9.12.1 Flow Around Circular Cylinder at Re = 20......Page 344
  9.12.2 Flow Around Circular Cylinder at Re = 200......Page 348
  9.12.3 Flow Around Circular Cylinder in a Channel  at Re = 200......Page 352
 10.1 Introduction......Page 361
  10.2.1 Overview......Page 364
  10.2.2 Discussion......Page 365
  10.2.3 Initial and Boundary Conditions......Page 369
  10.2.4 Examples of DNS Application......Page 372
  10.3.1 Model Categories......Page 377
  10.3.3 Large-Eddy Simulation (LES)......Page 380
  10.3.4 Examples of LES Application......Page 394
  10.3.5 Reynolds-Averaged Navier–Stokes (RANS) Simulations......Page 409
  10.3.6 Example of RANS Application: Flow Around a Sphere at Re = 500,000......Page 428
  10.3.7 Very-Large-Eddy Simulation/TRANS/DES......Page 431
 11.1 Introduction......Page 434
 11.2 Pressure-Correction Methods for Arbitrary  Mach Number......Page 435
  11.2.1 Implicit Fractional-Step Method for All Flow Speeds......Page 436
  11.2.2 SIMPLE Method for All Flow Speeds......Page 439
  11.2.3 Properties of the Pressure-Correction Equation......Page 440
  11.2.4 Boundary Conditions......Page 441
  11.2.5 Examples......Page 446
  11.3.1 Introduction......Page 451
  11.3.2 Discontinuities......Page 452
  11.3.3 Limiters......Page 453
  11.3.4 Preconditioning......Page 455
 11.4 Comments on Applications......Page 457
  12.1.1 Grid and Flow Feature Resolution......Page 459
  12.2.1 Description of Errors......Page 462
  12.2.2 Estimation of Errors......Page 465
  12.2.3 Recommended Practice for CFD Uncertainty Analysis......Page 476
 12.3 Grid Quality and Optimization......Page 480
 12.4 Multigrid Methods for Flow Calculation......Page 484
  12.5.1 Motivation for Adaptive Mesh Refinement......Page 491
  12.5.2 The AMR Strategy......Page 492
 12.6 Parallel Computing in CFD......Page 497
  12.6.1 Parallelization of Iterative Solvers for Linear Equation Systems......Page 498
  12.6.2 Domain Decomposition in Space......Page 500
  12.6.3 Domain Decomposition in Time......Page 503
  12.6.4 Efficiency of Parallel Computing......Page 504
  12.6.5 Graphics Processing Units (GPUs) and Parallel Processing......Page 509
 13.1 Introduction......Page 510
 13.2 Heat and Mass Transfer......Page 511
 13.3 Flows with Variable Fluid Properties......Page 521
 13.4 Moving Grids......Page 522
 13.5 Free-Surface Flows......Page 532
  13.5.1 Interface-Capturing Methods......Page 535
  13.5.2 Interface-Tracking Methods......Page 542
  13.5.3 Hybrid Methods......Page 547
 13.6 Solution Forcing......Page 548
 13.7 Meteorological and Oceanographic Applications......Page 549
 13.8 Multiphase Flows......Page 552
 13.9 Combustion......Page 559
 13.10 Fluid-Structure Interaction......Page 561
  13.10.1 Floating and Flying Bodies......Page 562
  13.10.2 Deformable Bodies......Page 571
 A.1  List of Computer Codes and How to Access Them......Page 576
 A.3  Other Free CFD Codes......Page 577
 BookmarkTitle:......Page 579
Index......Page 601