The finite volume method in computational fluid dynamics: an advanced introduction with OpenFOAM and Matlab
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2016
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| Series: | Fluid mechanics and its applications
113 |
| Subjects: | |
| Online Access: | Beschreibung & Leseproben Inhaltsverzeichnis |
| Item Description: | Copyright 2016 [published August 2015]. - Includes bibliographical references Authors: Dr. F. Moukalled and Dr. M. Darwish (Department of Mechanical Engineering, American University of Beirut, Beirut, Lebanon); Prof. Dr. L. Mangani (Engineering and Architecture, Lucerne University of Applied Science an Arts, Horw, Switzerland) |
| Physical Description: | XXIII, 791 S. Ill., graph. Darst. 242 mm |
| ISBN: | 3319168738 9783319168739 9783319348643 |
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| 245 | 1 | 0 | |a The finite volume method in computational fluid dynamics |b an advanced introduction with OpenFOAM and Matlab |c F. Moukalled ; L. Mangani ; M. Darwish |
| 246 | 1 | 0 | |a CFD FVM |
| 264 | 1 | |a Cham [u.a.] |b Springer |c 2016 | |
| 300 | |a XXIII, 791 S. |b Ill., graph. Darst. |c 242 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fluid mechanics and its applications |v 113 | |
| 500 | |a Copyright 2016 [published August 2015]. - Includes bibliographical references | ||
| 500 | |a Authors: Dr. F. Moukalled and Dr. M. Darwish (Department of Mechanical Engineering, American University of Beirut, Beirut, Lebanon); Prof. Dr. L. Mangani (Engineering and Architecture, Lucerne University of Applied Science an Arts, Horw, Switzerland) | ||
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| 650 | 0 | 7 | |a Finite-Volumen-Methode |0 (DE-588)4220855-5 |2 gnd |9 rswk-swf |
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| adam_text | Titel: The finite volume method in computational fluid dynamics
Autor: Moukalled, F
Jahr: 2016
Contents
Part I Foundation
1 Introduction........................................ 3
1.1 What Is Computational Fluid Dynamics (CFD)........... 3
1.2 What Is the Finite Volume Method................... 4
1.3 This Book.................................... 5
1.3.1 Foundation............................. 5
1.3.2 Numerics.............................. 6
1.3.3 Algorithms............................. 7
1.3.4 Applications............................ 8
1.4 Closure
Review of Vector Calculus............................. 9
2.1 Introduction................................... 9
2.2 Vectors and Vector Operations...................... 10
2.2.1 The Dot Product of Two Vectors............. 11
2.2.2 Vector Magnitude........................ 11
2.2.3 The Unit Direction Vector.................. 12
2.2.4 The Cross Product of Two Vectors............ 12
2.2.5 The Scalar Triple Product................... 14
2.2.6 Gradient of a Scalar and Directional
Derivatives............................. 15
2.2.7 Operations on the Nabla Operator............. 17
2.2.8 Additional Vector Operations................ 19
2.3 Matrices and Matrix Operations..................... 20
2.3.1 Square Matrices......................... 21
2.3.2 Using Matrices to Describe Systems
of Equations............................ 23
2.3.3 The Determinant of a Square Matrix........... 23
2.3.4 Eigenvectors and Eigenvalues................ 26
2.3.5 A Symmetrie Positive-Definite Matrix.......... 27
x Contents
2.3.6 Additional Matrix Operations................ 28
2.4 Tensors and Tensor Operations...................... 29
2.5 Fundamental Theorems of Vector Calculus.............. 32
2.5.1 Gradient Theorem for Line Integrals........... 32
2.5.2 Green s Theorem......................... 33
2.5.3 Stokes Theorem......................... 34
2.5.4 Divergence Theorem...................... 35
2.5.5 Leibniz Integral Rule...................... 37
2.6 Closure...................................... 38
2.7 Exercises..................................... 39
References.......................................... 41
3 Mathematical Description of Physical Phenomena............ 43
3.1 Introduction................................... 43
3.2 Classification of Fluid Flows....................... 44
3.3 Eulerian and Lagrangian Description of Conservation
Laws........................................ 45
3.3.1 Substantial Versus Local Derivative............ 46
3.3.2 Reynolds Transport Theorem................ 47
3.4 Conservation of Mass (Continuity Equation)............. 48
3.5 Conservation of Linear Momentum................... 50
3.5.1 Non-Conservative Form.................... 51
3.5.2 Conservative Form....................... 52
3.5.3 Surface Forces.......................... 52
3.5.4 Body Forces............................ 54
3.5.5 Stress Tensor and the Momentum Equation
for Newtonian Fluids...................... 55
3.6 Conservation of Energy........................... 57
3.6.1 Conservation of Energy in Terms of Specific
Internal Energy.......................... 60
3.6.2 Conservation of Energy in Terms of Specific
Enthalpy............................... 61
3.6.3 Conservation of Energy in Terms of Specific
Total Enthalpy.......................... 61
3.6.4 Conservation of Energy in Terms
of Temperature.......................... 62
3.7 General Conservation Equation...................... 65
3.8 Non-dimensionalization Procedure.................... 67
3.9 Dimensionless Numbers........................... 72
3.9.1 Reynolds Number........................ 72
3.9.2 Grashof Number......................... 73
3.9.3 Prandtl Number.......................... 73
3.9.4 Peclet Number.......................... 75
3.9.5 Schmidt Number......................... 75
Contents
3.9.6 Nusselt Number......................... 77
3.9.7 Mach Number........................... 77
3.9.8 Eckert Number.......................... 78
3.9.9 Froude Number.......................... 79
3.9.10 Weber Number.......................... 79
3.10 Closure...................................... 80
3.11 Exercises..................................... 80
References.......................................... 82
The Discretization Process.............................. 85
4.1 The Discretization Process......................... 85
4.1.1 Step I: Geometrie and Physical Modeling........ 87
4.1.2 Step II: Domain Discretization............... 88
4.1.3 Mesh Topology.......................... 90
4.1.4 Step IQ: Equation Discretization.............. 93
4.1.5 Step IV: Solution of the Discretized Equations .... 98
4.1.6 Other Types of Fields..................... 100
4.2 Closure...................................... 101
The Finite Volume Method............................. 103
5.1 Introduction................................... 103
5.2 The Semi-Discretized Equation...................... 104
5.2.1 Flux Integration Over Element Faces........... 105
5.2.2 Source Term Volume Integration.............. 107
5.2.3 The Discrete Conservation Equation
for One Integration Point................... 108
5.2.4 Flux Linearization........................ 109
5.3 Boundary Conditions............................. 111
5.3.1 Value Specified (Dirichlet Boundary Condition) ... 111
5.3.2 Flux Specified (Neumann Boundary Condition). ... 112
5.4 Order of Accuracy............................... 113
5.4.1 Spatial Variation Approximation.............. 113
5.4.2 Mean Value Approximation................. 114
5.5 Transient Semi-Discretized Equation.................. 117
5.6 Properties of the Discretized Equations................ 118
5.6.1 Conservation............................ 118
5.6.2 Accuracy.............................. 119
5.6.3 Convergence............................ 119
5.6.4 Consistency............................ 120
5.6.5 Stability............................... 120
5.6.6 Economy.............................. 120
5.6.7 Transportiveness......................... 120
5.6.8 Boundedness of the Interpolation Profile........ 121
xii Contents
5.7 Variable Arrangement............................ 122
5.7.1 Vertex-Centered FVM..................... 123
5.7.2 Cell-Centered FVM....................... 124
5.8 Implicit Versus Explicit Numerical Methods............. 126
5.9 The Mesh Support............................... 127
5.10 Computational Pointers........................... 128
5.10.1 uFVM................................ 128
5.10.2 OpenFOAM®........................... 129
5.11 Closure...................................... 133
5.12 Exercises..................................... 133
References.......................................... 134
6 The Finite Volume Mesh............................... 137
6.1 Domain Discretization............................ 137
6.2 The Finite Volume Mesh.......................... 138
6.2.1 Mesh Support for Gradient Computation........ 139
6.3 Structured Grids................................ 142
6.3.1 Topological Information.................... 142
6.3.2 Geometrie Information..................... 144
6.3.3 Accessing the Element Field................. 145
6.4 Unstructured Grids.............................. 146
6.4.1 Topological Information (Connectivities)........ 147
6.5 Geometrie Quantities............................. 152
6.5.1 Element Types.......................... 153
6.5.2 Computing Surface Area and Centroid
of Faces............................... 154
6.6 Computational Pointers........................... 162
6.6.1 uFVM................................ 162
6.6.2 OpenFOAM®........................... 164
6.7 Closure...................................... 170
6.8 Exercises..................................... 170
References.......................................... 170
7 The Finite Volume Mesh in OpenFOAM® and uFVM......... 173
7.1 uFVM....................................... 173
7.1.1 An OpenFOAM® Test Case................. 173
7.1.2 The polyMesh Folder...................... 175
7.1.3 The uFVM Mesh......................... 178
7.1.4 uFVM Geometrie Fields.................... 183
7.1.5 Working with the uFVM Mesh............... 187
7.1.6 Computing the Gauss Gradient............... 188
7.2 OpenFOAM®.................................. 191
7.2.1 Fields and Memory....................... 197
7.2.2 InternalField Data........................ 199
Contents
7.2.3 BoundaryField Data....................... 200
7.2.4 lduAddressing........................... 200
7.2.5 Computing the Gradient.................... 202
7.3 Mesh Conversion Tools........................... 204
7.4 Closure...................................... 205
7.5 Exercises..................................... 205
References.......................................... 207
Part II Discretization
8 Spatial Discretization: The Diffusion Term.................. 211
8.1 Two-Dimensional Diffusion in a Rectangular Domain...... 211
8.2 Comments on the Discretized Equation................ 216
8.2.1 The Zero Sum Rule....................... 216
8.2.2 The Opposite Signs Rule................... 217
8.3 Boundary Conditions............................. 217
8.3.1 Dirichlet Boundary Condition................ 218
8.3.2 Von Neumann Boundary Condition............ 220
8.3.3 Mixed Boundary Condition................. 222
8.3.4 Symmetry Boundary Condition............... 223
8.4 The Interface Diffusivity.......................... 224
8.5 Non-Cartesian Orthogonal Grids..................... 239
8.6 Non-orthogonal Unstructured Grid.................... 241
8.6.1 Non-orthogonality........................ 241
8.6.2 Minimum Correction Approach............... 242
8.6.3 Orthogonal Correction Approach.............. 243
8.6.4 Over-Relaxed Approach.................... 243
8.6.5 Treatment of the Cross-Diffusion Term......... 244
8.6.6 Gradient Computation..................... 244
8.6.7 Algebraic Equation for Non-orthogonal Meshes . . . 245
8.6.8 Boundary Conditions for Non-orthogonal Grids. . . . 252
8.7 Skewness..................................... 254
8.8 Anisotropie Diffusion............................ 255
8.9 Under-Relaxation of the Iterative Solution Process........ 256
8.10 Computational Pointers........................... 258
8.10.1 uFVM................................ 258
8.10.2 OpenFOAM®........................... 260
8.11 Closure...................................... 265
8.12 Exercises..................................... 265
References.......................................... 270
xiv Contents
9 Gradient Computation................................ 273
9.1 Computing Gradients in Cartesian Grids............... 273
9.2 Green-Gauss Gradient............................ 275
9.3 Least-Square Gradient............................ 285
9.4 Interpolating Gradients to Faces..................... 289
9.5 Computational Pointers........................... 290
9.5.1 uFVM................................ 290
9.5.2 OpenFOAM®........................... 295
9.6 Closure...................................... 298
9.7 Exercises..................................... 298
References.......................................... 302
10 Solving the System of Algebraic Equations.................. 303
10.1 Introduction................................... 303
10.2 Direct or Gauss Elimination Method.................. 305
10.2.1 Gauss Elimination........................ 305
10.2.2 Forward Elimination...................... 306
10.2.3 Forward Elimination Algorithm............... 307
10.2.4 Backward Substitution..................... 307
10.2.5 Back Substitution Algorithm................. 308
10.2.6 LU Decomposition....................... 308
10.2.7 The Decomposition Step................... 310
10.2.8 LU Decomposition Algorithm................ 311
10.2.9 The Substitution Step...................... 312
10.2.10 LU Decomposition and Gauss Elimination....... 312
10.2.11 LU Decomposition Algorithm by Gauss
Elimination............................. 313
10.2.12 Direct Methods for Banded Sparse Matrices...... 315
10.2.13 TriDiagonal Matrix Algorithm (TDMA)......... 316
10.2.14 PentaDiagonal Matrix Algorithm (PDMA)....... 317
10.3 Iterative Methods............................... 319
10.3.1 Jacobi Method.......................... 323
10.3.2 Gauss-Seidel Method...................... 325
10.3.3 Preconditioning and Iterative Methods.......... 327
10.3.4 Matrix Decomposition Techniques............. 329
10.3.5 Incomplete LU (ILU) Decomposition........... 329
10.3.6 Incomplete LU Factorization
with no Fill-in ILU(0)..................... 330
10.3.7 ILU(0) Factorization Algorithm............... 331
10.3.8 ILU Factorization Preconditioners............. 331
10.3.9 Algorithm for the Calculation of D*
in the DDLU Method...................... 332
10.3.10 Forward and Backward Solution Algorithm
with the DILU Method.................... 333
Contents xv
10.3.11 Gradient Methods for Solving Algebraic
Systems............................... 333
10.3.12 The Method of Steepest Descent.............. 335
10.3.13 The Conjugate Gradient Method.............. 337
10.3.14 The Bi-conjugate Gradient Method (BiCG)
and Preconditioned BICG................... 340
10.4 The Multigrid Approach........................... 343
10.4.1 Element Agglomeration/Coarsening............ 345
10.4.2 The Restriction Step and Coarse Level
Coefficients............................ 346
10.4.3 The Prolongation Step and Fine Grid Level
Corrections............................. 349
10.4.4 Traversal Strategies and Algebraic Multigrid
Cycles................................ 349
10.5 Computational Pointers........................... 350
10.5.1 uFVM................................ 350
10.5.2 OpenFOAM®........................... 351
10.6 Closure...................................... 358
10.7 Exercises..................................... 358
References.......................................... 362
11 Discretization of the Convection Term..................... 365
11.1 Introduction................................... 365
11.2 Steady One Dimensional Convection and Diffusion........ 366
11.2.1 Analytical Solution....................... 366
11.2.2 Numerical Solution....................... 368
11.2.3 A Preliminary Derivation: The Central
Difference (CD) Scheme................... 369
11.2.4 The Upwind Scheme...................... 375
11.2.5 The Downwind Scheme.................... 379
11.3 Truncation Error: Numerical Diffusion and Anti-Diffusion . . . 380
11.3.1 The Upwind Scheme...................... 381
11.3.2 The Downwind Scheme.................... 382
11.3.3 The Central Difference (CD) Scheme........... 383
11.4 Numerical Stability.............................. 385
11.5 Higher Order Upwind Schemes...................... 388
11.5.1 Second Order Upwind Scheme............... 389
11.5.2 The Interpolation Profile.................... 390
11.5.3 The Discretized Equation................... 390
11.5.4 Truncation Error......................... 391
11.5.5 Stability Analysis........................ 392
11.5.6 The QUICK Scheme...................... 392
11.5.7 The Interpolation Profile.................... 393
11.5.8 Truncation Error......................... 394
xvi Contents
11.5.9 Stability Analysis........................ 394
11.5.10 The FROMM Scheme..................... 395
11.5.11 The Interpolation Profile.................... 395
11.5.12 The Discretized Equation................... 396
11.5.13 Truncation Error......................... 397
11.5.14 Stability Analysis........................ 397
11.5.15 Comparison of the Various Schemes........... 398
11.5.16 Functional Relationships for Uniform
and Non-uniform Grids.................... 399
11.6 Steady Two Dimensional Advection.................. 400
11.6.1 Error Sources........................... 404
11.7 High Order Schemes on Unstructured Grids............. 406
11.7.1 Reformulating HO Schemes in Terms
of Gradients............................ 407
11.8 The Deferred Correction Approach................... 409
11.9 Computational Pointers........................... 411
11.9.1 uFVM................................ 411
11.9.2 OpenFOAM®........................... 413
11.10 Closure...................................... 421
11.11 Exercises..................................... 422
References.......................................... 426
12 High Resolution Schemes.............................. 429
12.1 The Normalized Variable Formulation (NVF)............ 429
12.2 The Convection Boundedness Criterion (CBC)........... 436
12.3 High Resolution (HR) Schemes...................... 438
12.4 The TVD Framework............................ 443
12.5 The NVF-TVD Relation........................... 450
12.6 HR Schemes in Unstructured Grid Systems............. 456
12.7 Deferred Correction for HR Schemes.................. 456
12.7.1 The Difficulty with the Direct Use
of Nodal Values......................... 458
12.8 The DWF and NWF Methods....................... 459
12.8.1 The Downwind Weighing Factor
(DWF) Method.......................... 460
12.8.2 The Normalized Weighing Factor
(NWF) Method.......................... 463
12.9 Boundary Conditions............................. 467
12.9.1 Inlet Boundary Condition................... 468
12.9.2 Outlet Boundary Condition.................. 470
12.9.3 Wall Boundary Condition................... 471
12.9.4 Symmetry Boundary Condition............... 472
Contents xvii
12.10 Computational Pointers........................... 472
12.10.1 uFVM................................ 472
12.10.2 OpenFOAM®........................... 475
12.11 Closure...................................... 483
12.12 Exercises..................................... 483
References.......................................... 487
13 Temporal Discretization: The Transient Term............... 489
13.1 Introduction................................... 489
13.2 The Finite Difference Approach..................... 492
13.2.1 Forward Euler Scheme..................... 492
13.2.2 Stability of the Forward Euler Scheme.......... 494
13.2.3 Backward Euler Scheme.................... 498
13.2.4 Crank-Nicolson Scheme.................... 500
13.2.5 Implementation Details..................... 502
13.2.6 Adams-Moulton Scheme................... 503
13.3 The Finite Volume Approach....................... 507
13.3.1 First Order Transient Schemes............... 508
13.3.2 First Order Implicit Euler Scheme............. 508
13.3.3 First Order Explicit Euler Scheme............. 510
13.3.4 Second Order Transient Euler Schemes......... 512
13.3.5 Crank-Nicholson (Central Difference Profile)..... 512
13.3.6 Second Order Upwind Euler (SOUE) Scheme..... 514
13.3.7 Initial Condition for the FV Approach.......... 515
13.4 Non-Uniform Time Steps.......................... 519
13.4.1 Non-Uniform Time Steps with the Finite
Difference Approach...................... 519
13.4.2 Adams-Moulton (or SOUE) Scheme........... 521
13.4.3 Non-Uniform Time Steps with the Finite
Volume Approach........................ 522
13.4.4 Crank-Nicolson Scheme.................... 523
13.4.5 Adams-Moulton (or SOUE) Scheme........... 524
13.5 Computational Pointers........................... 525
13.5.1 uFVM................................ 525
13.5.2 OpenFOAM®........................... 526
13.6 Closure...................................... 529
13.7 Exercises..................................... 529
References.......................................... 533
14 Discretization of the Source Term, Relaxation,
and Other Details.................................... 535
14.1 Source Term Discretization......................... 535
14.2 Under-Relaxation of the Algebraic Equations............ 538
14.2.1 Under-Relaxation Methods.................. 539
Contents
14.2.2 Explicit Under-Relaxation................... 540
14.2.3 Implicit Under-Relaxation Methods............ 540
14.3 Residual Form of the Equation...................... 544
14.3.1 Residual Form of Patankar s Under-Relaxation ... . 545
14.4 Residuais and Solution Convergence.................. 546
14.4.1 Residuais.............................. 546
14.4.2 Absolute Residual........................ 547
14.4.3 Maximum Residual....................... 547
14.4.4 Root-Mean Square Residual................. 547
14.4.5 Normalization of the Residual................ 548
14.5 Computational Pointers........................... 549
14.5.1 uFVM................................ 549
14.5.2 OpenFOAM®........................... 550
14.6 Closure...................................... 555
14.7 Exercises..................................... 555
References.......................................... 557
Part III Algorithms
15 Fluid Flow Computation: Incompressible Flows.............. 561
15.1 The Main Difficulty.............................. 561
15.2 A Preliminary Derivation.......................... 563
15.2.1 Discretization of the Momentum Equation....... 564
15.2.2 Discretization of the Continuity Equation........ 565
15.2.3 The Checkerboard Problem.................. 565
15.2.4 The Staggered Grid....................... 567
15.2.5 The Pressure Correction Equation............. 569
15.2.6 The SIMPLE Algorithm on Staggered Grid...... 572
15.2.7 Pressure Correction Equation in Two
Dimensional Staggered Cartesian Grids......... 578
15.2.8 Pressure Correction Equation in Three
Dimensional Staggered Cartesian Grid.......... 581
15.3 Disadvantages of the Staggered Grid.................. 582
15.4 The Rhie-Chow Interpolation....................... 585
15.5 General Derivation.............................. 588
15.5.1 The Discretized Momentum Equation.......... 588
15.5.2 The Collocated Pressure Correction Equation..... 592
15.5.3 Calculation of the Vf Term................. 596
15.5.4 The Collocated SIMPLE Algorithm............ 597
15.6 Boundary Conditions............................. 602
15.6.1 Boundary Conditions for the Momentum
Equation............................... 603
Contents xix
15.6.2 Boundary Conditions for the Pressure
Correction Equation....................... 617
15.7 The SIMPLE Family of Algorithms................... 621
15.7.1 The SIMPLEC Algorithm................... 623
15.7.2 The PRIME Algorithm..................... 624
15.7.3 The PISO Algorithm...................... 625
15.8 Optimum Under-Relaxation Factor Values for v and p ..... 628
15.9 Treatment of Various Terms with the Rhie-Chow
Interpolation................................... 630
15.9.1 Treatment of the Under-Relaxation Term........ 630
15.9.2 Treatment of the Transient Term.............. 631
15.9.3 Treatment of the Body Force Term............ 632
15.9.4 Combined Treatment of Under-Relaxation,
Transient, and Body Force Terms............. 636
15.10 Computational Pointers........................... 636
15.10.1 uFVM................................ 636
15.10.2 OpenFOAM®........................... 638
15.11 Closure...................................... 649
15.12 Exercises..................................... 649
References.......................................... 653
16 Fluid Flow Computation: Compressible Flows............... 655
16.1 Historical..................................... 655
16.2 Introduction................................... 656
16.3 The Conservation Equations........................ 657
16.4 Discretization of the Momentum Equation.............. 658
16.5 The Pressure Correction Equation.................... 659
16.6 Discretization of The Energy Equation................. 663
16.6.1 Discretization of the Extra Terms............. 663
16.6.2 The Algebraic Form of the Energy Equation...... 665
16.7 The Compressible SIMPLE Algorithm................. 666
16.8 Boundary Conditions............................. 667
16.8.1 Inlet Boundary Conditions.................. 669
16.8.2 Outlet Boundary Conditions................. 672
16.9 Computational Pointers........................... 673
16.9.1 uFVM................................ 673
16.9.2 OpenFOAM®........................... 674
16.10 Closure...................................... 687
16.11 Exercises..................................... 687
References.......................................... 689
xx Contents
Part IV Applications
17 Turbulence Modeling................................. 693
17.1 Turbulence Modeling............................. 693
17.2 Reynolds Averaging............................. 696
17.2.1 Time Averaging......................... 696
17.2.2 Spatial Averaging........................ 696
17.2.3 Ensemble Averaging...................... 697
17.2.4 Averaging Rules......................... 697
17.2.5 Incompressible RANS Equations.............. 697
17.3 Boussinesq Hypothesis............................ 699
17.4 Turbulence Models.............................. 700
17.5 Two-Equation Turbulence Models.................... 700
17.5.1 Standard k-e Model..................... 700
17.5.2 The k - co Model........................ 702
17.5.3 The Baseline (BSL) k - co Model............. 704
17.5.4 The Shear Stress Transport (SST) k - co Model ... 705
17.6 Summary of Incompressible Turbulent Flow Equations..... 707
17.7 Discretization of the Turbulent Flow Equations........... 707
17.7.1 The Discretized Form of the k Equation......... 708
17.7.2 The Discretized Form of the e Equation......... 708
17.7.3 The Discretized Form of the co Equation........ 709
17.8 Boundary Conditions............................. 710
17.8.1 Modeling Flow Near the Wall................ 710
17.8.2 Standard Wall Functions................... 711
17.8.3 Improved Wall Functions................... 716
17.8.4 Scalable Wall Functions.................... 718
17.8.5 Wall Boundary Conditions for Low
Reynolds Number Models.................. 719
17.8.6 Automatic Near-Wall Treatment.............. 720
17.8.7 Near-Wall Heat Transfer................... 721
17.8.8 Other Boundary Conditions................. 722
17.9 Calculating Normal Distance to the Wall............... 723
17.10 Computational Pointers........................... 725
17.10.1 The k - e Model......................... 727
17.10.2 The SST k - co Model..................... 734
17.10.3 simpleFoamTurbulent...................... 738
17.11 Closure...................................... 740
17.12 Exercises..................................... 740
References.......................................... 742
18 Boundary Conditions in OpenFOAM® and uFVM............ 745
18.1 Boundary Conditions in OpenFOAM®................. 745
18.2 Boundary Condition Customization................... 747
Contents xxi
18.3 Development of a New BC: No Slip Wall Condition....... 752
18.4 The No-Slip Boundary Condition in uFVM............. 756
18.5 Closure...................................... 759
Reference.......................................... 759
19 An OpenFOAM® Turbulent Flow Application............... 761
19.1 Introduction................................... 761
19.2 The Ahmed Bluff Body........................... 761
19.3 Domain Discretization............................ 763
19.3.1 Initial and Boundary Conditions.............. 768
19.3.2 Systems Files........................... 770
19.3.3 Running the Solver....................... 773
19.4 Conclusion.................................... 776
References.......................................... 776
20 Closing Remarks.................................... 777
Appendix: uFVM....................................... 779
|
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| author | Moukalled, F. Mangani, L. Darwish, M. |
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| ctrlnum | (OCoLC)922947288 (DE-599)GBV826482589 |
| discipline | Physik Mathematik |
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| id | DE-604.BV042926026 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T06:42:24Z |
| institution | BVB |
| isbn | 3319168738 9783319168739 9783319348643 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028353219 |
| oclc_num | 922947288 |
| open_access_boolean | |
| owner | DE-188 DE-706 DE-83 DE-29T DE-703 DE-862 DE-BY-FWS DE-91G DE-BY-TUM |
| owner_facet | DE-188 DE-706 DE-83 DE-29T DE-703 DE-862 DE-BY-FWS DE-91G DE-BY-TUM |
| physical | XXIII, 791 S. Ill., graph. Darst. 242 mm |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Springer |
| record_format | marc |
| series | Fluid mechanics and its applications |
| series2 | Fluid mechanics and its applications |
| spellingShingle | Moukalled, F. Mangani, L. Darwish, M. The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab Fluid mechanics and its applications Numerische Strömungssimulation (DE-588)4690080-9 gnd Finite-Volumen-Methode (DE-588)4220855-5 gnd |
| subject_GND | (DE-588)4690080-9 (DE-588)4220855-5 |
| title | The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab |
| title_alt | CFD FVM |
| title_auth | The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab |
| title_exact_search | The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab |
| title_full | The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab F. Moukalled ; L. Mangani ; M. Darwish |
| title_fullStr | The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab F. Moukalled ; L. Mangani ; M. Darwish |
| title_full_unstemmed | The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab F. Moukalled ; L. Mangani ; M. Darwish |
| title_short | The finite volume method in computational fluid dynamics |
| title_sort | the finite volume method in computational fluid dynamics an advanced introduction with openfoam and matlab |
| title_sub | an advanced introduction with OpenFOAM and Matlab |
| topic | Numerische Strömungssimulation (DE-588)4690080-9 gnd Finite-Volumen-Methode (DE-588)4220855-5 gnd |
| topic_facet | Numerische Strömungssimulation Finite-Volumen-Methode |
| url | http://www.springer.com/de/book/9783319168739 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028353219&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035417894 |
| work_keys_str_mv | AT moukalledf thefinitevolumemethodincomputationalfluiddynamicsanadvancedintroductionwithopenfoamandmatlab AT manganil thefinitevolumemethodincomputationalfluiddynamicsanadvancedintroductionwithopenfoamandmatlab AT darwishm thefinitevolumemethodincomputationalfluiddynamicsanadvancedintroductionwithopenfoamandmatlab AT moukalledf cfdfvm AT manganil cfdfvm AT darwishm cfdfvm |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 920 M925 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |