Large Eddy Simulation for Incompressible Flows (eBook)

Foreword to the Third Edition 5
Foreword to the Second Edition 8
Foreword to the First Edition 11
Preface to the Third Edition 14
Preface to the Second Edition 16
Preface to the First Edition 18
Contents 20
1. Introduction 27
1.1 Computational Fluid Dynamics 27
1.2 Levels of Approximation: General 28
1.3 Statement of the Scale Separation Problem 29
1.4 Usual Levels of Approximation 31
1.5 Large-Eddy Simulation: from Practice to Theory. Structure of the Book 35
2. Formal Introduction to Scale Separation: Band- Pass Filtering 40
2.1 Definition and Properties of the Filter in the Homogeneous Case 40
2.2 Spatial Filtering: Extension to the Inhomogeneous Case 56
2.3 Time Filtering: a Few Properties 68
3. Application to Navier–Stokes Equations 70
3.1 Navier–Stokes Equations 71
3.2 Filtered Navier–Stokes Equations in Cartesian Coordinates ( Homogeneous Case) 73
3.3 Decomposition of the Non-linear Term. Associated Equations for the Conventional Approach 74
3.4 Extension to the Inhomogeneous Case for the Conventional Approach 99
3.5 Filtered Navier–Stokes Equations in General Coordinates 102
3.6 Closure Problem 103
4. Other Mathematical Models for the Large- Eddy Simulation Problem 107
4.1 Ensemble-Averaged Models 107
4.2 Regularized Navier–Stokes Models 109
5. Functional Modeling (Isotropic Case) 114
5.1 Phenomenology of Inter-Scale Interactions 114
5.2 Basic Functional Modeling Hypothesis 127
5.3 Modeling of the Forward Energy Cascade Process 128
5.4 Modeling the Backward Energy Cascade Process 194
6. Functional Modeling: Extension to Anisotropic Cases 210
6.1 Statement of the Problem 210
6.2 Application of Anisotropic Filter to Isotropic Flow 210
6.3 Application of an Isotropic Filter to a Shear Flow 216
6.4 Remarks on Flows Submitted to Strong Rotation Effects 231
7. Structural Modeling 232
7.1 Introduction and Motivations 232
7.2 Formal Series Expansions 233
7.3 Scale Similarity Hypotheses and Models Using Them 254
7.4 Mixed Modeling 260
7.5 Differential Subgrid Stress Models 266
7.6 Stretched-Vortex Subgrid Stress Models 272
7.7 Explicit Evaluation of Subgrid Scales 274
7.8 Direct Identification of Subgrid Terms 295
7.9 Implicit Structural Models 298
8. Numerical Solution: Interpretation and Problems 303
8.1 Dynamic Interpretation of the Large- Eddy Simulation 303
8.2 Ties Between the Filter and Computational Grid. Pre- filtering 310
8.3 Numerical Errors and Subgrid Terms 312
9. Analysis and Validation of Large- Eddy Simulation Data 326
9.1 Statement of the Problem 326
9.2 Correction Techniques 334
9.3 Practical Experience 339
10. Boundary Conditions 344
10.1 General Problem 344
10.2 Solid Walls 347
10.3 Case of the Inflow Conditions 375
11. Coupling Large-Eddy Simulation with Multiresolution/ Multidomain Techniques 389
11.1 Statement of the Problem 389
11.2 Methods with Full Overlap 391
11.3 Methods Without Full Overlap 396
11.4 Coupling Large-Eddy Simulation with Adaptive Mesh Refinement 397
12. Hybrid RANS/LES Approaches 403
12.1 Motivations and Presentation 403
12.2 Zonal Decomposition 404
12.3 Nonlinear Disturbance Equations 410
12.4 Universal Modeling 411
12.5 Toward a Theoretical Status for Hybrid RANS/ LES Approaches 419
13. Implementation 421
13.1 Filter Identification. Computing the Cutoff Length 421
13.2 Explicit Discrete Filters 424
13.3 Implementation of the Structure Function Models 428
14. Examples of Applications 430
14.1 Homogeneous Turbulence 430
14.2 Flows Possessing a Direction of Inhomogeneity 433
14.3 Flows Having at Most One Direction of Homogeneity 438
14.4 Industrial Applications 451
14.5 Lessons 458
15. Coupling with Passive/Active Scalar 468
15.1 Scope of this Chapter 468
15.2 The Passive Scalar Case 469
15.3 The Active Scalar Case: Stratification and Buoyancy Effects 491
A. Statistical and Spectral Analysis of Turbulence 513
A.1 Turbulence Properties 513
A.2 Foundations of the Statistical Analysis of Turbulence 513
A.3 Introduction to Spectral Analysis of the Isotropic Turbulent Fields 517
A.4 Characteristic Scales of Turbulence 522
A.5 Spectral Dynamics of Isotropic Homogeneous Turbulence 522
B. EDQNM Modeling 525
B.1 Isotropic EDQNM Model 525
B.2 Cambon’s Anisotropic EDQNM Model 527
B.3 EDQNM Model for Isotropic Passive Scalar 529
References 531
Index 570