Multiscale and multiresolution approaches in turbulence

Title:

Personal Author:

Sagaut, Pierre, 1967-

Publication Information:

London : Imperial College Press, 2006

ISBN:

9781860946509

Subject Term:

Turbulence -- Mathematical models

Added Author:

Deck, Sebastien

Terracol, Marc

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010123578	TA357.5.T87 S234 2006	Open Access Book	Book	Searching... Unknown

This unique book gives a general unified presentation of the use of the multiscale/multiresolution approaches in the field of turbulence. The coverage ranges from statistical models developed for engineering purposes to multiresolution algorithms for the direct computation of turbulence. It provides the only available up-to-date reviews dealing with the latest and most advanced turbulence models (including LES, VLES, hybrid RANS/LES, DES) and numerical strategies.The book aims at providing the reader with a comprehensive description of modern strategies for turbulent flow simulation, ranging from turbulence modeling to the most advanced multilevel numerical methods.

Preface	p. vii
1 A Brief Introduction to Turbulence	p. 1
1.1 Common Features of Turbulent Flows	p. 1
1.1.1 Introductory concepts	p. 1
1.1.2 Randomness and coherent structure in turbulent flows	p. 3
1.2 Turbulent Scales and Complexity of a Turbulent Field	p. 5
1.2.1 Basic equations of turbulent flow	p. 5
1.2.2 Defining turbulent scales	p. 8
1.2.3 A glimpse at numerical simulations of turbulent flows	p. 13
1.3 Inter-scale Coupling in Turbulent Flows	p. 14
1.3.1 The energy cascade	p. 14
1.3.2 Inter-scale interactions	p. 16
2 Turbulence Simulation and Scale Separation	p. 21
2.1 Numerical Simulation of Turbulent Flows	p. 21
2.2 Reducing the Cost of the Simulations	p. 23
2.2.1 Scale separation	p. 24
2.2.2 Navier-Stokes-based equations for the resolved quantities	p. 24
2.2.3 Navier-Stokes-based equations for the unresolved quantities	p. 26
2.3 The Averaging Approach: Reynolds-Averaged Numerical Simulation (RANS)	p. 26
2.3.1 Statistical average	p. 26
2.3.2 Reynolds-Averaged Navier-Stokes equations	p. 28
2.3.3 Phase-Averaged Navier Stokes equations	p. 29
2.4 The Large Eddy Simulation Approach (LES)	p. 31
2.4.1 Large and small scales separation	p. 31
2.4.2 Filtered Navier-Stokes equations	p. 33
2.5 Multilevel/Multiresolution Methods	p. 35
2.5.1 Hierarchical multilevel decomposition	p. 36
2.5.2 Practical example: the multiscale/multilevel LES decomposition	p. 38
2.5.3 Associated Navier-Stokes-based equations	p. 39
2.5.4 Classification of existing multilevel methods	p. 41
2.5.4.1 Multilevel methods based on resolved-only wavenumbers	p. 41
2.5.4.2 Multilevel methods based on higher wavenumbers	p. 42
2.5.4.3 Adaptive multilevel methods	p. 43
2.6 Summary	p. 44
3 Statistical Multiscale Modelling	p. 51
3.1 General	p. 51
3.2 Exact Governing Equations for the Multiscale Problem	p. 54
3.2.1 Basic equations in physical and spectral space	p. 54
3.2.2 The multiscale splitting	p. 59
3.2.3 Governing equations for band-integrated approaches	p. 60
3.3 Spectral Closures for Band-integrated Approaches	p. 62
3.3.1 Local versus non-local transfers	p. 62
3.3.2 Expression for the spectral fluxes	p. 64
3.3.3 Dynamic spectral splitting	p. 67
3.3.4 Turbulent diffusion terms	p. 68
3.3.5 Viscous dissipation term	p. 68
3.3.6 Pressure term	p. 69
3.4 A Few Multiscale Models for Band-integrated Approaches	p. 69
3.4.1 Multiscale Reynolds stress models	p. 69
3.4.2 Multiscale eddy-viscosity models	p. 70
3.5 Spectral Closures for Local Approaches	p. 71
3.5.1 Local multiscale Reynolds stress models	p. 71
3.5.1.1 Closures for the linear transfer term	p. 72
3.5.1.2 Closures for the linear pressure term	p. 73
3.5.1.3 Closures for the non-linear homogeneous transfer term	p. 74
3.5.1.4 Closures for the non-linear non-homogeneous transfer term	p. 76
3.5.2 Local multiscale eddy-viscosity models	p. 77
3.6 Achievements and Open Issues	p. 78
4 Multiscale Subgrid Models: Self-adaptivity	p. 87
4.1 Fundamentals of Subgrid Modelling	p. 87
4.1.1 Functional and structural subgrid models	p. 87
4.1.2 The Gabor-Heisenberg curse	p. 88
4.2 Germano-type Dynamic Subgrid Models	p. 93
4.2.1 Germano identity	p. 93
4.2.1.1 Two-level multiplicative Germano Identity	p. 93
4.2.1.2 Multilevel Germano Identity	p. 95
4.2.1.3 Generalized Germano Identity	p. 96
4.2.2 Derivation of dynamic subgrid models	p. 96
4.2.3 Dynamic models and self-similarity	p. 99
4.2.3.1 Turbulence self-similarity	p. 99
4.2.3.2 Scale-separation operator self-similarity	p. 106
4.3 Self-Similarity Based Dynamic Subgrid Models	p. 108
4.3.1 Terracol-Sagaut procedure	p. 109
4.3.2 Shao procedure	p. 111
4.4 Variational Multiscale Methods and Related Subgrid Viscosity Models	p. 114
4.4.1 Hughes VMS approach and extended formulations	p. 115
4.4.2 Implementation of the scale separation operator	p. 119
4.4.3 Bridging with hyperviscosity and filtered models	p. 123
5 Structural Multiscale Subgrid Models: Small Scales Estimations	p. 125
5.1 Small-scale Reconstruction Methods: Deconvolution	p. 126
5.1.1 The velocity estimation model	p. 128
5.1.2 The Approximate Deconvolution Model (ADM)	p. 134
5.2 Small Scales Reconstruction: Multifractal Subgrid-scale Modelling	p. 141
5.2.1 General idea of the method	p. 141
5.2.2 Multifractal reconstruction of subgrid vorticity	p. 142
5.2.2.1 Vorticity magnitude cascade	p. 142
5.2.2.2 Vorticity orientation cascade	p. 144
5.2.2.3 Reconstruction of the subgrid velocity field	p. 146
5.3 Multigrid-based Decomposition	p. 146
5.4 Global Multigrid Approaches: Cycling Methods	p. 151
5.4.1 The multimesh method of Voke	p. 152
5.4.2 The multilevel LES method of Terracol et al.	p. 153
5.4.2.1 Cycling procedure	p. 154
5.4.2.2 Multilevel subgrid closures	p. 156
(a) Dynamic mixed multilevel closure	p. 157
(b) Generalized multilevel closure	p. 161
5.4.2.3 Examples of application	p. 162
5.5 Zonal Multigrid/Multidomain Methods	p. 163
6 Unsteady Turbulence Simulation on Self-adaptive Grids	p. 173
6.1 Turbulence and Self-adaptivity: Expectations and Issues	p. 173
6.2 Adaptive Multilevel DNS and LES	p. 178
6.2.1 Dynamic Local Multilevel LES	p. 179
6.2.2 The Dynamic MultiLevel (DML) method of Dubois, Jauberteau and Temam	p. 183
6.2.2.1 Spectral multilevel decomposition	p. 184
6.2.2.2 Associated Navier-Stokes-based equations	p. 185
6.2.2.3 Quasi-static approximation	p. 187
6.2.2.4 General description of the spectral multilevel method	p. 188
6.2.2.5 Dynamic estimation of the parameters i[subscript 1], i[subscript 2] and n[subscript V]	p. 189
6.2.3 Dynamic Global Multilevel LES	p. 191
6.3 Adaptive Wavelet-based Methods: CVS, SCALES	p. 195
6.3.1 Wavelet decomposition: brief reminder	p. 196
6.3.2 Coherency diagram of a turbulent field	p. 198
6.3.2.1 Introduction to the coherency diagram	p. 198
6.3.2.2 Threshold value and error control	p. 201
6.3.3 Adaptive Wavelet based Direct Numerical Simulation	p. 203
6.3.4 Coherent Vortex Capturing method	p. 204
6.3.5 Stochastic Coherent Adaptive Large Eddy Simulation	p. 205
6.4 DNS and LES with Optimal AMR	p. 207
6.4.1 Error definition: surfacic versus volumic formulation	p. 207
6.4.2 A posteriori error estimation and optimization loop	p. 209
6.4.3 Numerical results	p. 211
7 Global Hybrid RANS/LES Methods	p. 219
7.1 Bridging between Hybrid RANS/LES Methods and Multiscale Methods	p. 219
7.1.1 Concept: the effective filter	p. 219
7.1.2 Eddy viscosity effective filter	p. 221
7.1.3 Global hybrid RANS/LES methods as multiscale methods	p. 223
7.2 Motivation and Classification of RANS/LES Methods	p. 224
7.3 Unsteady Statistical Modelling Approaches	p. 228
7.3.1 Unsteady RANS approach	p. 228
7.3.2 The Semi-Deterministic Method of Ha Minh	p. 231
7.3.3 The Scale Adaptive Simulation	p. 237
7.3.4 The Turbulence-Resolving RANS approach of Travin et al.	p. 241
7.4 Global Hybrid Approaches	p. 243
7.4.1 The Approach of Speziale	p. 244
7.4.2 Limited Numerical Scales (LNS)	p. 247
7.4.2.1 General idea of LNS	p. 247
7.4.2.2 Example of application	p. 248
7.4.3 Blending methods	p. 249
7.4.3.1 General idea of blending methods	p. 249
7.4.3.2 Applications	p. 251
7.4.4 Detached-Eddy Simulation	p. 254
7.4.4.1 General idea	p. 254
7.4.4.2 DES based on the SA model	p. 256
7.4.4.3 Possible extensions of standard SA-DES	p. 259
7.4.4.4 Examples	p. 261
7.4.4.5 DES based on the [kappa] - [omega] model	p. 261
7.4.4.6 Extra-Large Eddy Simulation (XLES)	p. 265
7.4.5 Grey Area-Grid Induced Separation (GIS)	p. 267
7.4.6 Solutions against GIS	p. 270
7.4.6.1 Modifying the length scale	p. 270
7.4.6.2 Zonal-DES	p. 271
7.4.6.3 Shielding the boundary layer-Delayed Detached Eddy Simulation	p. 273
7.5 Summary	p. 276
8 Zonal RANS/LES Methods	p. 283
8.1 Theoretical Setting of RANS/LES Coupling	p. 285
8.1.1 Full-variables approach	p. 285
8.1.1.1 Enrichment procedure from RANS to LES	p. 287
8.1.1.2 Restriction procedure from LES to RANS	p. 289
8.1.2 Perturbation approach: NLDE	p. 290
8.2 Inlet Data Generation - Mapping Techniques	p. 294
8.2.1 Precursor calculation	p. 295
8.2.2 Recycling methods	p. 298
8.2.3 Forcing conditions	p. 303
8.3 Turbulence Reconstruction for Inflow Conditions	p. 306
8.3.1 Random fluctuations	p. 307
8.3.2 Inverse Fourier transform technique	p. 307
8.3.3 Random Fourier modes synthesization	p. 309
8.3.4 Synthetic turbulence	p. 315
Bibliography	p. 321
Index	p. 339

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