Multiscale and multiresolution approaches in turbulence

Contents......Page 10
Preface......Page 8
1.1.1 Introductory concepts......Page 16
1.1.2 Randomness and coherent structure in turbulent flows......Page 18
1.2.1 Basic equations of turbulent flow......Page 20
1.2.2 Defining turbulent scales......Page 23
1.2.3 A glimpse at numerical simulations of turbulent flows......Page 28
1.3.1 The energy cascade......Page 29
1.3.2 Inter-scale interactions......Page 31
2.1 Numerical Simulation of Turbulent Flows......Page 36
2.2 Reducing the Cost of the Simulations......Page 38
2.2.2 Navier-Stokes-based equations for the resolved quantities......Page 39
2.3.1 Statistical average......Page 41
2.3.2 Reynolds-Averaged Navier-Stokes equations......Page 43
2.3.3 Phase-Averaged Navier Stokes equations......Page 44
2.4.1 Large and small scales separation......Page 46
2.4.2 Filtered Navier-Stokes equations......Page 48
2.5 Multilevel/Multiresolution Methods......Page 50
2.5.1 Hierarchical multilevel decomposition......Page 51
2.5.2 Practical example: the multiscale/multilevel LES decomposition......Page 53
2.5.3 Associated Navier-Stokes-based equations......Page 54
2.5.4.1 Multilevel methods based on resolved-only wavenumbers......Page 56
2.5.4.2 Multilevel methods based on higher wavenumbers......Page 57
2.5.4.3 Adaptive multilevel methods......Page 58
2.6 Summary......Page 59
3.1 General......Page 66
3.2.1 Basic equations in physical and spectral space......Page 69
3.2.2 The multiscale splitting......Page 74
3.2.3 Governing equations for band-integrated approaches......Page 75
3.3.1 Local versus non-local transfers......Page 77
3.3.2 Expression for the spectral fluxes......Page 79
3.3.3 Dynamic spectral splitting......Page 82
3.3.5 Viscous dissipation term......Page 83
3.4.1 Multiscale Reynolds stress models......Page 84
3.4.2 Multiscale eddy-viscosity models......Page 85
3.5.1 Local multiscale Reynolds stress models......Page 86
3.5.1.1 Closures for the linear transfer term......Page 87
3.5.1.2 Closures for the linear pressure term......Page 88
3.5.1.3 Closures for the non-linear homogeneous transfer term......Page 89
3.5.1.4 Closures for the non-linear non-homogeneous transfer term......Page 91
3.5.2 Local multiscale eddy-viscosity models......Page 92
3.6 Achievements and Open Issues......Page 93
4.1.1 Functional and structural subgrid models......Page 102
4.1.2 The Gabor-Heisenberg curse......Page 103
4.2.1.1 Two-level multiplicative Germano Identity......Page 108
4.2.1.2 Multilevel Germano Identity......Page 110
4.2.2 Derivation of dynamic subgrid models......Page 111
4.2.3.1 Turbulence self-similarity......Page 114
4.2.3.2 Scale-separation operator self-similarity......Page 121
4.3 Self-Similarity Based Dynamic Subgrid Models......Page 123
4.3.1 Terracol-Sagaut procedure......Page 124
4.3.2 Shao procedure......Page 126
4.4 Variational Multiscale Methods and Related Subgrid Viscosity Models......Page 129
4.4.1 Hughes VMS approach and extended formulations......Page 130
4.4.2 Implementation of the scale separation operator......Page 134
4.4.3 Bridging with hyperviscosity and filtered models......Page 138
5 Structural Multiscale Subgrid Models: Small Scales Estimations......Page 140
5.1 Small-scale Reconstruction Methods: Deconvolution......Page 141
5.1.1 The velocity estimation model......Page 143
5.1.2 The Approximate Deconvolution Model (ADM)......Page 149
5.2.1 General idea of the method......Page 156
5.2.2.1 Vorticity magnitude cascade......Page 157
5.2.2.2 Vorticity orientation cascade......Page 159
5.3 Multigrid-based Decomposition......Page 161
5.4 Global Multigrid Approaches: Cycling Methods......Page 166
5.4.1 The multimesh method of Voke......Page 167
5.4.2 The multilevel LES method of Terracol et al......Page 168
5.4.2.1 Cycling procedure......Page 169
5.4.2.2 Multilevel subgrid closures......Page 171
a) Dynamic mixed multilevel closure......Page 172
b) Generalized multilevel closure......Page 176
5.4.2.3 Examples of application......Page 177
5.5 Zonal Multigrid/Multidomain Methods......Page 178
6.1 Turbulence and Self-adaptivity: Expectations and Issues......Page 188
6.2 Adaptive Multilevel DNS and LES......Page 193
6.2.1 Dynamic Local Multilevel LES......Page 194
6.2.2 The Dynamic MultiLevel (DML) method of Dubois Jauberteau and Temam......Page 198
6.2.2.1 Spectral multilevel decomposition......Page 199
6.2.2.2 Associated Navier-Stokes-based equations......Page 200
6.2.2.3 Quasi-static approximation......Page 202
6.2.2.4 General description of the spectral multilevel method......Page 203
6.2.2.5 Dynamic estimation of the parameters i1 i2 and nv......Page 204
6.2.3 Dynamic Global Multilevel LES......Page 206
6.3 Adaptive Wavelet-based Methods: CVS SCALES......Page 210
6.3.1 Wavelet decomposition: brief reminder......Page 211
6.3.2.1 Introduction to the coherency diagram......Page 213
6.3.2.2 Threshold value and error control......Page 216
6.3.3 Adaptive Wavelet based Direct Numerical Simulation......Page 218
6.3.4 Coherent Vortex Capturing method......Page 219
6.3.5 Stochastic Coherent Adaptive Large Eddy Simulation......Page 220
6.4.1 Error definition: surfacic versus volumic formulation......Page 222
6.4.2 A posteriori error estimation and optimization loop......Page 224
6.4.3 Numerical results......Page 226
7.1.1 Concept: the effective filter......Page 234
7.1.2 Eddy viscosity effective filter......Page 236
7.1.3 Global hybrid RANS/LES methods as multiscale methods......Page 238
7.2 Motivation and Classification of RANS/LES Methods......Page 239
7.3.1 Unsteady RANS approach......Page 243
7.3.2 The Semi-Deterministic Method of Ha Minh......Page 246
7.3.3 The Scale Adaptive Simulation......Page 252
7.3.4 The Turbulence-Resolving RANS approach of Travin et al......Page 256
7.4 Global Hybrid Approaches......Page 258
7.4.1 The Approach of Speziale......Page 259
7.4.2.1 General idea of LNS......Page 262
7.4.2.2 Example of application......Page 263
7.4.3.1 General idea of blending methods......Page 264
7.4.3.2 Applications......Page 266
7.4.4.1 General idea......Page 269
7.4.4.2 DES based on the SA model......Page 271
7.4.4.3 Possible extensions of standard SA-DES......Page 274
7.4.4.5 DES based on the k - w model......Page 276
7.4.4.6 Extra-Large Eddy Simulation (XLES)......Page 280
7.4.5 Grey Area-Grid Induced Separation (GIS)......Page 282
7.4.6.1 Modifying the length scale......Page 285
7.4.6.2 Zonal-DES......Page 286
7.4.6.3 Shielding the boundary layer-Delayed Detached Eddy Simulation......Page 288
7.5 Summary......Page 291
8 Zonal RANS/LES Methods......Page 298
8.1.1 Full-variables approach......Page 300
8.1.1.1 Enrichment procedure from RANS to LES......Page 302
8.1.1.2 Restriction procedure from LES to RANS......Page 304
8.1.2 Perturbation approach: NLDE......Page 305
8.2 Inlet Data Generation - Mapping Techniques......Page 309
8.2.1 Precursor calculation......Page 310
8.2.2 Recycling methods......Page 313
8.2.3 Forcing conditions......Page 318
8.3 Turbulence Reconstruction for Inflow Conditions......Page 321
8.3.2 Inverse Fourier transform technique......Page 322
8.3.3 Random Fourier modes synthesization......Page 324
8.3.4 Synthetic turbulence......Page 330
Bibliography......Page 336
Index......Page 354