Contents -- Preface -- 1 A Brief Introduction to Turbulence -- 1.1 Common Features of Turbulent Flows -- 1.1.1 Introductory concepts -- 1.1.2 Randomness and coherent structure in turbulent flows -- 1.2 Turbulent Scales and Complexity of a Turbulent Field -- 1.2.1 Basic equations of turbulent flow -- 1.2.2 Defining turbulent scales -- 1.2.3 A glimpse at numerical simulations of turbulent flows -- 1.3 Inter-scale Coupling in Turbulent Flows -- 1.3.1 The energy cascade -- 1.3.2 Inter-scale interactions -- 2 Turbulence Simulation and Scale Separation -- 2.1 Numerical Simulation of Turbulent Flows -- 2.2 Reducing the Cost of the Simulations -- 2.2.1 Scale separation -- 2.2.2 Navier-Stokes-based equations for the resolved quantities -- 2.2.3 Navier-Stokes-based equations for the unresolved quantities -- 2.3 The Averaging Approach: Reynolds-Averaged Numerical Simulation (RANS) -- 2.3.1 Statistical average -- 2.3.2 Reynolds-Averaged Navier-Stokes equations -- 2.3.3 Phase-Averaged Navier Stokes equations -- 2.4 The Large Eddy Simulation Approach (LES) -- 2.4.1 Large and small scales separation -- 2.4.2 Filtered Navier-Stokes equations -- 2.5 Multilevel/Multiresolution Methods -- 2.5.1 Hierarchical multilevel decomposition -- 2.5.2 Practical example: the multiscale/multilevel LES decomposition -- 2.5.3 Associated Navier-Stokes-based equations -- 2.5.4 Classification of existing multilevel methods -- 2.5.4.1 Multilevel methods based on resolved-only wavenumbers -- 2.5.4.2 Multilevel methods based on higher wavenumbers -- 2.5.4.3 Adaptive multilevel methods -- 2.6 Summary -- 3 Statistical Multiscale Modelling -- 3.1 General -- 3.2 Exact Governing Equations for the Multiscale Problem -- 3.2.1 Basic equations in physical and spectral space -- 3.2.2 The multiscale splitting.

3.2.3 Governing equations for band-integrated approaches -- 3.3 Spectral Closures for Band-integrated Approaches -- 3.3.1 Local versus non-local transfers -- 3.3.2 Expression for the spectral fluxes -- 3.3.3 Dynamic spectral splitting -- 3.3.4 Turbulent diffusion terms -- 3.3.5 Viscous dissipation term -- 3.3.6 Pressure term -- 3.4 A Few Multiscale Models for Band-integrated Approaches -- 3.4.1 Multiscale Reynolds stress models -- 3.4.2 Multiscale eddy-viscosity models -- 3.5 Spectral Closures for Local Approaches -- 3.5.1 Local multiscale Reynolds stress models -- 3.5.1.1 Closures for the linear transfer term -- 3.5.1.2 Closures for the linear pressure term -- 3.5.1.3 Closures for the non-linear homogeneous transfer term -- 3.5.1.4 Closures for the non-linear non-homogeneous transfer term -- 3.5.2 Local multiscale eddy-viscosity models -- 3.6 Achievements and Open Issues -- 4 Multiscale Subgrid Models: Self-adaptivity -- 4.1 Fundamentals of Subgrid Modelling -- 4.1.1 Functional and structural subgrid models -- 4.1.2 The Gabor-Heisenberg curse -- 4.2 Germano-type Dynamic Subgrid Models -- 4.2.1 Germano identity -- 4.2.1.1 Two-level multiplicative Germano Identity -- 4.2.1.2 Multilevel Germano Identity -- 4.2.1.3 Generalized Germano Identity -- 4.2.2 Derivation of dynamic subgrid models -- 4.2.3 Dynamic models and self-similarity -- 4.2.3.1 Turbulence self-similarity -- 4.2.3.2 Scale-separation operator self-similarity -- 4.3 Self-Similarity Based Dynamic Subgrid Models -- 4.3.1 Terracol-Sagaut procedure -- 4.3.2 Shao procedure -- 4.4 Variational Multiscale Methods and Related Subgrid Viscosity Models -- 4.4.1 Hughes VMS approach and extended formulations -- 4.4.2 Implementation of the scale separation operator -- 4.4.3 Bridging with hyperviscosity and filtered models.

5 Structural Multiscale Subgrid Models: Small Scales Estimations -- 5.1 Small-scale Reconstruction Methods: Deconvolution -- 5.1.1 The velocity estimation model -- 5.1.2 The Approximate Deconvolution Model (ADM) -- 5.2 Small Scales Reconstruction: Multifractal Subgrid-scale Modelling -- 5.2.1 General idea of the method -- 5.2.2 Multifractal reconstruction of subgrid vorticity -- 5.2.2.1 Vorticity magnitude cascade -- 5.2.2.2 Vorticity orientation cascade -- 5.2.2.3 Reconstruction of the subgrid velocity field -- 5.3 Multigrid-based Decomposition -- 5.4 Global Multigrid Approaches: Cycling Methods -- 5.4.1 The multimesh method of Voke -- 5.4.2 The multilevel LES method of Terracol et al -- 5.4.2.1 Cycling procedure -- 5.4.2.2 Multilevel subgrid closures -- (a) Dynamic mixed multilevel closure -- (b) Generalized multilevel closure -- 5.4.2.3 Examples of application -- 5.5 Zonal Multigrid/Multidomain Methods -- 6 Unsteady Turbulence Simulation on Self-adaptive Grids -- 6.1 Turbulence and Self-adaptivity: Expectations and Issues -- 6.2 Adaptive Multilevel DNS and LES -- 6.2.1 Dynamic Local Multilevel LES -- 6.2.2 The Dynamic MultiLevel (DML) method of Dubois Jauberteau and Temam -- 6.2.2.1 Spectral multilevel decomposition -- 6.2.2.2 Associated Navier-Stokes-based equations -- 6.2.2.3 Quasi-static approximation -- 6.2.2.4 General description of the spectral multilevel method -- 6.2.2.5 Dynamic estimation of the parameters i1 i2 and nv -- 6.2.3 Dynamic Global Multilevel LES -- 6.3 Adaptive Wavelet-based Methods: CVS SCALES -- 6.3.1 Wavelet decomposition: brief reminder -- 6.3.2 Coherency diagram of a turbulent field -- 6.3.2.1 Introduction to the coherency diagram -- 6.3.2.2 Threshold value and error control -- 6.3.3 Adaptive Wavelet based Direct Numerical Simulation -- 6.3.4 Coherent Vortex Capturing method.

6.3.5 Stochastic Coherent Adaptive Large Eddy Simulation -- 6.4 DNS and LES with Optimal AMR -- 6.4.1 Error definition: surfacic versus volumic formulation -- 6.4.2 A posteriori error estimation and optimization loop -- 6.4.3 Numerical results -- 7 Global Hybrid RANS/LES Methods -- 7.1 Bridging between Hybrid RANS/LES Methods and Multiscale Methods -- 7.1.1 Concept: the effective filter -- 7.1.2 Eddy viscosity effective filter -- 7.1.3 Global hybrid RANS/LES methods as multiscale methods -- 7.2 Motivation and Classification of RANS/LES Methods -- 7.3 Unsteady Statistical Modelling Approaches -- 7.3.1 Unsteady RANS approach -- 7.3.2 The Semi-Deterministic Method of Ha Minh -- 7.3.3 The Scale Adaptive Simulation -- 7.3.4 The Turbulence-Resolving RANS approach of Travin et al -- 7.4 Global Hybrid Approaches -- 7.4.1 The Approach of Speziale -- 7.4.2 Limited Numerical Scales (LNS) -- 7.4.2.1 General idea of LNS -- 7.4.2.2 Example of application -- 7.4.3 Blending methods -- 7.4.3.1 General idea of blending methods -- 7.4.3.2 Applications -- 7.4.4 Detached-Eddy Simulation -- 7.4.4.1 General idea -- 7.4.4.2 DES based on the SA model -- 7.4.4.3 Possible extensions of standard SA-DES -- 7.4.4.4 Examples -- 7.4.4.5 DES based on the k - w model -- 7.4.4.6 Extra-Large Eddy Simulation (XLES) -- 7.4.5 Grey Area-Grid Induced Separation (GIS) -- 7.4.6 Solutions against GIS -- 7.4.6.1 Modifying the length scale -- 7.4.6.2 Zonal-DES -- 7.4.6.3 Shielding the boundary layer-Delayed Detached Eddy Simulation -- 7.5 Summary -- 8 Zonal RANS/LES Methods -- 8.1 Theoretical Setting of RANS/LES Coupling -- 8.1.1 Full-variables approach -- 8.1.1.1 Enrichment procedure from RANS to LES -- 8.1.1.2 Restriction procedure from LES to RANS -- 8.1.2 Perturbation approach: NLDE -- 8.2 Inlet Data Generation - Mapping Techniques.

8.2.1 Precursor calculation -- 8.2.2 Recycling methods -- 8.2.3 Forcing conditions -- 8.3 Turbulence Reconstruction for Inflow Conditions -- 8.3.1 Random fluctuations -- 8.3.2 Inverse Fourier transform technique -- 8.3.3 Random Fourier modes synthesization -- 8.3.4 Synthetic turbulence -- Bibliography -- Index.