Multiscale and Multiresolution Approaches in Turbulence

The following sections are included:

• Foreword to the Second Edition

• Foreword to the First Edition

• Contents

The following sections are included:

• Common Features of Turbulent Flows
  • Introductory concepts
  • Randomness and coherent structure in turbulent flows

• Turbulent Scales and Complexity of a Turbulent Field
  • Basic equations of turbulent flow
  • Defining turbulent scales
  • A glimpse at numerical simulations of turbulent flows

• Inter-scale Coupling in Turbulent Flows
  • The energy cascade
  • Inter-scale interactions

The following sections are included:

• Numerical Simulation of Turbulent Flows

• Reducing the Cost of the Simulations
  • Scale separation
  • Navier–Stokes-based equations for the resolved quantities
  • Navier–Stokes-based equations for the unresolved quantities

• The Averaging Approach: Reynolds-Averaged Numerical Simulation (RANS)
  • Statistical average
  • Reynolds-Averaged Navier–Stokes equations
  • Phase-Averaged Navier–Stokes equations

• The Large-Eddy Simulation Approach (LES)
  • Large and small scales separation
  • Filtered Navier–Stokes equations

• Multilevel/Multiresolution Methods
  • Hierarchical multilevel decomposition
  • Practical example: the multiscale/multilevel LES decomposition
  • Associated Navier–Stokes-based equations
  • Classification of existing multilevel methods
    • Multilevel methods based on resolved-only wave numbers
    • Multilevel methods based on higher wave numbers
    • Adaptive multilevel methods

• Summary

The following sections are included:

• General

• Exact Governing Equations for the Multiscale Problem
  • Basic equations in physical and spectral space
  • Themultiscale splitting
  • Governing equations for band-integrated approaches

• Spectral Closures for Band-integrated Approaches
  • Local versus non-local transfers
  • Expression for the spectral fluxes
  • Dynamic spectral splitting
  • Turbulent diffusion terms
  • Viscous dissipation term
  • Pressure term

• A Few Multiscale Models for Band-integrated Approaches
  • Multiscale Reynolds stress models
  • Multiscale eddy viscosity models

• Spectral Closures for Local Approaches
  • Local multiscale Reynolds stress models
    • Closures for the linear transfer term
    • Closures for the linear pressure term
    • Closures for the non-linear homogeneous transfer term
    • Closures for the non-linear non-homogeneous transfer term
  • Local multiscale eddy viscosity models

• Achievements and Open Issues

The following sections are included:

• Fundamentals of Subgrid Modelling
  • Functional and structural subgrid models
  • The Gabor–Heisenberg curse

• Germano-type Dynamic Subgrid Models
  • Germano identity
    • Two-level multiplicative Germano identity
    • Multilevel Germano identity
    • Generalized Germano identity
  • Derivation of dynamic subgrid models
  • Dynamic models and self-similarity
    • Turbulence self-similarity
    • Scale separation operator self-similarity

• Self-Similarity Based Dynamic Subgrid Models
  • Terracol–Sagaut procedure
  • Shao procedure

• Variational Multiscale Methods and Related Subgrid Viscosity Models
  • Hughes VMS approach and extended formulations
  • Implementation of the scale separation operator
  • Bridging with hyperviscosity and filtered models

The following sections are included:

• Small-scale Reconstruction Methods: Deconvolution
  • The velocity estimation model
  • The Approximate Deconvolution Model (ADM)
    • The original ADM approach of Stolz, Adams and Kleiser
    • Example of application
    • Alternative formulation by explicit filtering
    • Alternative regularization by standard subgrid models
    • Relaxation-based approaches
    • Subgrid scales estimation by approximate deconvolution

• Small Scales Reconstruction: Multifractal Subgrid-scale Modelling
  • General idea of the method
  • Multifractal reconstruction of subgrid vorticity
    • Vorticity magnitude cascade
    • Vorticity orientation cascade
    • Reconstruction of the subgrid velocity field

• Variational Multiscale Methods

• Multigrid-based Decomposition

• Global Multigrid Approaches: Cycling Methods
  • The multimesh method of Voke
  • The multilevel LES method of Terracol et al
    • Cycling procedure
    • Multilevel subgrid closures
    • Examples of application

• Zonal Multigrid/Multidomain Methods

The following sections are included:

• Turbulence and Self-adaptivity: Expectations and Issues

• Adaptive Multilevel DNS and LES
  • Dynamic local multilevel LES
  • The dynamic multilevel (DML) method of dubois, jauberteau and temam
    • Spectral multilevel decomposition
    • Associated Navier–Stokes-based equations
    • Quasi-static approximation
    • General description of the spectral multilevel method
    • Dynamic estimation of the parameters i₁, i₂ and n_V
  • Dynamic global multilevel LES

• Adaptive Wavelet-based Methods: CVS, SCALES
  • Wavelet decomposition: brief reminder
  • Coherency diagram of a turbulent field
    • Introduction to the coherency diagram
    • Threshold value and error control
    • Adaptive wavelet-based direct numerical simulation
    • Coherent vortex capturing method
    • Stochastic coherent adaptive large-eddy simulation

• DNS and LES with Optimal AMR
  • Error definition: surfacic versus volumic formulation
  • A posteriori error estimation and optimization loop
  • Numerical results

The following sections are included:

• Bridging between Hybrid RANS/LES Methods and Multiscale Methods
  • Concept: the effective filter
  • Eddy viscosity effective filter
  • Global hybrid RANS/LES methods asmultiscale methods

• Motivation and Classification of RANS/LES Methods

• Unsteady Statistical Modelling Approaches
  • Unsteady RANS approach
  • The Semi-Deterministic Method of Ha Minh
  • The Scale Adaptive Simulation (SAS)
  • The Turbulence-Resolving RANS approach of Travin et al

• Global Hybrid Approaches
  • The Approach of Speziale
  • Limited Numerical Scales (LNS)
    • General idea of LNS
    • Example of application
  • Blending methods
    • General idea of blending methods
    • Applications
  • Other approaches: PITM and PANS
    • Partially Integrated Transport Model (PITM)
    • Partially Averaged Navier–Stokes (PANS)
  • Detached Eddy Simulation
    • General idea
    • DES based on the SA model
    • Possible extensions of standard SA-DES
    • Examples
    • DES based on the k – ω model
    • Extra-Large Eddy Simulation (XLES)
  • Grey-Area Modelled-Stress-Depletion (MSD) Grid and Induced Separation (GIS)
  • Further interpretation of MSD: non-local error analysis
  • Delayed Detached Eddy Simulation (DDES)
    • Formulation
    • Improved Delayed Detached Eddy Simulation (IDDES)
  • Zonal Detached Eddy Simulation (ZDES)
    • Formulation
    • Implementation
    • Interpretation and further discussion

The following sections are included:

• Theoretical Setting of RANS/LES Coupling
  • Full-variables approach
    • Enrichment procedure from RANS to LES
    • Restriction procedure from LES to RANS
  • Perturbation approach: NLDE

• Inlet Data Generation – Mapping Techniques
  • Precursor calculation
  • Recycling methods
  • Main issues and possible improvements of recycling methods

• Synthetic Turbulence
  • Spectral methods
    • Inverse Fourier transform technique
    • Random Fourier modes synthesization
  • Digital filtering procedure by Klein–Sadiki–Janicka
  • The Sandham–Yao–Lawal procedure
  • Synthetic Eddy Method (SEM)
    • The original procedure by Jarrin et al
    • Further improvements of the SEM method
    • Adaptations to ZDES

• Forcing Methods
  • The Spille-Kohoff–Kaltenbach controlled forcing method
  • The dynamic forcing method by Laraufie–Deck–Sagaut
  • The Dahlström and Davidson procedure

The following sections are included:

• Flow Physics Classification and Modelling Strategy Suitability

• Illustrative Examples
  • Practical industrial applications
  • Wall turbulence simulation

• Further Discussion
  • Numerical discretization effects
    • General statement
    • Grid resolution requirements
    • More detailed discussion: classical LES
  • Zonal vs. non-zonal treatment of turbulence

The following sections are included:

• Bibliography

• Index