Contents	6
	Introduction	11
	LES Governing Equations	15
	Preliminary Discussion	15
	Governing Equations	16
	Fundamental Assumptions	16
	Conservative Formulation	17
	Alternative Formulations	19
	Filtering Operator	19
	Definition	20
	Fundamental Properties	20
	Additional Hypothesis	22
	Three Classical Filters for Large Eddy Simulation	22
	Differential Interpretation of the Filters	23
	Discrete Representation of Filters	24
	Filtering of Discontinuities	26
	Filter Associated to the Numerical Method	28
	Commutation Error	30
	Favre Filtering	30
	Summary of the Different Type of Filters	32
	Formulation of the Filtered Governing Equations	32
	Enthalpy Formulation	33
	Temperature Formulation	34
	Pressure Formulation	34
	Entropy Formulation	35
	Filtered Total Energy Equations	36
	A System for E, p, T	37
	A System for E, p, T	38
	A System for E, P, T	38
	A System for E, p, T	39
	Momentum Equations	39
	Simplifying Assumptions	40
	SGS Force Terms	40
	Small Scales Incompressibility	41
	Additional Relations for LES of Compressible Flows	43
	Preservation of Original Symmetries	43
	Discontinuity Jump Relations for LES	45
	Shock Modeling and Jump Relations	45
	Filtered Jump Relations and Associated Constrains on Subgrid Terms	46
	Second Law of Thermodynamics	47
	Model Construction	48
	Basic Hypothesis	48
	Modeling Strategies	49
	Compressible Turbulence Dynamics	50
	Scope and Content of This Chapter	50
	Kovasznay Decomposition of Turbulent Fluctuations	51
	Kovasznay's Linear Decomposition	51
	Weakly Nonlinear Kovasznay Decomposition	54
	Statistical Description of Compressible Turbulence	55
	Shock-Turbulence Interaction	57
	Introduction to the Linear Interaction Approximation Theory	57
	Vortical Turbulence-Shock Interaction	58
	Mixed-Mode Turbulence-Shock Interaction	66
	Influence of the Upstream Entropy Fluctuations	67
	Influence of the Upstream Acoustic Fluctuations	71
	Consequences for Subgrid Modeling	71
	Different Regimes of Isotropic Compressible Turbulence	73
	Quasi-Isentropic-Turbulence Regime	74
	Nonlinear Subsonic Regime	80
	Conditions for Occurrence of Shocklets	80
	Energy Budget and Shocklet Influence	80
	Enstrophy Budget and Shocklet Influence	81
	Supersonic Regime	83
	Consequences for Subgrid Modeling	84
	Functional Modeling	86
	Basis of Functional Modeling	86
	Phenomenology of Scale Interactions	86
	Basic Functional Modeling Hypothesis	88
	SGS Viscosity	88
	The Boussinesq Hypothesis	88
	Smagorinsky Model	90
	Structure Function Model	91
	Mixed Scale Model	91
	Isotropic Tensor Modeling	92
	SGS Heat Flux	93
	Modeling of the Subgrid Turbulent Dissipation Rate	94
	Improvement of SGS models	94
	Structural Sensors and Selective Models	94
	Accentuation Technique and Filtered Models	96
	High-Pass Filtered Eddy Viscosity	97
	Wall-Adapting Local Eddy-Viscosity Model	97
	Dynamic Procedure	98
	Computation of the Deviatoric SGS Tensor	98
	Computation of the Isotropic Part of the SGS Tensor	101
	Computation of the Dynamic Prandtl Number	101
	Implicit Diffusion and the Implicit LES Concept	102
	Explicit Structural Modeling	103
	Motivation of Structural Modeling	103
	Models Based on Deconvolution	105
	Scale-Similarity Model	108
	Approximate Deconvolution Model	111
	Tensor-Diffusivity Model	113
	Regularization Techniques	113
	Eddy-Viscosity Regularization	114
	Relaxation Regularization	117
	Regularization by Explicit Filtering	119
	Multi-Scale Modeling of Subgrid-Scales	121
	Multi-Level Approaches	121
	Stretched-Vortex Model	124
	Variational Multi-Scale Model	125
	Relation Between SGS Model and Numerical Discretization	127
	Systematic Procedures for Nonlinear Error Analysis	127
	Error Sources	127
	Modified Differential Equation Analysis	129
	Modified Differential Equation Analysis in Spectral Space	134
	Implicit LES Approaches Based on Linear and Nonlinear Discretization Schemes	137
	The Volume Balance Procedure of Schumamm	137
	The Kawamura-Kuwahara Scheme	138
	The Piecewise-Parabolic Method	139
	The Flux-Corrected-Transport Method	140
	The MPDATA Method	144
	The Optimum Finite-Volume Scheme	146
	Implicit LES by Adaptive Local Deconvolution	148
	Fundamental Concept of ALDM	148
	ALDM for the Incompressible Navier-Stokes Equations	151
	ALDM for the Compressible Navier-Stokes Equations	156
	Boundary Conditions for Large-Eddy Simulation of Compressible Flows	162
	Introduction	162
	Wall Modeling for Compressible LES	163
	Statement of the Problem	163
	Wall Boundary Conditions in the Kovasznay Decomposition Framework: an Insight	163
	Turbulent Boundary Layer: Vorticity and Temperature Fields	166
	Turbulent Boundary Layer Vortical Dynamics: a Brief Reminder	166
	Turbulent Boundary Layer: Mean Flow Features	167
	Turbulent Boundary Layer: Acoustic Field	170
	A First Insight: Surface Pressure Fluctuations	170
	Production of Pressure Fluctuations by the Vorticity Field	172
	Attenuation of Acoustic Modes by Vorticity and Entropy Modes	175
	Consequences for the Development of Compressible Wall Models	176
	Extension of Existing Wall Models for Incompressible Flows	177
	Algebraic Two-Layer Wall Models	177
	Thin-Boundary Layer Equations Based Models	178
	Unsteady Turbulent Inflow Conditions for Compressible LES	179
	Fundamentals	179
	Precursor Simulation: Advantages and Drawbacks	181
	Extraction-Rescaling Techniques	182
	Synthetic-Turbulence-Based Models	186
	Subsonic Applications with Compressibility Effects	192
	Homogeneous Turbulence	192
	Context	192
	A Few Realizations	193
	Influence of the Numerical Method	194
	SGS Modeling	197
	Channel Flow	198
	Context	198
	A Few Realizations	198
	Influence of the Numerical Method	199
	Influence of the SGS Model	201
	Mixing Layer	202
	Context	202
	A Few Realizations	202
	Influence of the Numerical Method	203
	Influence of the SGS Model	204
	Boundary-Layer Flow	205
	Context	205
	A Few Realizations	205
	Jets	207
	Context	207
	A Few Realizations	208
	Influence of the Numerical Method	209
	Influence of the SGS Model	211
	Physical Analysis	212
	Flows over Cavities	213
	Context	213
	A Few Realizations	213
	Influence of the Numerical Method	214
	Influence of the SGS Model	215
	Physical Analysis	215
	Supersonic Applications	217
	Homogeneous Turbulence	217
	Channel Flow	218
	Context	218
	A Few Realizations	218
	Influence of the Numerical Method	219
	Influence of the Grid Resolution	220
	Influence of the SGS Model	221
	Boundary Layers	221
	Context	221
	A Few Realizations	222
	Influence of the Numerical Method	222
	Influence of the Grid Resolution	223
	SGS Modeling	225
	Jets	226
	Context	226
	A Few Realizations	226
	Influence of the Numerical Method	227
	Influence of the SGS Model	227
	Physical Analysis	227
	Supersonic Applications with Shock-Turbulence Interaction	229
	Shock-Interaction with Homogeneous Turbulence	230
	Phenomenology of Shock-Interaction with Homogeneous Turbulence	230
	LES of Shock-Interaction with Homogeneous Turbulence	234
	Shock-Turbulence Interaction in Jets	236
	Phenomenology of Shock-Turbulence Interaction in Jets	236
	LES of Shock-Turbulence Interaction in Jets	237
	Shock-Turbulent-Boundary-Layer Interaction	239
	Phenomenology of Shock-Turbulent-Boundary-Layer Interaction	239
	LES of Compression-Ramp Configurations	243
	Normal Shock Configurations	250
	Impinging Shock Configurations	254
	References	260
	Index	277