Mathematics of large eddy simulation of turbulent flows /
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| Author / Creator: | Berselli, L. C. (Luigi C.) |
|---|---|
| Imprint: | Berlin : Springer-Verlag, c2006. |
| Description: | xvii, 348 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Scientific computation, 1434-8322 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5813342 |
Table of Contents:
- Part I. Introduction
- 1. Introduction
- 1.1. Characteristics of Turbulence
- 1.2. What are Useful Averages?
- 1.3. Conventional Turbulence Models
- 1.4. Large Eddy Simulation
- 1.5. Problems with Boundaries
- 1.6. The Interior Closure Problem in LES
- 1.7. Eddy Viscosity Closure Models in LES
- 1.8. Closure Models Based on Systematic Approximation
- 1.9. Mixed Models
- 1.10. Numerical Validation and Testing in LES
- 2. The Navier-Stokes Equations
- 2.1. An Introduction to the NSE
- 2.2. Derivation of the NSE
- 2.3. Boundary Conditions
- 2.4. A Few Results on the Mathematics of the NSE
- 2.4.1. Notation and Function Spaces
- 2.4.2. Weak Solutions in the Sense of Leray-Hopf
- 2.4.3. The Energy Balance
- 2.4.4. Existence of Weak Solutions
- 2.4.5. More Regular Solutions
- 2.5. Some Remarks on the Euler Equations
- 2.6. The Stochastic Navier-Stokes Equations
- 2.7. Conclusions
- Part II. Eddy Viscosity Models
- 3. Introduction to Eddy Viscosity Models
- 3.1. Introduction
- 3.2. Eddy Viscosity Models
- 3.3. Variations on the Smagorinsky Model
- 3.3.1. Van Driest Damping
- 3.3.2. Alternate Scalings
- 3.3.3. Models Acting Only on the Smallest Resolved Scales
- 3.3.4. Germano's Dynamic Model
- 3.4. Mathematical Properties of the Smagorinsky Model
- 3.4.1. Further Properties of Monotone Operators
- 3.5. Backscatter and the Eddy Viscosity Models
- 3.6. Conclusions
- 4. Improved Eddy Viscosity Models
- 4.1. Introduction
- 4.2. The Gaussian-Laplacian Model (GL)
- 4.2.1. Mathematical Properties
- 4.3. [kappa] - [epsilon] Modeling
- 4.3.1. Selective Models
- 4.4. Conclusions
- 5. Uncertainties in Eddy Viscosity Models and Improved Estimates of Turbulent Flow Functionals
- 5.1. Introduction
- 5.2. The Sensitivity Equations of Eddy Viscosity Models
- 5.2.1. Calculating [characters not reproducible]
- 5.2.2. Boundary Conditions for the Sensitivities
- 5.3. Improving Estimates of Functionals of Turbulent Quantities
- 5.4. Conclusions: Are u and p Enough?
- Part III. Advanced Models
- 6. Basic Criteria for Subfilter-scale Modeling
- 6.1. Modeling the Subfilter-scale Stresses
- 6.2. Requirements for a Satisfactory Closure Model
- 7. Closure Based on Wavenumber Asymptotics
- 7.1. The Gradient (Taylor) LES Model
- 7.1.1. Derivation of the Gradient LES Model
- 7.1.2. Mathematical Analysis of the Gradient LES Model
- 7.1.3. Numerical Validation and Testing
- 7.2. The Rational LES Model (RLES)
- 7.2.1. Mathematical Analysis for the Rational LES Model
- 7.2.2. On the Breakdown of Strong Solutions
- 7.2.3. Numerical Validation and Testing
- 7.3. The Higher-order Subfilter-scale Model (HOSFS)
- 7.3.1. Derivation of the HOSFS Model
- 7.3.2. Mathematical Analysis of the HOSFS Model
- 7.3.3. Numerical Validation and Testing
- 7.4. Conclusions
- 8. Scale Similarity Models
- 8.1. Introduction
- 8.1.1. The Bardina Model
- 8.2. Other Scale Similarity Models
- 8.2.1. Germano Dynamic Model
- 8.2.2. The Filtered Bardina Model
- 8.2.3. The Mixed-scale Similarity Model
- 8.3. Recent Ideas in Scale Similarity Models
- 8.4. The S[superscript 4] = Skew-symmetric Scale Similarity Model
- 8.4.1. Analysis of the Model
- 8.4.2. Limit Consistency and Verifiability of the S[superscript 4] Model
- 8.5. The First Energy-sponge Scale Similarity Model
- 8.5.1. "More Accurate" Models
- 8.6. The Higher Order, Stolz-Adams Deconvolution Models
- 8.6.1. The van Cittert Approximations
- 8.7. Conclusions
- Part IV. Boundary Conditions
- 9. Filtering on Bounded Domains
- 9.1. Filters with Nonconstant Radius
- 9.1.1. Definition of the Filtering
- 9.1.2. Some Estimates of the Commutation Error
- 9.2. Filters with Constant Radius
- 9.2.1. Derivation of the Boundary Commutation Error (BCE)
- 9.2.2. Estimates of the BCE
- 9.2.3. Error Estimates for a Weak Form of the BCE
- 9.2.4. Numerical Approximation of the BCE
- 9.3. Conclusions
- 10. Near Wall Models in LES
- 10.1. Introduction
- 10.2. Wall Laws in Conventional Turbulence Modeling
- 10.3. Current Ideas in Near Wall Modeling for LES
- 10.4. New Perspectives in Near Wall Models
- 10.4.1. The 1/7th Power Law in 3D
- 10.4.2. The 1/nth Power Law in 3D
- 10.4.3. A Near Wall Model for Recirculating Flows
- 10.4.4. A NWM for Time-fluctuating Quantities
- 10.4.5. A NWM for Reattachment and Separation Points
- 10.5. Conclusions
- Part V. Numerical Tests
- 11. Variational Approximation of LES Models
- 11.1. Introduction
- 11.2. LES Models and their Variational Approximation
- 11.2.1. Variational Formulation
- 11.3. Examples of Variational Methods
- 11.3.1. Spectral Methods
- 11.3.2. Finite Element Methods
- 11.3.3. Spectral Element Methods
- 11.4. Numerical Analysis of Variational Approximations
- 11.5. Introduction to Variational Multiscale Methods (VMM)
- 11.6. Eddy Viscosity Acting on Fluctuations as a VMM
- 11.7. Conclusions
- 12. Test Problems for LES
- 12.1. General Comments
- 12.2. Turbulent Channel Flows
- 12.2.1. Computational Setting
- 12.2.2. Definition of Re[subscript tau]
- 12.2.3. Initial Conditions
- 12.2.4. Statistics
- 12.2.5. LES Models Tested
- 12.2.6. Numerical Method and Numerical Setting
- 12.2.7. A Posteriori Tests for Re[subscript tau] = 180
- 12.2.8. A Posteriori Tests for Re[subscript tau] = 395
- 12.2.9. Backscatter in the Rational LES Model
- 12.2.10. Numerical Results
- 12.2.11. Summary of Results
- 12.3. A Few Remarks on Isotropic Homogeneous Turbulence
- 12.3.1. Computational Setting
- 12.3.2. Initial Conditions
- 12.3.3. Experimental Results
- 12.3.4. Computational Cost
- 12.3.5. LES of the Comte-Bellot Corrsin Experiment
- 12.4. Final Remarks
- References
- Index
