Data Driven Analysis and Modeling of Turbulent Flows

1st Edition - March 17, 2025
Editor: Karthik Duraisamy
Language: English
Paperback ISBN:
9 7 8 - 0 - 3 2 3 - 9 5 0 4 3 - 5
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 9 5 0 4 4 - 2

Data-driven Analysis and Modeling of Turbulent Flows provides an integrated treatment of modern data-driven methods to describe, control, and predict turbulent flows through the… Read more

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Data-driven Analysis and Modeling of Turbulent Flows provides an integrated treatment of modern data-driven methods to describe, control, and predict turbulent flows through the lens of both physics and data science.

The book is organized into three parts:
• Exploration of techniques for discovering coherent structures within turbulent flows, introducing advanced decomposition methods
• Methods for estimation and control using data assimilation and machine learning approaches
• Finally, novel modeling techniques that combine physical insights with machine learning

This book is intended for students, researchers, and practitioners in fluid mechanics, though readers from related fields such as applied mathematics, computational science, and machine learning will find it also of interest.

Title of Book
Cover image
Title page
Table of Contents
Copyright
Contributors
Preface
Chapter 1: Introduction to turbulence & learning from data
1.1. Scales of turbulence
1.2. Coarse graining
1.2.1. Averaging and RANS
1.2.2. Filtering & LES
1.2.3. PDFs and FDFs
1.3. Insight into the structure of turbulent flows
1.4. Data-driven learning
1.5. Turbulent flow data
1.5.1. Example: compression of turbulent flow fields
1.6. Data-driven models
1.6.1. Dimensionality reduction
1.6.2. Dynamical systems models
1.6.3. Norms and loss functions
1.7. Roadmap
1.7.1. Part A: quest to find structure
1.7.2. Part B: estimation and control
1.7.3. Part C: modeling and prediction
Chapter 2: Modal decomposition
2.1. Introduction
2.2. Preliminaries
2.2.1. Bases
2.2.2. Inner product
2.2.3. Projection
2.2.4. Shifting the origin: affine subspaces
2.2.5. Stochastic processes
2.2.6. Symmetries, stationarity, and the ergodic hypothesis
2.2.7. What constitutes a good basis?
2.3. Decomposition methods for turbulence and other flows
2.3.1. Operator-based decomposition methods
2.3.2. Data-driven decomposition methods
2.4. Examples
2.4.1. Flow over a circular cylinder at low Reynolds number
2.4.2. Turbulent jet
2.5. Outlook
Chapter 3: Resolvent analysis for turbulent flows
3.1. Overview
3.2. Fundamentals
3.2.1. Definitions
3.2.2. Resolvent analysis of dynamical systems
3.2.3. Why it works, or, the relationship between strong system response, non-normality, and the spectrum of the Jacobian
3.2.4. Nonlinear feedback, solutions to the nonlinear system and the Lur'e decomposition
3.3. Resolvent operator for the Navier-Stokes equations
3.3.1. Choice of variables
3.3.2. Choice of base (mean) field
3.3.3. The Fourier transformed Navier-Stokes-equations
3.3.4. Practical considerations
3.3.5. Examples: one-dimensional and two-dimensional flows
3.3.6. Physical interpretation of resolvent modes and the origins of amplification
3.4. The role of nonlinearity
3.4.1. The importance of the Helmholtz decomposition
3.4.2. Nonlinearity and the turbulent mean field
3.4.3. Modal weights determined from the resolvent response basis
3.4.4. Modeling the nonlinearity
3.4.5. Relationship between data-driven and resolvent basis sets
3.5. Data-driven flow estimation and reconstruction
3.5.1. Batch estimation
3.5.2. Online estimation using a Kalman filter
3.5.3. Resolvent-based estimation of statistics
3.6. Extensions and outlook
3.6.1. Extended resolvent formulations
3.6.2. Modified boundary conditions and control
3.6.3. Closed models, nonlinear solutions and exact coherent structures
3.6.4. Closing and outlook
Chapter 4: Data assimilation and flow estimation
4.1. Overview
4.2. Filtering techniques
4.2.1. Continuous data assimilation
4.2.2. Ensemble Kalman filter
4.3. Smoothing techniques
4.3.1. Ensemble variational method
4.3.2. Adjoint-variational data assimilation
4.3.3. Machine learning for data assimilation
4.4. Conclusions
Chapter 5: Data-driven control of fluid flows
5.1. Introduction
5.2. Control setup and fundamental concepts
5.3. Principles of system identification: from data to models
5.4. System identification with impulse-response models
5.5. Subspace system identification
5.6. Dynamic observers
Dynamic observer using subspace system-identification techniques
5.7. DMDc and Koopman linearization
5.8. Data-based model-predictive control
5.9. Conclusions
Chapter 6: Algebraic tensorial representations
6.1. Introduction
6.2. Galilean invariance
6.3. Constitutive formulas
6.3.1. Constitutive representations
6.3.2. Relation to algebraic stress approximation
6.3.3. Algebraic stress approximation
6.3.4. Rotation and curvature
6.3.5. Scalar dispersion
6.4. Eigenvalues
6.4.1. Realizability
6.4.2. Barycentric representations
6.4.3. Additional considerations
Chapter 7: Parameter estimation and uncertainty quantification in turbulence modeling
7.1. Introduction and motivation
7.1.1. Turbulence closure modeling
7.1.2. Probability in computational science and engineering
7.2. Bayesian parameter estimation
7.2.1. Bayes' theorem
7.2.2. Parameter identification for a CFD problem
7.2.3. Application to regression: model inadequacy
7.2.4. Computational considerations
7.3. RANS closure model coefficient calibration
7.3.1. Classical identification of closure coefficients
7.3.2. Bayesian calibration of closure model coefficient
7.3.3. Bayesian model selection and model averaging
7.3.4. Discussion
7.4. Bayesian estimation of Reynolds stress anisotropy
7.4.1. Learning Reynolds-stress anisotropy from surface pressure
7.5. Conclusions
Appendix 7.A. Probability refresher
Multivariate random-variables
Chapter 8: Machine learning augmented modeling of turbulence
8.1. Introduction
8.2. Model inadequacies and augmentation
8.2.1. Model augmentation
8.2.2. Introducing model inadequacy
8.2.3. A priori learning and model inconsistency
8.3. Inferring a model-consistent augmentation
8.3.1. Field inversion and machine learning
8.3.2. Feature selection
8.3.3. Learning augmentation functions from augmentation fields
8.3.4. Fully differentiable learning
8.4. PDE-constrained optimization and learning
8.4.1. Method of adjoints for steady problems
8.4.2. Method of adjoints for unsteady problems
8.4.3. Calculating Jacobians
8.4.4. Obtaining sensitivities
8.5. A simple example: improving 1-D channel flow predictions
8.6. Sources of error
8.7. Bayesian approaches and sampling techniques
8.7.1. Maximum a posteriori estimate
8.7.2. Monte Carlo methods
8.8. Designing features
8.9. Functional forms for augmentation functions
8.9.1. Overfitting
8.9.2. Extrapolation
8.10. Applications
8.11. A perspective on generalizability
Chapter 9: Symbolic regression methods
9.1. Introduction
9.2. Literature review
9.2.1. Generalities
9.2.2. Symbolic regression in fluid mechanics
9.3. Introduction to selected SR techniques
9.3.1. Gene expression programming
9.3.2. Sparse symbolic identification
9.3.3. Sparse Bayesian regression
9.4. SR for data-driven RANS modeling
9.4.1. Training methods
9.4.2. GEP regression of data-driven RANS closures
9.4.3. SpaRTA
9.4.4. SBL-SpaRTA
9.5. Application examples
9.6. Summary
Index

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Data Driven Analysis and Modeling of Turbulent Flows

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