Turbulent Flow Simulations with Physical and Data-Driven Methods

Master | 6 ECTS | SS

Links
C@MPUS Module Catalog

General Information

Cycle

Annually, in the summer semester

Language

German/English

Course Components
  • Weekly lectures on Mondays and Thursdays
  • Weekly exercise sessions on Tuesdays

Having completed this course, students will be able to: 

  • Explain the statistical description of turbulence, including probability theory, correlations, and spectra.
  • Apply Reynolds decomposition to derive the RANS equations and the turbulent kinetic energy transport equation.
  • Differentiate different RANS closure models, including algebraic models, one- and two-equation models.
  • Explain Reynolds stress transport modeling and nonlinear closures.
  • Derive the LES filtered equations and sub-grid models, such as the Smagorinsky model.
  • Describe the concepts of implicit LES, wall-resolved LES, and wall-modeled LES.
  • Understand the basics of neural networks and implement modern neural network architectures in PyTorch, such as CNN, U-Net, and TBNN.
  • Develop a surrogate model using U-Net for porous media (Project).

This course provides an in-depth study into the modeling of turbulent flows. It focuses on general principles in high-fidelity physical modeling and how such principles can be enforced in data-driven methods.  It is expected that such insights can be valuable for students concerned with physical modeling in other disciplines. Specific course contents include:

  • Introduction to turbulent flows and statistical description of turbulence
  • Reynolds-averaged Navier-Stokes Equation (RANS): derivation of RANS equations, RANS linear model, nonlinear model and RSTM
  • Large-eddy simulation (LES): explicit models, implicit methods, wall-resolved LES and wall-modeled LES
  • Basics of neural networks: MLP, backpropagation, SGD
  • Modern neural network architecture: CNN, U-Net, TBNN
  • Applications of machine learning in fluid dynamics (e.g., surrogate model for the porous media, data augmentation in turbulence)
  • Physics-informed data-driven turbulence models (e.g., invariance properties, nondimensionalization)
  • Hands-on programming and practice with neural network using pytorch
  • J. Frölich, Large Eddy Simulation turbulenter Strömungen, Springer, 2006 
  • D. C. Wilcox, Turbulence Modeling for CFD, 3rd Ed., DCW Industries, 2006
  • S. Pope, Turbulent Flows, Cambridge University Press, 2000

Oral examination lasting 40 minutes.

Before the examination, consultation sessions will be offered and announced in due time via Ilias or during the lecture. These sessions are primarily intended to clarify any remaining questions that arise during exam preparation.

Additionally, to summarize the lecture and support exam preparation, we will offer an overview lecture on the exam content. In this session, the general structure and procedure of the exam as well as example questions will be presented. The materials for the overview lecture will be made available on Ilias at the appropriate time.

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