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Turbulence Modeling
Last Updated: 2026-02-05 15:18:57
Abstract
In the study of turbulent flows the objective is to obtain a tractable quantitative theory or model to calculate quantities of interest. A century of expertise has shown the 'turbulence problem' to be notoriously difficult, and there are no prospects of a simple analytic theory. In this class, five of the leading computational approaches to turbulent flows are described and examined.
Objective
The goal of this class is to give an good overview of current turbulence modeling approaches, but also to help developing a feeling for advantages and limitations of the various classes of models.
Content
1. Introduction to Modeling: The goal here is to present an overview of different approaches, point out the main challenges and discuss general criteria for turbulence models 2. Direct Numerical Simulation (DNS): After the basics of DNS are introduced, applications to homogeneous and inhomogeneous turbulent flows are discussed. 3. Turbulent-Viscosity Models: The implications due to the underlying assumption, the turbulent viscosity hypothesis, are explained and discussed. Then, specific models belonging to the classes of algebraic, one-equation and two-equation models are introduced. 4. Reynolds-Stress Models: After a brief discussion of the concept and the advantage above turbulent-viscosity models, most of the time will be spent for "return-to-isotropy models, near-wall treatments and algebraic stress models. 5. Probability Density Function (PDF) Methods: This part is at the center of this class. First, the concept of PDF modeling is explained and the PDF transport equation is derived, discussed and analyzed. It is shown that turbulent transport and reaction source terms appear in closed form. However, models are required to close other terms. Then, consistent Lagrangean models are presented. Using these equations and models, corresponding Reynolds-stress models are derived. It is demonstrated how the PDF transport equation can be used to analyze turbulent flows, even without using the PDF approach for simulations. 6. Large-Eddy Simulation (LES) The basic concepts of LES are introduced. After a discussion of filtering, the filtered conservation equations are derived. As an example of a sub-grid model the Smagorinsky model is presented and finally the perspectives of LES are discussed.
Resources
Lecture Notes
The course is partly based on part two of the book "Turbulent Flows" by Stephen B. Pope published by Cambridge University Press, 2000. In addition, we hand out a manuscript, which contains not all the course material, however.
Literature
S. B. Pope, Turbulent Flows, Cambridge University Press, 2000
General Information
- Language
- English
- Levels
- DS , BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Turbulence Modeling |
|
2 h weekly |
| exercise | Turbulence Modeling |
|
1 h weekly |