• 097632 - COMPUTATIONAL FLUID DYNAMICS [2]

This course is part of the Computational Science and Engineering track in the Master Program in Mathematical Engineering. The aim is to provide students with the fundamentals of mathematical models and numerical methods for partial differential equations that describe the motion of fluids in both laminar and turbulent regimes. This is a very dynamic area of study full of new contributions. Therefore the course, in addition to the basic aspects, aims to encourage the study of the latest methodological approaches. In this part of the integrated course the focus will be on the statistical description of turbulence and on its modelling.

This course is also offered in a reduced 3 CFU version 052029 - COMPUTATIONAL FLUID DYNAMICS [2] which together with the course on 052028 - COMPUTATIONAL FLUID DYNAMICS [1] (5 CFU) defines the integrated course on 052030 - COMPUTATIONAL FLUID DYNAMICS [C.I.] (8 CFU). The present sheet defines the objectives, programs and learning outcomes for both courses.

The student will be able to:

- formulate the statistical quantities that are useful to describe the main features of a turbulent flow

- understand and derive the Kolmogorov theory for statistically homogeneous, stationary and incompressible turbulence

- understand the limitations of Kolmogorov theory and describe subsequent developments that overcome such limitations

- (*) characterize the main transport and diffusion properties of a passive scalar in a turbulent flow.

- (*) understand the features of two-dimensional turbulence and the main differences with respect to three-dimensional turbulence

- (*) characterize and describe the laminar and turbulent boundary layers

- understand and formulate the main families of turbulent models: Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES)

- understand the properties and limits of the different turbulent models

- implement simple turbulence models in finite element solvers.

(*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.

- Statistical description of turbulence.

- Kolmogorov's theory of statistically homogeneous and stationary incompressible turbulent flows. Limitations and subsequent developments of Kolmogorov's theory.

- (*) Transport and diffusion of a passive scalar in a turbulent flow.

- (*) Two-dimensional turbulence.

- (*) Laminar boundary layer; Blasius and Falkner-Skan equations. Turbulent boundary layer; wall law.

- Turbulence models for Reynolds Averaged Navier Stokes (RANS) equation; turbulent viscosity models, mixing length,

two equation models: k-epsilon model, k-omega model.

- Large Eddy Simulation (LES) turbulence models; filtering technique, Smagorinsky turbulent viscosity model,

similarity scale models, dynamic models, dynamic mixed models, anisotropic models.

(*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.

Students are required to

- know differential calculus for two- and three-dimensional domains for scalar and vector quantities

- know the main properties of partial differential equations

- have basic notions of statistics

The student will attend a written test, followed by an oral examination. A minimum mark of 18/30 in the written exam evaluation is required for admission to the oral part.

The student must prove to know the main definitions and concepts inherent in turbulent flows.

He must be able to critically discuss the different theoretical aspects of turbulent phenomena: the characteristics of the relevant statistical descriptors; the Kolmogorov's theory of statistically homogeneous and stationary incompressible turbulent flows and subsequent developments; (*) the transport and diffusion of a passive scalar in a turbulent flow; (*) two-dimensional turbulence; (*) the turbulent boundary layer and the laminar one as well; the turbulence models both in the framework of Reynolds Averaged Navier Stokes and of Large Eddy Simulation.

He must be able to propose the most adequate analytic and modelling approach that guarantees the best compromize in terms of accuracy and computational efficiency for a given turbulent flow.

In particular during the oral part the student should be able to present complex arguments in a rigorous, clear and concise way.

(*) In the reduced 3 CFU version of the course the points marked with an asterisk will not be included.