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Scheda Riassuntiva
Anno Accademico 2015/2016
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 097634 - COMPUTATIONAL FLUID DYNAMICS [C.I.]
Docente Parolini Nicola , Valdettaro Lorenzo
Cfu 10.00 Tipo insegnamento Corso Integrato

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - BV (478) NUCLEAR ENGINEERING - INGEGNERIA NUCLEARE*AZZZZ097634 - COMPUTATIONAL FLUID DYNAMICS [C.I.]
Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA*AZZZZ097634 - COMPUTATIONAL FLUID DYNAMICS [C.I.]

Programma dettagliato e risultati di apprendimento attesi

This course is part of the Computational Science and Engineering track in the Master Program in Mathematical Engineering. It aims 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. Finally, since the course is oriented to the use of computer for the simulation of physical and engineering processes, an important part of the course will be devoted to the programming lab activities.

Contents:

Laminar incompressible fluid dynamics

Navier-Stokes equations in primitive variables.
Galerkin/finite elements discretization methods
Compatibility between finite element spaces for velocity and pressure.
Preconditioners.
Other discretization techniques: finite differences, finite volumes, spectral methods.
Stready state Navier-Stokes equations: fixed point and Newton algorithms.
Unsteady Navier-Stokes equations: time marching schemes; treatment of the convective term; projection methods.

Compressible fluid dynamics: Euler equations and their properties.
1D case: finite volume methods.
Godunov and Roe solvers.
Brief mention of flux and slope limiters and extension to the multi-dimensional case.

 

Turbulent incompressible fluid dynamics

Statistical description of turbulence.
Kolmogorov's theory and subsequent developments; intermittency.
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.

Brief mention of numerical methods for the main turbulence models.


Compressible fluid dynamics

Euler equations and their properties.
1D case: finite volume methods.
Godunov and Roe solvers.
Brief mention of flux and slope limiters and extension to the multi-dimensional case.

 

Lab activity

The numerical methods introduced in the course will be implemented during programming lab activities.


Note Sulla Modalità di valutazione

Students will attend a written test including theory and programming exercises, followed by an oral examination. A minimum mark of 18/30 in
the written exam evaluation is required for admission to the oral part.


Bibliografia
Risorsa bibliografica facoltativaA. Quarteroni, Numerical Models for Differential Problems, Editore: Springer, Anno edizione: 2014
Risorsa bibliografica facoltativaA. Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations, Editore: Springer-Verlag
Risorsa bibliografica facoltativaH.C. Elman, D.J. Silvester, A.J. Wathen, Finite Elements and Fast Iterative Solvers: with applications in Incompressible Fluid Dynamics, Editore: Oxford Univ. Press, Anno edizione: 2005
Risorsa bibliografica facoltativaM. Gunzburger, Finite Element Method for viscous Incompressible Flows, Editore: Academic press, Anno edizione: 1989
Risorsa bibliografica facoltativaJ. Ferziger, M. Peric, Computational Methods for Fluid Dynamics, Editore: Springer-Verlag, Anno edizione: 1996
Risorsa bibliografica facoltativaR. Le Veque, Numerical Methods for Conservation Laws, Editore: Birkhauser, Anno edizione: 1988
Risorsa bibliografica facoltativaP.A. Davidson, turbulence - an introduction for scientists and engineers, Editore: Oxford University Press, Anno edizione: 2004, ISBN: 0198529481
Risorsa bibliografica facoltativaU. Frisch, Turbulence, Editore: Cambridge University Press, Anno edizione: 1995, ISBN: 0-521-45103-5
Risorsa bibliografica obbligatoriaLecture notes http://www1.mate.polimi.it/CN/CSFluid/

Mix Forme Didattiche
Tipo Forma Didattica Ore didattiche
lezione
64.0
esercitazione
8.0
laboratorio informatico
36.0
laboratorio sperimentale
0.0
progetto
0.0
laboratorio di progetto
0.0

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
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schedaincarico v. 1.6.5 / 1.6.5
Area Servizi ICT
27/09/2020