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Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2018/2019
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 097634 - COMPUTATIONAL FLUID DYNAMICS [C.I.]
  • 097630 - COMPUTATIONAL FLUID DYNAMICS [1]
Docente Docente Non Definito
Cfu 5.00 Tipo insegnamento Modulo Di Corso Strutturato

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.]
052030 - COMPUTATIONAL FLUID DYNAMICS [C.I.]

Obiettivi dell'insegnamento

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.

 

This course is associated with a joint course named 052028 - COMPUTATIONAL FLUID DYNAMICS [1] (5 CFU). The current sheet specifies goals, program and expected learning results for both courses.


Risultati di apprendimento attesi

The student will be able to:

- analyze a physical problem involving fluid dynamics phenomena and identify the mathematical model which better describes it

- derive the incompressible Navier-Stokes equations in conservative and differential forms

- derive the weak formulation of Stokes and Navier-Stokes equations for different choices of boundary conditions

- derive and understand the Galerkin formulation and be able to prove the main stability and convergence results

- formulate suitable preconditioning strategies for the solution of saddle point problems

- formulate and analyze iterative schemes for treating the nonlinearity in Navier-Stokes equations

- understand and formulate stabilized methods for inf-sup non compatible discretizations as well as convection dominated problems

- formulate and analyze time advancing schemes for the solution of time dependent Navier-Stokes equations

- select among the different discretization approaches the one that guarantees the best compromize in terms of accuracy and computational efficiency for a given fluid dynamics problem

- formulate different numerical strategies for the solution of free surface problems

- implement a block preconditioner for saddle point problems

- implement stabilized finite element solvers

- implement different time-advancing schemes (including semi-Lagrangian and projection methods) for the time dependent Navier-Stokes equations


Argomenti trattati

- Navier-Stokes equations in primitive variables.

- Weak formulation of Stokes and Navier-Stokes equations with different choices of boundary conditions.

- Galerkin/finite elements discretization methods.

- Compatibility between finite element spaces for velocity and pressure.

- Preconditioners for saddle point problems.

- Brief discussion of other discretization techniques: finite differences, finite volumes, spectral methods.

- Steady state Navier-Stokes equations: fixed point and Newton algorithms.

- Unsteady Navier-Stokes equations: time marching schemes; treatment of the convective term; projection methods.

- Numerical approaches for free surface problems.

- Brief dicussion of numerical schemes for compressible flows.


Prerequisiti

Students are required to:

- know basic linear algebra

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

- know the main properties of partial differential equations

- know the main properties of numerical approximation of elliptic and parabolic differential equations


Modalità di valutazione

The student 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.

The student proves to know the main definitions and concepts inherent in weak formulation of Stokes and Navier-Stokes equations with different boundary conditions.

He must be able to critically discuss the governing equations for incompressible flows and the related approximated techniques for their numerical solution.

He must be able to propose the most adequate analytic, modelling and numerical approach that guarantees the best compromize in terms of accuracy and computational efficiency for a given fluid dynamics problem.

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


Bibliografia
Risorsa bibliografica obbligatoriaLecture notes available on beep channel
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 facoltativaHC. Elman, D.J. Silvester, A.J. Wathen, Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, Editore: Oxford University 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. LeVeque, Numerical Methods for Conservation Laws, Editore: Birkhäuser, Anno edizione: 1988

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
(hh:mm)
Ore di studio autonome
(hh:mm)
Lezione
35:00
52:30
Esercitazione
0:00
0:00
Laboratorio Informatico
15:00
22:30
Laboratorio Sperimentale
0:00
0:00
Laboratorio Di Progetto
0:00
0:00
Totale 50:00 75:00

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
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
schedaincarico v. 1.6.5 / 1.6.5
Area Servizi ICT
30/09/2020