Dettagli sull'Insegnamento per l'A.A. 2017/2018

Le informazioni che state leggendo si riferiscono all'anno accademico 2017/2018. Per questo molti collegamenti non sono disponibili e i dati potrebbero essere incompleti. Per leggere le informazioni correnti sul corso, se ancora erogato, consulta il catalogo corsi di ateneo. Per consultare le informazioni relative ad altri anni accademici, usa la lista in fondo a questa pagina.

A. Accademico:

2017/2018

Nome:

Mathematical fluid dynamics / Mathematical fluid dynamics

Tipo:

Corso singolo

Informazioni

Codice:

DT0247

SSD:

MAT/05

Crediti:

: Master Degree in Mathematics 6 CFU (c)

Periodo:

1^st semester

Erogazione:

Master Degree in Mathematics 2^nd anno curriculum Generale Elective

Lingua:

Inglese

Docenti:

Donatella Donatelli

Mutua:

Mathematical fluid dynamics

Prerequisiti

Basic notions of functional analysis, functions of complex values, standard properties of the heat equation, wave equation, Laplace and Poisson's equations.

Obiettivi

This course is designed to give an overview of fluid dynamics from a mathematical viewpoint, and to introduce students to the mathematical modeling of fluid dynamic type. At the end of the course students will be able to perform a qualitative and quantitative analysis of solutions for particular fluid dynamics problems and to use concepts and mathematical techniques learned from this course for analysis of other partial differential equations.

Sillabo

Derivation of the governing equations: Euler and Navier-Stokes
Eulerian and Lagrangian description of fluid motion; examples of fluid flows
Vorticiy equation in 2D and 3D
Dimensional analysis: Reynolds number, Mach Number, Frohde number.
From compressible to incompressible models
Fluid dynamic modeling in various fields: magnetohydrodynamics, combustion, astrophysics, biofluids.
Existence of solutions for viscid and inviscid fluids

Descrittori di Dublino

Alla fine del corso, lo studente dovrebbe

understand the basic principles governing the dynamics of non-viscous fluids;
be able to derive and deduce the consequences of the equation of conservation of mass;
be able to apply Bernoulli's theorem and the momentum integral to simple problems including river flows;
understand the concept of vorticity and the conditions in which it may be assumed to be zero;
calculate velocity fields and forces on bodies for simple steady and unsteady flows derived from potentials;
demonstrate skill in mathematical reasoning and ability to conceive proofs for fluid dynamics equations.
demonstrate capacity for reading and understand other texts on related topics.

Testi di riferimento

Alexandre Chorin, Jerrold E. Marsden, A Mathematical Introduction to Fluid Mechanics , Springer.
Roger M. Temam, Alain M. Miranville, Mathematical Modeling in Continum Mechanics , Cambridge University Press.
Franck Boyer, Pierre Fabrie, Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models , Springer-Verlag Italia.
Andrea Bertozzi, Andrew Majda, Vorticity and Incompressible Flow , Cambridge University Press.

Modalità d'esame

Written exam.

Aggiornamenti alla pagina del corso

Le informazioni sulle editioni passate di questo corso sono disponibili per i seguenti anni accademici:

Per leggere le informazioni correnti sul corso, se ancora erogato, consulta il catalogo corsi di ateneo.

Ultimo aggiornamento delle informazioni sul corso: 18 ottobre 2017, 09:58