Course Details for A.Y. 2016/2017

The information on this page refer to the academic year 2016/2017. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2016/2017

Name:

Mathematical fluid dynamics / Mathematical fluid dynamics

Type:

Course

Basic information

Code:

DT0247

Sector:

MAT/05

Credits:

: Master Degree in Mathematics 6 CFU (c)

Term:

1^st semester

Degree(s):

Master Degree in Mathematics 2^nd anno curriculum Generale Elective

Language:

English

Teacher(s):

Donatella Donatelli

Same as:

Mathematical fluid dynamics

Course Objectives

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.

Course Content

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

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

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.

Prerequisites and Learning Activities

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

Assessment Methods and Criteria

Written exam.

Textbooks

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.

Course page updates

This course page is available (with possible updates) also for the following academic years:

To read the current information on this course, if it is still available, go to the university course catalogue .

Course information last updated on: 31 ottobre 2016, 17:53