Course Details for A.Y. 2016/2017
Name:
Mathematical fluid dynamics / Mathematical fluid dynamics
Basic information
Credits:
: Master Degree in Mathematics 6 CFU (c)
Degree(s):
Master Degree in Mathematics 2nd anno curriculum Generale Elective
Language:
English
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