Mathematical fluid dynamics
- Unit Coordinator: Donatella Donatelli
- Programme: InterMaths
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Delivery: In-class
- Aims:
This course is designed to give an overview of luid dynamics from a mathematical viewpoint and to introduce students to the mathematical modeling of luid dynamic type. At the end of the course students will be able to perform a qualitative and quantitative analysis of solutions for particular luid dynamics problems and to use concepts and mathematical techniques learned from this course for analysis of other partial differential equations.
- Content:
- Derivation of the governing equations: Euler and Navier-Stokes
- Eulerian and Lagrangian description of fluid motion; examples of fluid flows
- Poiseulle and Couette fluid types
- Vorticity equation in 2D and 3D
- Dimensional analysis: Reynolds number, Mach Number, Frohde number.
- From compressible to incompressible models
- Existence of solutions for viscid and inviscid fluids
- Fluid dynamic modeling in various fields: mixture of fluids, combustion, astrophysics, geophysical fluids (atmosphere, ocean)
- Modeling for biofluids: hemodynamics, cerebrospinal fluids, cancer modelling, animal locomotion, bioconvection for swimming microorganisms. - Pre-requisites:
Basic notions of functional analysis, functions of complex values, standard properties of the heat equation, wave equation, Laplace and Poisson's equations.
