Mathematical fluid and biofluid dynamics
- Unit Coordinator: Donatella Donatelli
- Programme: Erasmus Mundus
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Aims:
The aim of the course is to give an overview of fluid dynamics from a mathematical viewpoint, and to introduce students to the mathematical modeling of fluid dynamic type with a particular attention to biofluid dynamics.
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 the 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
- 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: magnetohydrodynamics, combustion, astrophysics.
- Modeling for biofluids: hemodynamics, cerebrospinal fluids, cancer modelling, animal locomotion, bioconvection for swimming microorganisms.
- Pre-requisites:
Basic notions of functional analysis and multi variable calculus, standard properties of the heat equation, wave equation, Laplace and Poisson's equations.