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.


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