Course Unit

Catalogue

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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