Mathematical fluid and biofluid dynamics
Additional Info
- ECTS credits: 6
- University: University of L'Aquila
- Semester: 3
- Lecturer 1: Donatella Donatelli
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Objectives:
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. -
Topics:
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. -
Prerequisites:
Basic notions of functional analysis and multi variable calculus, standard properties of the heat equation, wave equation, Laplace and Poisson's equations.