Mathematical fluid dynamics
Additional Info
- ECTS credits: 6
- University: University of L'Aquila
- Semester: 3
- Lecturer 1: Donatella Donatelli
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Objectives:
This course is designed 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 the 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.
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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. Modeling for biofluids mechanics: hemodynamics, cerebrospinal fluids, animal locomotion: swimming and flying; Bioconvection for swimming microorganisms.
