Mathematical modelling of continuum media

Additional Info

  • ECTS credits: 3
  • Semester: 1
  • University: University of L'Aquila
  • 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.

    At the end of the course students will be able to understand constitutive models for fluids and to be able to solve simple boundary value problems for fluids and solids.

  • 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
    • Example of fluid models in various fields
  • Prerequisites:

     

    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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