Math Courses

An Introduction to Continuum Mechanics (1/3)

by Francesco Viola (GSSI), Roberto Verzicco (GSSI)


Roberto Verzicco (GSSI)
Francesco Viola (GSSI)

Contacts (Office PT-F, Mariani Building) (Office S2-B, Mariani Building)

Course outcomes
The students attending this course are expected to become familiar with vector spaces relevant to continuum mechanics and to perform vector and tensor manipulations. They will be able to describe motion, deformation and forces in a continuum, derive equations of motion and conservation laws and use constitutive models for fluids and solids. With these tools at hand
students will be able to solve simple boundary value problems for fluids and solids. As an application of a challenging problem of continuum mechanics, the final part of the course will be devoted to introduce the basics of turbulence and some related computational method.

- Reminders on Linear Algebra and Tensor Calculus
- The Continuum hypothesis: from microscopic to macroscopic
- Kinematics of deformable bodies
- Eulerian and Lagrangian descriptions of motion
- The balance laws of continuum mechanics: Conservation of Mass and Energy, Momentum Balance
- Constitutive Equations
- Fluid dynamics: the Navier Stokes equations
- Solid mechanics: nonlinear and linearized elasticity
- An introduction to the physics of fluid turbulence
- Energy cascade
- Kolmogorov theory and wall turbulence
- Basic concepts on computational methods for fluid dynamics and turbulence simulation

Lectures: 60 hours
Homework assignments: 4 at 4 hours each
Final project and exam: 20 hours

Suggested Books
M. Gurtin, Introduction to Continuum Mechanics, Academic Press 1981
S. Pope, Turbulent Flows, Cambridge University Press 2000