Math Courses

An introduction to Continuum Mechanics

by Francesco Viola, Roberto Verzicco




Roberto Verzicco,
Francesco Viola,

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

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

1. Reminders on Linear Algebra and Tensor Calculus
2. The Continuum hypothesis: from microscopic to macroscopic
3. Kinematics of deformable bodies
4. Eulerian and Lagrangian descriptions of motion
5. The balance laws of continuum mechanics: Conservation of Mass and Energy, MomentumBalance
6. Constitutive Relations
7. Solid mechanics: nonlinear and linearized elasticity
8. Fluid dynamics: the Navier Stokes equations
9. Analytical and asymptotic solutions of the Navier Stokes equations
10. An introduction to hydrodynamic instabilities
11. An introduction to the physics of fluid turbulence
12. Kolmogorov theory and wall turbulence
13. Basic concepts on computational methods for fluid dynamics and turbulence simulation

Examination and grading
Each student, after having delivered a written report on the final project, will be evaluated andranked according to the ECTS grading scale.

Suggested references

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