• Italiano
  • English

Department of Mathematics and Applications
"Renato Caccioppoli"


Fluid Dynamics

Home > Exams > Fluid Dynamics

Fluid Dynamics

Credits

6

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/07 Mathematical Physics.

Examination method

Oral exam.

Learning
objectives

The course aims to give students an in-depth knowledge of fluid-dynamic phenomena and of the models capable of representing them. In particular, the main objective of the course is – starting from the specific fluid-dynamic phenomenon – to provide students with sufficient knowledge to identify the mathematical model most appropriate to the phenomenon under examination.

Syllabus

Kinematics of deformable continua. Cardinal equations of Mechanics for continuous systems. Stress axiom. Cauchy’s theorem and the stress tensor. Local formulation of the cardinal equations of Mechanics. Fundamental problem of the Mechanics of continuous systems. Laws of Thermodynamics. Viscous fluids. Navier-Stokes equations. Analysis and role of boundary conditions. Qualitative analysis of a motion. Stability of fluid motions. Topological dependence of the notion of stability, with examples. Arnold’s theorem. Non-isothermal viscous fluids. The problem of natural convection in a clear fluid and in a porous medium.

Expected learning
outcomes

On completion of the course, students must demonstrate that they

  • understand and know the general issues relating to the study of the evolution of fluid-dynamic phenomena;
  • can apply the knowledge acquired to tackle applied problems in the modelling and analysis of the evolution of fluid-dynamic systems;
  • can communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
  • can identify the most appropriate methods to analyse and solve a problem relating to the course topics and interpret the results correctly.

Learning outcomes
to be assessed

Ability to formulate physical-mathematical models (systems of partial differential equations) for fluid-dynamic phenomena and to obtain solutions of such models, with particular reference to non-isothermal fluid dynamics, demonstrating clarity, correctness and completeness in the oral presentation of the course topics.