Mathematics

Turbulence plays a fundamental role in many different applications varying from aeronautical to environmental simulations. This course aims at giving an overview of the phenomenology and mathematical modelling of compressible turbulent flows. We will start from a first part focused on gasdynamics (thermodynamics, compressible navier-stokes equations, speed of sound, shock waves). The second part of the course will instead be focused on turbulence phenomenology and modelling.

Lectures

The course provides an introduction to the numerical simulation of laminar and turbulent incompressible flows by using a finite volume method. Each topic will be corroborated by a set of numerical examples to be performed within the open source C++ finite volume library OpenFOAM.

Module 0

• Well posedness of an abstract problem
• Numerical approximation of an abstract problem: consistency, convergence and stability
• Lax–Richtmyer theorem

Module 1

This is a 60-hours introductory course on continuum mechanics and its applications. The aim is to provide first year students with a solid understanding of the fundamental principles of the subject.