Instructor: Alessio Roccon

Numero ore: 8

SSD: ING-IND/06

Learning objectives:
Knowledge and understanding: During the course, the fundamental concepts required for solving the differential equations governing mass, momentum, and energy transport problems will be introduced. The aim of the course is to enable students to identify the most appropriate numerical method for solving time- and/or space-dependent transport problems and to solve them by implementing the selected method. The course is therefore intended for PhD students whose research projects require the use and numerical solution of such equations.
Applied knowledge and understanding: By the end of the course, students will be able to identify the different types of differential equations and select the most appropriate method for their numerical solution.
Autonomy of judgment: Students will develop the ability to properly interpret the differential equations of classical mechanics and to use the acquired tools in a critical manner.
Communication skills: Students will acquire the ability to communicate and discuss issues related to the subject of the course. They will be able to use appropriate technical terminology to present topics clearly and rigorously.
Learning skills: Students will have acquired the basic knowledge and tools needed to tackle the numerical solution of partial differential equations.

Course contents:
Introduction to differential problems
a. Ordinary differential equations (ODEs) and partial differential equations (PDEs)
b. Classification of PDEs
Numerical methods for ordinary differential equations
a. Finite difference methods
b. Time integration techniques
c. Solution methods for systems of equations: direct and implicit methods
d. Finite volume methods (overview)
e. Spectral methods (overview)
Application examples
a. Burgers’ equation
b. Navier–Stokes equations (seminar)

Teaching methods: lectures
Assessment methods: final written report
Additional information: the course can be delivered in English if required