Course Coordinator: 
Marco Edoardo Rosti
Computational Mechanics

Students who complete this course will be able to:

  • understand the most common techniques for the numerical solution of partial differential problems (such as finite differences and finite volumes),
  • evaluate and comment on the stability and convergence of the numerical methods,
  • and solve numerically diffusion, convection and transport problems in multiple dimensions.

Target Students: Students interested in solving partial differential equations numerically and in understating possibilities and limitations of numerical techniques. Students should have a general knowledge of partial differential equations.

This course aims to provide the mathematical and numerical tools to solve problems governed by partial differential equations. These techniques have wide application in many areas of physics, engineering, mechanics, and applied mathematics.
Course Content: 

Revision of numerical differentiation and integration.
Classification of PDE - elliptic, parabolic and hyperbolic equations.
Introduction to Python/MATLAB.
Elliptic equations.
Finite difference method, convergence and stability.
Parabolic equations.
Iterative methods.
Finite volume method.
Analogy with finite differences.
Hyperbolic equations.
Method of characteristics.
System of partial differential equations.
Navier-Stokes equations
Note on multiphase flows.
Final overview and questions

Course Type: 
Weekly exercise solutions (60%), Final exam (40%)
Reference Book: 
Smith, Numerical solution of partial differential equations: Finite Difference methods
Ferziger and Peric, Computational Methods for Fluid Dynamics
Quarteroni, Numerical Models for Differential Problems
Prior Knowledge: 

Students should have a general knowledge of partial differential equations. such as from the course B28.
A basic knowledge of Python, MATLAB or any other programming language is preferred but not essential.