LMECA2300 - Advanced Numerical Methods

The objective of the course is to familiarize the students with innovative numerical methods. The main themes that have been covered up to now are: integral methods for solving wave-like problems, Discontinuous Galerkin methods for solving shallow water systems, adaptive grids, multigrid solvers, particle methods and granular flows.

The principal objective of the course is to write a numerical code. 

This year, the course will focus on numerical methods for granular materials. 
Granular materials are widespread in various fields and at various scales: they are implied in the mining, chemical, and pharmaceutical industries, as well in geophyiscal flows such as avalanches or volcanic eruptions, and even in astronomy with asteroid belts and the rings of Saturn. 
However, their divided nature makes them difficult to describe with classical continuum mechanics laws. 
Numerical methods thus appear as a key tool in the study of the behaviour of granular materials. 
Together, we will explore the different approaches used in the Discrete Elements Method, which is widely used in the simulation on such materials. 

This course will also give insights on state-of-the art research in the field, by presenting research results obtained with MigFlow, an open-source software developed at UCLouvain and dedicated to the study of immersed granular flows.