Numerical methods applied to standard telluric hazard problems (METH901_ALEA)

This course aims at providing a wide introduction to numerical methods applied to standard telluric hazard problems, including both fluid and solid materials.
Referring to concrete examples, both fundamental input and hands-on exercises (TD/TP) with Matlab programming language will enable the students to understand, implement and use the most popular, widely used, numerical tools.

1) Fundamentals on partial derivative equations
   - Introduction : from a physical problem to a numerical scheme (example)
   - Elliptic systems - Examples
   - Hyperbolic systems - Examples
   - TP : Numerical methods for solving linear scalar advection equation

2) Finite Difference Method
   - Fundamentals
   - Notion of stability and convergence
   - TP : Numerical modeling of mudflows  

3) Discrete Element Methods
   - Fundamental aspects of particle methods
   - Smooth Particle Hydrodynamics Method
   - TP : DEM applied to rockfall modeling

4) Finite Element Method:
   - Boundary value problems in one space dimension
   - From a continuous to a discretized formulation
   - TP : Developing a finite element method engine for modeling landslide triggering

At the end of the course, the students will be able to:  

• understand basic numerical schemes for classical governing equations
• carry out a numerical analysis of the schemes in terms of stability and convergence
• design, develop and use discrete element methods and finite element methods
• implement the schemes in Matlab programming language