Numerical methods applied to standard telluric hazard problems (METH901_ALEA)
Présentation
Objectifs
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.
Heures d'enseignement
| Cours Magistral | 15h | |
| Travaux Dirigés | 15h |
Plan du cours
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
Compétences visées
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