Numerical Methods for Geosciences

Period: Second semester

Course unit contents: 

1. Mathematical basis for partial differential equations (derivatives, gradient, divergency, laplacian operator)
2. Rock physical properties (viscosity, elastic moduli, cohesion and friction coefficient, density, thermal conductivity and diffusivity, heat capacity)
3. Thermal, chemical, hillslope and fluid overpressure diffusion equations
4. Stress, strain and strain rate tensors and constitutive relationships.
5. Visco-elasto-plastic deformation
6. Conservation of mass
7. Conservation of momentum
8. Conservation of energy
9. Numerical method: finite difference with particle-in-cell (mixed Eulerian-Lagrangian scheme)
10. Solution of systems of equation with iterative (Gauss-Siedel) ir direct (Gauss elimination) methods.

Planned learning activities and teaching methods: There are two types of learning activities and teaching methodologies:
1) Lecture about numerical and associated mathematical methods, and physical laws describing the behavior of geological systems
2) Computer laboratory where the student practices to program numerical codes and visualize results with MatLab