# Simulation of Geophysical Systems

10 credits

Syllabus, Master's level, 1GE015

A revised version of the syllabus is available.
Code
1GE015
Education cycle
Second cycle
Main field(s) of study and in-depth level
Earth Science A1N, Physics A1N
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 15 March 2007
Responsible department
Department of Earth Sciences

## Entry requirements

Bachelor's degree in physics

## Learning outcomes

The general topic of the course is the theory and the solution of dynamical, geophysical systems. The aim is for the student to be able to qualitatively analyse a geophysical setting, identify the dominant physical processes, derive an appropriate set of equations that describe the situation, and finally solve these equations. The emphasis in this course is placed on developing the necessary tools, i.e., the geophysical theory and the solution, which in most cases will be numerical rather than analytical. Dynamical theory will be interspersed with numerical applications. Relatively simple numerical techniques (finite differences; spectral methods) will be derived from basics and the students will write their own, short codes. Once the students have gained an elementary understanding of numerical modelling, they will use a powerful commercial code which removes much of the programming work and allows more complex and more realistic models.

After successful completion of the course, the student is expected to:

- understand and be able to write down the conservation equations of momentum, energy, and mass.

- be able to describe conceptually and in equations the fundamentally different types of material behaviours (rheologies).

- be able to form a complete set of dynamical equations.

- be able to find the principal orientations of the tensor fields of stress and strain.

- be able to derive the Navier-Stokes equation from the conservation equations and a viscous rheology.

- understand and be able to write down the flexure equation for an elastic plate.

- be able to analytically solve the flexure equation in one dimension.

- understand and be able to write down the equations for heat flux and heat diffusion.

- understand and be able to write down Darcy's Law and derive the resulting equation for the pressure as a potential.

- be able to code one- and two-dimensional finite difference models of linear dynamical systems using MATLAB.

- be able to code spectral models of linear systems with constant coefficients using MATLAB.

- understand the differences and limitations of the different numerical techniques and be able to choose the appropriate method accordingly.

- know the difference between Dirichlet and Neumann boundary conditions.

- be able to use the commercial code FEMLAB to solve (almost all?) dynamical problems.

- be able to produce visualisation of the output (graphs, contour plots, movies, etc.)

## Content

Geodynamics:

Stress and strain in solids.

Elasticity and flexure.

Heat transfer.

Fluid mechanics.

Rock rheology.

Fluid flow through porous media.

Numerical Methods:

Theory of finite differences with simple applications.

Basic techniques of forward timestepping.

Fast Fourier Transform and spectral methods with simple applications.

Basics of the finite element method.

Applications using the commercial finite element package FEMLAB (a.k.a. Comsol Multiphysics)

## Instruction

Lectures, homework, problem solving and computer exercises.

## Assessment

Written examination. The written examination corresponds to 8 ECTS and the compulsory part 2 ECTS.