69721 - Laboratory of Numerical Geophysics

Learning outcomes

At the end of the course, students will possess basic knowledge of the main numerical techniques used for solving ordinary differential equations (ODEs) and partial differential equations (PDEs), identifying and understanding the conditions for which numerical instabilities may arise. They will be also able to implement these methods in numerical codes, personally developed in MATLAB environment.

Course contents

Module 1 – Theory (Prof. Tinti)

Discretization methods for solving ordinary differential equations (ODE) based on finite-difference schemes. Implicit and explicit multi-step methods. Runge-Kutta methods. Accuracy.

Partial differential equations (PDE). Parabolic and hyperbolic systems. Transport equation. Method of characteristics. Discrete differential operators. Stability analysis. Equation of heat transfer. Equation of waves propagation. Application to propagation of long ocean waves. Staggered grids technique.

Module 2 – Laboratory (Prof. Zaniboni)

Design and implementation of numerical algorithms for:

- Generic ODEs, using multistep methods and Runge-Kutta methods

- PDEs describing specific geophysical problems (transport equation, heat equation, wave equation)

The students will develop the numerical codes on their own PC (or on a computer provided in the lab, if available) and will verify their stability conditions and accuracy by comparing them with the corresponding analytical solutions. This activity will be carried out using MATLAB software.

Readings/Bibliography

Module 1 – Theory (Prof. Tinti)

Slides presented during the lectures.

Module 2 – Laboratory (Prof. Zaniboni)

Outlines of the exercises performed in the laboratory.

Teaching methods

Module 1 – Theory (Prof. Tinti)

Classroom lectures, projection of slides.

Module 2 – Laboratory (Prof. Zaniboni)

Laboratory exercises carried out on own computer. 

Attendance of this training activity requires the prior participation of all students to modules 1 and 2 of training on safety in the places of study, through e-learning mode (see the link https://corsi.unibo.it/magistrale/FisicaSistemaTerra/formazione-obbligatoria-su-sicurezza-e-salute).

Assessment methods

The final test is joint for the two modules, exclusively oral, with duration ranging between an hour and an hour and a half. It will concern the theory as well as the numerical tests carried out in the laboratory.

The examinee will be asked to show, discuss and run the numerical codes solving the differential equations developed in the laboratory.

Teaching tools

Projector; PC and MATLAB.

Students with Specific Learning Disabilities (SLD) or temporary or permanent disabilities are advised to contact the relative University Office (https://site.unibo.it/studenti-con-disabilita-e-dsa/en). The office will be responsible for proposing any necessary accommodations for the students concerned. These adaptations must be submitted to the teacher at least 15 days in advance for approval, who will evaluate their appropriateness, also in relation to the learning objectives of the course.

Office hours

See the website of Filippo Zaniboni

See the website of Stefano Tinti