MM827: Mathematical and Numerical Analysis of Hyperbolic Conservation Laws (5 ECTS)

STADS: 13008001

Level
Master's level course

Teaching period
The course is offered in the autumn semester.
The course is offered when needed.

Teacher responsible
Email: achim@imada.sdu.dk

Additional teachers
debrabant@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. 4. kvartal. Fælles undervisning med MM527 Matematisk og numerisk analyse af hyperbolske bevarelseslove

Prerequisites:
None

Academic preconditions:
Basic skills in programming (DM502 Programming A or equivalent), Introduction to Numerical Analysis (MM518 or equivalent).
Students who have passed MM527 Mathematical and Numerical Analysis of Hyperbolic Conservation Laws cannot sign up for this course.

Course introduction
Conservation laws are basic principles in science. For example, hyperbolic conservation laws describe wave propagation; all kinds of waves. The callenge is that waves may break and solutions become discontinous. That requires non standart techniques for both the mathematical and numerical analysis. Students that follow the course will aquire a basic understanding of entropy solutions to hyperbolic conservation laws and their numerical approximation.

Expected learning outcome
At the end of the course the student is expected to be able to:

• formulate conservation laws in integral and differential form.
• explain the Kruzkov entropy solution.
• describe with the issues that arise when computing weak solutions like contact discontinuities and shock waves.
• construct exact and approximate solutions to Riemann problems.
• implement modern high resolution algorithms in one space dimension.
• apply the CLAWPACK package to simulate multidimensional flows.

Subject overview

1. Conservation laws as integral and partial differential equations (PDEs).
2. Shock formation, weak solutions and entropy conditions.
3. The Kruzkov entropy solution.
4. Finite Volume methods and the Riemann Problem.
5. Godunov-, upwind-, and Lax-Friedrichs methods.
6. High resolution methods: ENO, WENO, and TeCNO schemes.
7. Simulate multidimensional flows in CLAWPACK.

Literature
There isn't any litterature for the course at the moment.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a) Mandatory assignments, pass/fail, internal evaluation by the teacher. To pass the mandatory assignements is a precondition to take the oral exam.
b) Oral exam, grades according to the 7-point grading scale, internal examiner.

Re-examination according to the rules approved by the Study Board.
The re-exam may differ from the ordinary exam.

 

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 24 timer
Eksaminatorietimer/opgaveregning: 7 timer
Laboratorieøvelser: 7 timer
Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Remarks
The course is taught together with the bachelor's course MM527 Mathematical and Numerical Analysis of Hypberbolic Conservation Laws.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.