MM527: Mathematical and Numerical Analysis of Hyperbolic Conservation Laws (5 ECTS)

STADS: 13009101

Level
Bachelor course

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

Teacher responsible
Email: achim@imada.sdu.dk

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

Comment:
Ubegrænset deltagerantal.

Prerequisites:
None

Academic preconditions:
Basic skills in programming (DM502 Programming A or equivalent), Calculus (DM502 or equivalent), or Linear Algebra (MM505 or equivalent).

Course introduction
Conservation laws are basic principles in science. For example, hyperbolic conservation laws describe wave propagation. The challenge is that waves may break and solutions become discontinous. This requires non-standard 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. The course begins with an introduction to Runge-Kutta methods for time integrator.

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.
• describe the issues that arise when computing weak solutions like contact discontinuities and shock waves.
• implement stable algorithms in one space dimension.

Subject overview

1. Ordinary differential equations and Runge-Kutta methods.
2. Conservation laws as integral and partial differential equations (PDEs).
3. Shock formation and weak solutions.
4. The Kruzkov entropy solution.
5. Finite Volume methods and the Riemann Problem.
6. Godunov-, upwind-, and Lax-Friedrichs methods.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Mandatory assignments, pass/fail, internal evaluation by the teacher. (13009102)

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: 12 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.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.