Mathematical and Numerical Modelling of Conservation Laws (MOD600)
The course gives an introduction to the theory and applications of partial differential equations for modelling transport processes, with a particular focus on hyperbolic conservation laws. The structure of wave phenomena inherent in such models will be discussed, both for a scalar conservation law as well as systems. Furthermore, principles for the design and use of numerical methods to solve such models are presented. Examples of such models for different applications are also discussed.
Course description for study year 2023-2024
Course code
MOD600
Version
1
Credits (ECTS)
10
Semester tution start
Spring
Number of semesters
1
Exam semester
Spring
Language of instruction
English
Content
Learning outcome
Knowledge:
The student will have an extended understanding of the following concepts in the context of an important class of partial differential equations:
1) Nonlinear and linear conservation laws;
2) Eigenvalue analysis and characteristics;
3) Analytical solutions and weak solutions;
4) Numerical discretization techniques;
5) Stability and accuracy of numerical approximations of the continuous model;
6) Insight into the connection between mathematical models for transport processes and
physical wave phenomena;
7) Practical coding experience through project work.
Skills:
The student will be able to
- understand how nonlinear and linear conservation laws naturally occur in the modeling of different dynamic processes that vary in space and time, man-made as well as phenomenon found in nature;
- be able to construct analytical solutions of certain classes of problems;
- formulate discrete schemes that can be used to compute numerical solutions of general conservation laws, both in the case of a single conservation law and a system of conservation laws;
- have an understanding of the challenges with finding solutions of nonlinear conservation laws and the need of concepts like shock wave and rarefaction wave, crossing characteristics, Rankine-Hugoniot jump condition, Riemann problem, entropy solution, and weak solutions;
- be able to implement in matlab/python a numerical scheme, compute and visualize approximate solutions.
Required prerequisite knowledge
Recommended prerequisites
Exam
Form of assessment | Weight | Duration | Marks | Aid |
---|---|---|---|---|
Oral exam | 1/1 | Letter grades |
Coursework requirements
Course teacher(s)
Course coordinator:
Steinar EvjeCourse teacher:
Tore Halsne FlåttenHead of Department:
Øystein ArildMethod of work
Overlapping courses
Course | Reduction (SP) |
---|---|
Mathematical and Numerical Modelling of Transport Processes (PET565_1) | 10 |