# 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 2021-2022. Please note that changes may occur.*

**Emnekode**

MOD600

**Vekting (SP)**

10

**Semester undervisningsstart**

Spring

**Antall semestre**

1

**Vurderingsemester**

Spring

**Undervisningsspråk**

English

**Tilbys av**

Faculty of Science and Technology, Department of Energy and Petroleum Engineering

**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.

**Content**

**Required prerequisite knowledge**

**Recommended prerequisites**

**Eksamen / vurdering**

Vurderingsform | Vekting | Varighet | Karakter | Hjelpemiddel |
---|---|---|---|---|

Written exam | 1/1 | 4 Hours | A - F |

Written exam (4 hours).

**Coursework requirements**

**Course teacher(s)**

**Course coordinator:**Steinar Evje

**Course teacher:**Tore Halsne Flåtten

**Head of Department:**Øystein Arild

**Method of work**

**Open for**

**Course assessment**

**Overlapping courses**

Course | Reduction (SP) |
---|---|

Mathematical and Numerical Modelling of Transport Processes (PET565) | 10 |

**Literature**