In this special topic course, I will focus on the numerical solution of hyperbolic conservation laws using finite volume methods.
Conservation laws are used for modeling various physical phenomena: the flow around an airplane at high speed, combustion processes, explosions of supernovae in astrophysis, traffic flow, and many more.
The goal of this course is to develop a two-dimensional solver for the compressible Euler equations. All necessary ingredients will be discussed in class. This includes Riemann solvers for the Euler equations in one dimension, limiter techniques, and the extension from one to two dimensions using split and unsplit approaches. I will start the course with a short review so that everybody is on the same page.
Although the focus of the course is on numerical methods, I will discuss theoretical aspects of conservation laws whenever they are necessary for a better understanding of the methods used.
* The course will be taught in English.
* The course builds upon the course 'Numerik hyperbolischer Erhaltungsgleichungen' taught by Prof. Dmitri Kuzmin in SS 2016. This roughly corresponds to the content of the book 'Numerical methods for conservation laws' by Randy LeVeque. If you are in doubt whether you have the appropriate prerequisites, please contact me.