65-437 Advanced Numerical Methods for Conservation Laws

Lehrende: Dr. Claus Rüdiger Goetz

Veranstaltungsart: Vorlesung

Anzeige im Stundenplan: M-WR-V

Semesterwochenstunden: 2

Unterrichtssprache: Englisch

Min. | Max. Teilnehmerzahl: - | -

Kommentare/ Inhalte:
Hyperbolic conservation laws are first-order partial differential equations in space and time that arise in a wide range of applications, ranging from gas and fluid dynamics to the modelling of traffic flow or elasticity. From a mathematical point of view the outstanding  property of nonlinear hyperbolic conservation laws is that solutions may develop discontinuities in finite time, even for arbitrarily smooth initial data.

In this class we will discuss advanced numerical methods for the solution of hyperbolic conservation laws, in particular for nonlinear system, such as the Euler equations or shallow water equations. This will also require the study of some of their analytical properties.


Topics covered in this class will include:

• the Godunov scheme
  
• slope- and flux-limiters
  
• the Riemann problem
  
• approximate Riemann solvers
  
• high-order WENO reconstruction
  
• generalized Riemann problems
  

• partial differential equations
  
• finite volume methods
  

Lernziel:
The goal of this class is to understand the key analytical properties of hyperbolic conservation laws, how they translate to state-of-the-art numerical methods, and how to implement those methods.

Literatur:
There will be a script. Additional references and material will be provided in the lecture.

Modulkürzel:
Ma-M-WR_I, Ma-M-WR_II