Numerical Methods for Hyperbolic PDEs - Summer 13

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Term
Summer 13
Lecturer
Prof. Dr. Michael Bader, Alexander Breuer, Oliver Meister
Time and Place
see below
Audience
Computational Science and Engineering (IN2183, 2nd and 4th semester), Informatics (Master), Mathematics (Master)
Tutorials
-
Exam
-
Semesterwochenstunden / ECTS Credits
2 SWS (2S) / 4 Credits
TUMonline
https://campus.tum.de/tumonline/lv.detail?clvnr=950093910&cperson_nr=&sprache=2



Description

In this seminar we address numerical methods for hyperbolic partial differential equations. We discuss important examples of governing equations, namely the elastic wave equations (earthquakes) and shallow water equations (tsunamis). In this context challenges typical for hyperbolic PDEs are tackled: Non-linearities, Riemann solvers, dimensional splitting, high-order discretization.. Besides numerical theory a strong focus of the seminar is given by application and implementation of the learned concepts: Each participant works during the seminar on a small project, which requires extensive use of the learned theory.

Organization

General remarks about schedule and organization: Remarks

Slides:

Preliminary schedule:

  • Jan 25, 2013, 13pm (MI 02.09.23, preliminary session)
  • April 17, 2013 (MI 01.06.011, Kickoff)
  • May 29, 2013
  • June 05, 2013
  • June 12, 2013

Topics

Topic Student Presentation date (preliminary) Advisor
1D traffic flow: exact solution Z. Shan May 29 Oliver Meister
1D traffic flow: numerics M. Homolya May 29 Oliver Meister
Euler equations V. Mikerov June 05 Oliver Meister
Roe solver H. Stotz June 05 Alexander Breuer
f-wave solver A. Shukaev June 05 Alexander Breuer
Tsunami simulation O. Annamanthadoo June 12 Alexander Breuer
Earthquake simulation (& Elastics) R. Kommajosyula June 12 Alexander Breuer

Examples

Mpi.png

Propagation of the Tohoku 2011 tsunami using 16 MPI ranks.


Dynrup.png

Dynamic Rupture propagation (source: De la Puente, Josep, Jean-Paul Ampuero, and Martin Käser (2009), Dynamic Rupture Modeling on Unstructured Meshes Using a Discontinuous Galerkin Method, J. Geophys. Res., 114, B10302, doi:10.1029/2008JB006271).