Numerical Methods for Hyperbolic Systems
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Lecturer:
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Jesper Oppelstrup
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Exercises:
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Daniel Ritter
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Extent:
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2 SWS, 2.5 ECTS
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Intended Audience:
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Primarily students of the Bavarian Graduate School in Computational Engineering
and students who apply for the double master degree with KTH Stockholm.
If space is available also other students from related fields are welcome.
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Annotation:
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The number of participants is limited.
Register now via email to
daniel.ritter@informatik.uni-erlangen.de!
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Place and time:
Room:
Lectures : 0.111, Cauerstrasse 6.
Tutorials: 0.139, Cauerstrasse 6.
Date: August 9th-13th
Time: 9 a.m.-4 p.m. (approximately)
Overview:
The development of numerical methods for simulation of non-linear conservation laws and fast methods for short-wavelength wave propagation are two relatively recent success stories in scientific computing. Technologies for supersonic aerodynamics, acoustics, tele-com and optronics have been the main driving applications. The algorithmic development has been intensive for the last forty or so years, and the course reviews a few relatively mature key subjects.
The format is a one-week intensive course with lectures in the morning and computer labs in the afternoons, with lecture notes and computer lab handouts provided as documentation.
The lectures give overview of methods for problems with discontinuous solutions, based partly on the textbook by R.Leveque. The material on short wavelength problems ranges from ray asymptotics to multi-scale methods and fast algorithms for the Eikonal equation.
The lab sessions give students hands-on experience with shock problems, high-resolution schemes, and fast methods for wave propagation. The lab projects were developed for implementation in MATLAB, and students are of course free to choose other tools.
Material
Course Overview
MATLAB Example Code High-Resolution Scheme
For the Roe Scheme roemat.m and limiter.m
The solution for the high-resolution scheme lab: roeflux.m.
Literature
R.Leveque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, edition 2003 or later.
