Fundamentals of Wave Simulation - Solving Hyperbolic Systems of PDEs - Winter 17
- Term
- Winter 17
- Lecturer
- Univ.-Prof._Dr._Michael_Bader, Leonhard Rannabauer
- Time and Place
- Th. 8:00 - 10:00 in 02.07.23 (only on selected dates)
- Audience
- Computational Science and Engineering (Seminar, module IN2183),
Informatics (Master-Seminar, module IN2107) - Tutorials
- -
- Exam
- -
- Semesterwochenstunden / ECTS Credits
- 2 SWS (2S) / 5 Credits
- TUMonline
- tumonline
Contents
Organization
- preliminary session: Friday, July 14, 12:00pm. Room: 02.07.023 (attend for guaranteed registration) (Slides)
- Kick-off session: Thursday, October 19, 08:00 am (Slides)(Paper Template)
Topics
| Name | Topic | Presentation | Supervisor | Slides |
| Ioannis Kouroudis | Introduction to hyperbolic PDEs and Shallow Water Equations | December 8th | Leonhard_Rannabauer,_M.Sc. | link |
| David Frank | Finite Volume Method: Acoustic Wave Equation | December 8th | Severin_Reiz,_M.Sc.__(hons) | |
| Subhan-Jamal Sohail | Finite Volume Method: Elastic Wave Equation | December 14th | Carsten_Uphoff,_M.Sc. | |
| Fukushi Sato | Finite Volume Method: Shallow Water Equations | December 14th | Roland_Wittmann,_M.Sc. | |
| Nathan Brei | Riemann Solvers: Lax Friedrichs and Rusanov Flux | December 14th | Roland_Wittmann,_M.Sc. | |
| Dewitte Thiebout | Riemann Solvers: Roe Flux | January 11th | Leonhard_Rannabauer,_M.Sc. | |
| Kislaya | Finite Volume: Multiple Dimensions | January 11th | Severin_Reiz,_M.Sc.__(hons) | |
| Finite Volume: Shallow Water Equations Wetting & Drying by HLLE Solver | January 18th | Leonhard_Rannabauer,_M.Sc. | ||
| Discontinuous Galerkin method | January 18th | Benjamin_Rüth,_M.Sc.__(hons) | ||
| Discontinuous Galerkin: Nodal representation | January 18th | Carsten_Uphoff,_M.Sc. | ||
| Emily Bourne | Discontinuous Galerkin & Shallow Water Equations: Well balanced scheme | January 25th | Benjamin_Rüth,_M.Sc.__(hons) | |
| Discontinuous Galerkin: Limiting | January 25th | Leonhard_Rannabauer,_M.Sc. |
Registration
- Register via the matching system (only if you are sure you want to join !)
- After Registration: Send me an E-Mail with you prior knowledge + points of interest or a topic you have in mind (-> Leonhard Rannabauer).
Description
In this seminar we address numerical methods for the simulation of hyperbolic partial differential equations. We discuss important examples of governing equations. In this context challenges typical for hyperbolic PDEs are tackled: Non-linearities with analytical solution approaches, Riemann solvers, domain decomposition, finite volume methods, high-order discretization, time stepping schemes, adaptivity, parallelization etc. Besides numerical theory we expect the students to apply and implement the learned concepts in the form of a small project, which requires extensive use of the learned theory.
Literature
Finite Volume Methods for Hyperbolic Problems, Randall J. LeVeque (ub.tum):
- Standard work, with insights on hyperbolic PDEs, FV Methods and several Applications on PDEs (traffic, tsunamis ...)
Nodal Discontinuous Galerkin Methods, Jan S. Hestaven et al (springer):
- Introductory guide on discontinuous Galerkin methods.
An Introduction to Seismology, Earthquakes, and Earth Structure, Seth Stein (google)
Riemann Solvers and Numerical Methods for Fluid Dynamics, Eleuterio F. Toro (ub.tum):
- Advanced work on Riemann Solvers with insights into Euler equations, viscous stresses ..
Example Topics
- 1D traffic flow analytical and numerical
- Linear Systems and elastic waves
- Tsunami simulation with finite volume methods
- F-Wave Solver for Riemann problems
Examples
Propagation of the Tohoku 2011 tsunami using 16 MPI ranks.
