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Fundamentals of Wave Simulation - Solving Hyperbolic Systems of PDEs - Winter 17

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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

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)
Bodhinanda Chandra Finite Volume: Shallow Water Equations Wetting & Drying by HLLE Solver January 18th Leonhard_Rannabauer,_M.Sc.
Ayman Noureldin Discontinuous Galerkin method January 18th Benjamin_Rüth,_M.Sc.__(hons)
Dominik Volland 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)
Ashwary Pande 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

Mpi.png

Propagation of the Tohoku 2011 tsunami using 16 MPI ranks.