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Technical University of Munich

Discontinuous Galerkin Methods for Numerical Simulation

5 ECTS (3 SWS), Summer term

Overview

This course introduces discontinuous Galerkin methods for approximately solving partial differential equations and their efficient realization for large-scale problems in fluid dynamics and acoustics. The following topics will be covered:

  • Derivation of discontinuous Galerkin methods and comparison against finite difference, finite volume, and continuous finite element methods.
  • Numerical flux functions for scalar conservation laws.
  • Higher order basis functions: nodal and modal representations.
  • Extension to higher dimensions, efficient evaluation of weak forms.
  • Discontinuous Galerkin schemes for second spatial derivatives.
  • Explicit versus implicit time integration.
  • Discontinuous Galerkin schemes for nonlinear equations.
  • Applications: Euler equations, acoustic wave equation, compressible and incompressible Navier-Stokes equations.

The theoretical content is accompanied by exercise and programming sessions in MATLAB and C++. The C++ part includes programming in the deal.II finite element library, in particular the step-67 tutorial program for a parallel implementation of an Euler solver suitable for large-scale computations.

Teacher

Maximilian Bergbauer, Prof. Dr.-Ing. Wolfgang A. Wall.

Teaching outline

The course is accompanied by lecture notes (available through the Moodle portal). The content is discussed by lectures and exercise sessions as well as autonomously by the student from the given material.

Language

English.

Dates and places summer term 2024

Introduction lecture: Friday, April 19 from 11:00 to 11:30, MW1237 and Zoom

Office hours

Friday, 14:30-15:00, MW1230/MW1237 (Maximilian Bergbauer)

Literature

Jan S. Hesthaven, Tim Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, Springer, 2008. Fulltext @ UB-TUM.

Martin Kronbichler, Per-Olof Persson, Efficient High-Order Discretizations for Computational Fluid Dynamics, Springer, 2021. Fulltext @ UB-TUM

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