Diskontinuierliche Galerkin-Verfahren in der Numerischen Simulation

What it is about

In this module you will learn about and apply discontinuous (Discontinuous) Galerkin methods for the numerical solution of partial differential equations. You can explain various variants (including higher order), their properties compared to finite differences, finite volumes and continuous finite elements, and implement and evaluate simple simulations in fluid dynamics and acoustics.

What you will be able to do

• Derivation of discontinuous Galerkin methods for relevant PDEs
• Distinction from finite differences, finite volumes and continuous finite elements
• Knowledge and assessment of numerical flux functions for conservation laws
• Handling of higher-order basis functions (nodal and modal)
• Extension and efficient implementation in higher dimensions
• Treatment of diffusion / second derivatives in DG methods
• Use of explicit and implicit time integration
• Development of simple simulation programs in MATLAB or C++ for Euler, acoustic and Navier–Stokes equations

What the module consists of

• LectureConveying theoretical foundations, derivation and distinction from other methods (approx. half of the lecture time)
• TutorialJoint deepening of algorithms and implementations as well as practical programming tasks (approx. the other half of the lecture time)

Teaching method

• Lecture (with script and tablet PC notes)Establishment of theoretical foundations and active supplementation by students
• Exercise and programming partsPractical implementation of algorithms and development of own programming solutions in MATLAB or C++
• Computer exercisesEnable implementation and evaluation of stability and approximation quality
• Learning platformProvision of materials and tasks for independent work