Models and Numerical Methods for Eulerian and Lagrangian Hyperbolic Equations

What it is about

In this module you will learn mathematical models and numerical methods for hyperbolic conservation laws in Eulerian and Lagrangian representations. You will engage with fundamentals such as Burgers’, shallow-water and gas dynamics, learn concepts such as weak solutions, shock and rarefaction structure as well as entropy conditions, and implement robust finite-volume methods, also for moving meshes.

What you will be able to do

• Understanding the mathematical structure of Lagrangian procedures for conservation laws
• Knowledge of weak and strong hyperbolicity as well as shock and rarefaction phenomena
• Umgang with entropy conditions (continuous and discrete)
• Introduction to moving grids, ALE methods and Lagrange finite-volume techniques
• Ability to implement basic robust numerical methods for simulating shocks

What the module consists of

• LecturesPresentation of concepts, examples, discussions; motivation for independent literature work and implementation
• Project (group work, optional)Offer of a project on the Lagrange finite-volume method on the sphere; for the project group the presentation serves as the examination performance

Teaching method

• Lecture on the boardConcepts are explained step by step on the board and illustrated with examples
• Discussion and questionsEncourages independent thinking, comprehension verification and deepening of the content
• Project workApplication of the learned methods in a concrete numerical project (Lagrange finite-volume on the sphere)