Introduction to Conservation Laws

What it is about

You learn the fundamentals and properties of hyperbolic conservation laws, in particular the occurrence and handling of discontinuities (e.g. shock waves). By the end you can solve the Riemann problems for simple systems, apply the entropy condition to select physically relevant weak solutions, and assess and develop basic finite-difference and finite-volume methods along with modern Riemann solvers for compressible flows.

What you will be able to do

• Understanding the solution theory for conservation laws, especially the compressible Euler equations
• Recognizing and analyzing discontinuous solutions (e.g. shocks, rarefactions)
• Applying the entropy condition to select unique weak solutions
• Solving the Riemann problem for selected systems
• Analyzing and developing modern numerical methods (Finite Difference/Finite Volume, Riemann solvers) for compressible flow

What the module consists of

• VorlesungIntroduction to concepts and theorems on conservation laws
• ÜbungApplication of concepts to examples and deepening understanding

Teaching method

• VorlesungIntroduction and presentation of theoretical concepts
• Übungsaufgaben/ÜbungssitzungenApplying what has been learned, solving examples; checking understanding
• optionale ProgrammieraufgabenPractical implementation and experiments with numerical methods