Leiden University Student Repository

Post, Jonah (2020)

Lax Entropy Conditions for the One-Dimensional Riemann Problem

Bachelor thesis | Natuurkunde (BSc)

To find solutions to systems of conservation laws with discontinuities, weak solutions will be studied. To pick a unique weak solution one requires some additional conditions. In this thesis we will see that for the Riemann problem in one spatial dimension, the Lax entropy conditions are a way to do this. By considering the Euler equations we will see that these conditions are equivalent to the second law of thermodynamics and therefore pick the physically relevant solution. Furthermore, we construct numerical solutions to a specific Riemann problem using a standard discretization method and a method based on nonlinear shocks, followed by a on discussion their strengths and weaknesses.

Entropy Conditions

Riemann Problem

Weak Solutions

Shock Waves

Author

Post, Jonah

Faculty

Faculty of Science

Specialisation

Physics and Astronomy

Supervisors

Schalm, Koenraad
Ecker, Christian
Icke, Vincent

ECTS Credits

3

Language

en