Introduction to Hyperbolic Conservation Laws

Numerical Methods for Geophysical Flows

(B.Sc. Mathematik, M.Sc. Simulation Sciences) (M.Sc. Applied Geophysics)

Prof. Dr. Sebastian Noelle ✉
Yogiraj Mantri, M.Sc. ✉


The module offers an introduction to the mathematical structure and fundamental phenomena of hyperbolic conservation laws, which are the basis of continuum mechanics. It comprises (i) linear and nonlinear transport phenomena such as the formation and propagation of shock waves; the mathematical concept of weak solutions and the Rankine-Hugoniot jump condition; the selection of a unique shock solution via an entropy condition; (ii) Godunov’s fundamental finite volume scheme; (iii) the derivation of the laws of mass and momentum from general transport theorems and Newton’s law of force and acceleration. (iv) In an accompanying lab you will expand a given matlab code and develop simulations of scalar conservation laws as well as shallow water flows such as lakes, channels and dambreaks.