Riemann Problem in Gas Dynamics by Vincent Degrooff

The study of conservation laws leads us to work with hyperbolic PDE's. Such systems can generate discontinuous solutions in finite time from continuous data. Bernhard Riemann was one of the first to investigate these discontinuous solutions in a paper published in 1860. In it, he investigated the apparently simple problem that bears his name today: a hyperbolic PDE with initial data consisting of two constant states separated by a discontinuity. We will focus on a specific hyperbolic system, namely the Euler equations of gas dynamics, and we will see that the analytical solution is not as trivial as it might seem.