{#sec:matcons}
===========================

a shows a sketch of a 1D shock tube filled with an inviscid, compressible isothermal fluid. We split the spatial domain into three distinct regions, an upstream region $\left( \mathrm{u}\right)$, a downstream region $\left( \mathrm{d}\right)$ and an infinitesimally thin region around the shock at $r=r_{\mathrm s}$. The sketch further shows a rigid wall on the left hand side where the inflowing gas with velocity $u\left(r, t\right)<0$ gets reflected. Hence, a shock wave arises propagating to the right with shock speed $v_{\mathrm s}$. Now, the velocity in the downstream region becomes $u\left(r, t\right)\geq0$, but always equals zero at the origin where the fluid necessarily stagnates. The shock itself becomes apparent through a discontinuity or jump.

To draw a more general picture we can easily enlarge the above scenario by introducing 1D polar coordinates or even 1D spherical coordinates instead of 1D cartesian coordinates [@Gehmeyr1997] with respect to the corresponding symmetries (see \[fig:Figtube\]b). The basic equations are very similar and can be distinguished by the exponent $\alpha\in\left\{0,1,2\right\}$ of the radius (see ). The rigid wall changes to the center of the disk or sphere and the fluid flows radially.

In the case of the EP, the only difference lies in 