In this section we compare the performance of the numerical
methods described in the previous sections based on a couple of
test problems which have an analytical solution. In
6.1
we compare how the different methods handle the relativistic
shock heating of a cold gas in different geometries based on
previously published data. In Table
4
we summarize the results and give for every numerical method
both the highest Lorentz factor achieved for this problem and the
mean error in the computation of the post-shock density. The
results obtained with different numerical methods for two Riemann
problems involving shock waves and relativistic velocities appear
in Section
6.2.1
(mildly relativistic Riemann problem) and Section
6.2.2
(highly relativistic Riemann problem), respectively. The
performance of the methods is summarized in Tables
6
and
7
. Finally, a challenging test problem based on the collision of
two relativistic blast waves is discussed in Section
6.2.3
.