5 levels of grid refinement rather than the 6 levels used for the 2D runs. We have found, by doing 2D runs at 5 and 6 levels of refinement, that while there are minor differences in the density distributions, with more filamentary structure visible in the higher resolution runs, the overall evolution of the remnants are nearly identical. Thermal conduction aids in this respect since small scale details tend to be smoothed out when it is included.

The expansion law for the runs shown in Figure \[fig:rs\_evol\] is generally not far from the WL $t^{2/5}$ value, though again there are significant variations around that. One way to test that is to compute $v_s t/r_s$, which for a $t^{2/5}$ expansion law should give 2/5. Doing this involves taking numerical derivatives of the shock radius expansion curve which inevitably results in a noisy curve. In general we find that the expansion law is close to but slightly below this value on average, though with excursions above and below it.

In Figure \[fig:rs\_C\] we show the shock radius evolution for runs with different $C$ values. Since the mean density in the medium increases with $C$ it is expected that the shock expansion rate 