To verify our results, we ran a simulation in the RICH code\cite{Yalinewich_2015} (version 2 branch). We have also released a complete listing of the source code for the simulation. We were working in 2D cylindrical coordinates, assuming azimuthal symmetry. The boundaries of the computational domain were: \(1.8>z>-0.2\) and \(0.5>r>0\). The wind velocity was 1, and it was directed in the positive \(z\) direction. The obstacle was a circle of radius 0.01, located at the origin \(\left(0,0\right)\). We ran the simulation to time \(t=10\), and compared the numerical results to our analytic predictions. First, we fit the shock front to a parabola (figure \ref{parabolic_shock_front}). As can be seen from the figure, the deviation from a parabolic is minuscule. Next, we compared the numerical profiles inside the bow shock to the analytical prediction (figure \ref{profiles}). In order to do that, we interpolated the variables on the curve \(\tau=1.5\). The agreement between the two is reasonable. The deviations are due to two main reasons. The first is that since we are working in cylindrical coordinates, the relative error at each radius is equal to the ratio between the cell’s width and the radius. The second is that the slope of the density is very steep next to the shock front, so a very fine resolution is required to resolve it.