A systematic study of the effects of the numerics on the simulation of a steady hypersonic flow past a sharp double cone is presented. Previous studies have shown that the double-cone flow is challenging to compute, making it useful for testing both numerical schemes and physical models. We focus on the numerical aspects only and show that the results are very sensitive to the numerical flux evaluation method and slope limiter used. We find that, when the grid is fine enough, all of the flux evaluation schemes give the same results, though this may require a very large number of points for the most dissipative schemes. The least dissipative schemes have the great advantage of giving accurate results on a coarser grid and are, therefore, less costly. Interestingly, it is also shown that the modified Steger-Warming solver gives as accurate results as other well-known high-quality schemes, such as the Roe scheme with the van Leer slope limiter. Finally, note that an efficient approach such as a parallel implicit method was required.