This paper presents the results of a study on the effects of the numerics on the simulation of a hypersonic flow past a sharp doublecone. Previous studies have shown that the double-cone flow is challenging to compute, making it interesting for testing both numerical schemes and physical models. In the present study we focus on the numerical aspects only, and show that the results are very sensitive to the numerical flux evaluation method used. However, when the grid is fine enough, all the flux evaluation schemes give the same results, though this may require a very large number of points for the most dissipative schemes. On the other hand, the most accurate schemes have the great advantage of giving the final results on a coarser grid, and are therefore cheaper. Interestingly, this study also shows that the modified StegerWarming solver gives as accurate results as other wellknown accurate schemes, such as the Roe scheme. Finally, it is important to point out that this work could not have been done without an implicit code.