The numerical computation of hypersonic flows over blunt bodies is challenging due to the difficulty in robust and accurate wall heat flux prediction and proper capturing of shock waves free from the “carbuncle” phenomenon and other shock anomalies. It is important to understand how this behavior is affected due to rarefaction, which in turn will help to improve the study of aerospace vehicles flowing in rarefied and hypersonic regime. Recently, the SLAU2 convective scheme was shown to suppress the shock anomalies found in capturing strong shocks, however, it still showed a wavy pattern of heating. We have proposed a modification to the SLAU2 convective scheme to improve the accuracy of flow predictions in the presence of strong shocks. We then perform the numerical simulation of hypersonic viscous flow over a cylinder at Mach 8 and 16.34 at different Knudsen numbers. We carry out the study using the modified SLAU2 and the classical Roe schemes. We study how the shock anomalies found in the continuum hypersonic flows behave with the degree of rarefaction. It is found that the modified SLAU2 captures the shock free from the shock anomalies at all Kn, while the Roe scheme lacks robustness for . The variation of different flow properties such as heat flux, wall shear stress, and the Mach number is investigated. The peak heating value was observed to decrease with the degree of rarefaction.