Construction of shock stable scheme based on RoeM scheme

Roe's flux difference splitting (FDS), a widely used scheme today, encounters shock inability that needs to be avoided in hypersonic flows. Moreover, it can't preserve the total enthalpy while in steady inviscid flows' simulations. To get over the defects above, schemes called RoeMW1, RoeMW2 that are based on the construction of RoeM scheme were proposed to cure the shock inability and preserve the total enthalpy while in steady inviscid flows' simulations. The results tell that in most simulations the RoeMW1 and RoeMW2 schemes can achieve the goal of curing the shock inability and keeping the conservation of total enthalpy. In addition, both RoeMW1 and RoeMW2 are better than RoeM. However, in some complex situation the RoeMW2 scheme constructed by some improvement of the RoeMW1 is more robust than RoeMW1.