With the rapid development of new algorithms and computational techniques, today's main trend of spatial discretization is either flux vector splitting (FVS) or flux difference splitting (FDS). FVS (Van Leer 1971) methods are very robust and can be used for complex flows, like reacting flows but they have accuracy problems in resolving shear layer regions due to the excessive numerical dissipation error associated with them.
In contrast, FDS such as Roe's (1981) scheme that utilizes the solution of the local Riemann problem usually provides accurate solutions. with they have the disadvantage of lacking in robustness.
Hence, the necessity of a hybrid scheme is raised, which is as robust as FVS, simultaneously keeping the accuracy of FDS.Liou and Steffen (1993)suggested a method known as the advection upstream splitting method (AUSM).