Abstract: In the RANS-LES hybrid simulation of turbulent boundary layers, adding reasonable turbulent fluctuations at the inlet can shorten the recovery distance of the flow field to fully developed turbulent flow, improve the simulation accuracy and efficiency. In this paper, the SA-IDDES method is used to the research on numerical simulation study of channel turbulence and compressible turbulent boundary layer. And three commonly turbulence synthetic methods are compared , including synthetic turbulence generator (STG), digital filter method (DFM) and synthetic eddy method (SEM). The development of wall friction, flow structure and Reynolds stress under different synthetic turbulence inflow conditions is studied, and the performance of each method is evaluated in wall turbulence. In the simulation of incompressible and compressible turbulent boundary layers, STG method shows the shorter recovery distance. The flow field structure and Reynolds stress development of STG also have advantages over DFM. In addition to velocity fluctuations, compressible turbulent boundary layer also includes fluctuations of thermodynamic variables such as temperature, density and pressure. Furthermore, in the numerical simulation of turbulent boundary layer in high Mach number, ignoring the thermodynamic fluctuations may reduce the speed at which the boundary layer return to fully-developed turbulence flow. The ST method can only provide velocity fluctuations, while the strong Reynolds analogy methods can obtain thermodynamic fluctuations based on velocity fluctuations. Therefore, based on the velocity fluctuations given by STG, thermodynamic fluctuation is added at the inlet by several strong Reynolds analogy methods (SRA, GSRA, HSRA), and the effects on the development of compressible turbulent boundary layer are evaluated. The results show that the addition of thermodynamic fluctuation has little effect on the development of friction and Reynolds stress, but has a significant effect on the development of thermodynamic quantities in the flow field. Among them, using GSRA generating thermodynamic fluctuation as inlet boundary condition has the fastest thermodynamic recovery.