A hypersonic aerothermodynamic analysis method with a new HLLEM scheme is presented. Several entropy correction techniques for Roe scheme are studied and an entropy corrected HLLEM schems is proposed in order to maintain the accuracy and to enhance the robustness of HLLEM scheme.
Although the Roe scheme require the entropy correction for all characteristic fields, the HLLEM scheme need the correction for linear-degenerated field only since it is automatically satisfied with the entropy condition. The proposed HLLEM scheme with Lin-type entropy correction function is proved to be a simple, accurate and robust spatial discretization method.
The steady-state solutions are obtained using an DADI time marching method which is proposed in order to improve the convergence of FDS schemes. In addition, the mesh sequencing technique is used to stabilize initial transient modes and improve the convergence.
To demonstrate the accuracy and the robustness of present method, a shock/laminar boundary layer interaction problem is presented. Hypersonic flows past Mach 16 cylinder and Mach 20 axisymmetric cone shape vehicle are also analyzed using perfect gas and equilibrium real gas models. The results show that the proposed method not only prevents the nonphysical solutions of FDS methods, but also maintains the accuracy of FDS at hypersonic viscous boundary layer.
