The applications of pressure work, pressure-dilatation, and dilatation-dissipation (Sarkar, Zeman, and Wilcox) models to hypersonic boundary flows are investigated. The flat plate boundary layer flows of Mach number 5-11 and shock wave/ boundary layer interactions of compression corners are simulated numerically. For the flat plate boundary layer flows, original turbulence models overestimate the heat flux with Mach number high up to 10, and compressibility corrections applied to turbulence models lead to a decrease in friction coefficients and heating rates. The pressure work and pressure-dilatation models yield the better results. Among the three dilatation-dissipation models, Sarkar and Wilcox corrections present larger deviations from the experiment measurement, while Zeman correction can achieve acceptable results. For hypersonic compression corner flows, due to the evident increase of turbulence Mach number in separation zone, compressibility corrections make the separation areas larger, thus cannot improve the accuracy of calculated results. It is unreasonable that compressibility corrections take effect in separation zone. Density-corrected model by Catris and Aupoix is suitable for shock wave/boundary layer interaction flows which can improve the simulation accuracy of the peak heating and have a little influence on separation zone.

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The hybrid dynamic mesh method combining finite macro-element with transfinite interpolation (TFI) is adopted in this paper which ensures mesh quality for large deformations and high efficiency. Besides, TFI is modified to preserve the grid orthogonality near the boundary using rotation correction and weighted approach in order to solve its orthogonal problem. The numerical simulation of oscillating airfoil is performed by solving Reynolds Averaged Navier-Stokes (RANS) equations with hybrid dynamic mesh method. The influences of oscillation parameters and Mach number on the hysteresis effect are investigated and the separation vortex pattern and evolution procedure are presented. Moreover, numerical results show the occurrence of lock-in zone. The effect of oscillation amplitude and frequency on it and the characteristics of vortex shedding are discussed.

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