Search

The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled scheme, a formal analysis is conducted on the upwind CESE discretization applied to the linear advection problem. The modified equation and the effective modified wavenumber are derived, which theoretically confirm the order of accuracy and reveal the dissipation and dispersion properties of this scheme. Several examples are considered to demonstrate the capabilities of the upwind CESE scheme for simulating compressible flows, including shock-vortex and shock-bubble interactions. The results of the present scheme agree well with exact solutions, results of other numerical methods, and experimental data. This demonstrates the high resolution of the scheme in capturing shock waves, material interfaces, and small-scale flow structures.

The rarefied flows encountered by the hypersonic vehicles in their high-altitude flights call for investigations coupling the shock-shock interaction and the rarefied-gas effect. An in-house direct simulation Monte Carlo (DSMC) solver is employed to simulate a series of hypersonic air flows over a wedge-cylinder configuration at the freestream Mach number of 10. The DSMC simulations cover 15 different Knudsen numbers, spanning from 0.006688 to 0.6688. At the lowest Knudsen number, the numerical results are validated by the corresponding wind-tunnel experiment, and demonstrate the features of an Edney type IV shock-shock interaction, including the type IV wave pattern, the supersonic jet impingement, the augmentations of surface shear stress, pressure and heat flux, as well as the shifts in the angular positions of the peak shear stress, pressure and heat flux over the cylinder surface. In ascending order of Knudsen number, the overviews and details of the flow fields with and without shock-shock interaction, as well as the distributions of the shear stress, pressure and heat flux over the cylinder surface are displayed and analyzed. The increase of flow rarefaction continuously alters the flow pattern of the shock-shock interaction, in which the wave system gradually losses the abilities to deflect the streamlines or to concentrate the energy in the flow. As the flow becomes more rarefied, the shock-shock interaction will result in smaller augmentation factors and less angular shifts of the peak aerodynamic/aerothermal loads. At the highest Knudsen number in this study, the augmentation factors for skin friction and heat flux are found to be less than unity. The existence/vanishment of the supersonic jet and its position relative to the cylinder account for the distribution characteristics of aerodynamic/aerothermal loads over the cylinder surface.