| The cavity flow is very complex, and there are phenomena such as shear layer motion, vortex shedding and rupture, as well as interaction between shock and shock, shock and shear layer, shock and expansion wave, shock wave, vortex and shear layer. Especially at high Mach number（M>2）, the shear layer and shock wave are stronger, and the interaction between shock waves is more serious. Therefore, high Mach number cavity simulation requires higher numerical scheme. It is necessary for the scheme to not only have low dissipation and high simulation accuracy for separated vortices, but also have large dissipation near the shock wave to better capture the shock wave and prevent the emergence of non-physical understanding. The approximate Riemann schemes such as Roe, HLLC and so on may appear ‘Ruby’ phenomenon at high Mach number strong shock wave, and the HLLE scheme greatly improves this defect. HLLE scheme avoids the occurrence of Ruby phenomenon when capturing hypersonic shock wave, and maintains the low numerical dissipation in the boundary layer. Based on the HLLE scheme on the structured grid, the HLLE method on the unstructured hybrid grid is established by improving the solving method of shock detection. The ability of the HLLE scheme to simulate high Mach number flow is verified by the inviscid slope example. The HLLE scheme is applied to the numerical simulation of high Mach number cavity flow, and the effects of grids and turbulence model are studied. At the same time, the reliability and effectiveness of the method for simulating the flow of high Mach number cavity are verified. |
