Calculation of transonic internal flows using an efficient high-resolution upwind scheme

TLDR: In this article, a new upwind scheme based on the concept of convective upwind and split pressure is developed, which has low diffusion to resolve accurately wall boundary layers and is able to capture crisp shock waves and exact contact discontinuities.

Abstract: A new efficient upwind scheme based on the concept of convective upwind and split pressure is developed. The upwinding of the convective term and the pressure split are consistent with their characteristic directions. The scheme has low diffusion to resolve accurately wall boundary layers and is able to capture crisp shock waves and exact contact discontinuities. The accuracy of the scheme is compared with other popularly used schemes including the Roe scheme, the Liou's latest advection upstream splitting method scheme (AUSM + ), the Van Leer scheme, and the Van Leer-Hanel scheme. The new scheme is tested for the one-dimensional Sod shock tube problem, one-dimensional slowly moving contact surface, supersonic flat plate laminar boundary layer, a transonic nozzle with oblique shock waves and reflections that do not align with the mesh lines, and a transonic inlet diffuser with shock wave/turbulent boundary-layer interaction