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In this study a retarded pressure and a retarded density approach, controlled by a Mach-unmber-dependent monitor function, was incorporated within the pressure correction framework to ensure the hyperbolic nature in supersonic zone. The governing equations are constructed on curvilinear coordinates and the grids are arranged in a non-staggered manner. Differential equations are discretized by finite-volume method. The system of discretized equations is solved by the SIMPLE-type algorithm.
Capabilities of the numerical method were examined by applying to several inviscid and turbulent transonic flows, including a quasi-one-dimensional nozzle flow with different back pressures,flows over a bump in an inviscid channel, flow over an airfoil, and a turbulent flow with shick-boundary layer interaction. In the inviscid flow calculations, is was found that the present schemes give predictions of the shock except that a slightly smearing occurs due to introduction of the excessive artificial dissipation. As regards turbulent flow computations, the k-E model and wall-function were incorporated to exam the shock wave /boundary lager interaction . It was in poor agreement with the experimental data especially in recirculating region.
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