## Abstract

This study investigates a new algorithm for modeling viscous transonic flow at high Reynolds number cases suitable for unstructured grids. The challenge of modeling viscous transonic flow around airfoils becomes intense at high Reynolds number cases due to a variety of flow regimes encountered, such as boundary layer growth and the shockwave/turbulent boundary-layer interaction, accompanied by large separation bubble. Therefore, it is highly demanded to develop robust and efficient models that can capture the shock-induced problems of turbulent flows for aircraft design purposes. The new model is essentially a hybrid algorithm to address the conflict between turbulence modeling and shock-capturing requirements. A skew-symmetric form of a collocated finite volume scheme with minimum aliasing errors was implemented to model the turbulent region in the combination of a semidiscrete, central difference scheme to capture discontinuities with adequately low numerical dissipation for the minimal effect on turbulent flows. To evaluate the effectiveness of the model, it was tested in three conventional cases. The computational results are close to measured data for predicting the shock locations. This implies that the model is able to predict the scale of the separation bubble and the main characteristics of turbulent transonic flow adequately.

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