Calculation of Reynolds stresses in turbulent supersonic flows

The baseline numerical procedure of interest in this study combines flux vector splitting, flux difference splitting and an explicit treatment of the diffusion terms of the flow equations. The viscous terms are treated explicitly to preserve the wave propagation properties of the Euler fluxes and permit splitting. The experience with this scheme has been limited to laminar or, at best, ‘eddy viscosity’ flows. In this paper the applicability of the scheme is extended to include the calculation of turbulent Reynolds stresses in supersonic flows. The schemes and our implementation are discussed. Both laminar and turbulence subsets of the Reynolds/Favre‐averaged equations are tested, with a discussion of relative performance. The test problem for turbulence consists of a zero‐pressure‐gradient supersonic boundary layer as well as a supersonic boundary layer experiencing the combined effects of adverse pressure gradient, bulk compression and a concave streamline curvature. Excellent agreement with experimental measurements is observed for most of the quantities compared, which suggests that the numerical procedures presented in this paper are potentially very useful.