On the Behaviour of High-Order One-Step Monotonicity-Preserving Scheme for Direct Numerical Simulation of Shocked Turbulent Flows

Abstract

The objective of this paper is to check the ability of the high-order OSMP scheme [Daru, V., and C. Tenaud. 2004. “HighOrder One-Step Monotonicity-Preserving Schemes for Unsteady Compressible Flow Calculations.” Journal of Computational Physics 193 (2): 563–594] to accurately compute turbulent compressible flows with a special focus on the effect of the MP constraints on solutions of wall bounded turbulent shocked flows. We first validate numerical approaches on two canonical test cases: the 3D Taylor-Green vortex and the steady 2D shock-wave laminar boundary layer interaction. The emblematic case where a shock wave interacts with a turbulent boundary layer is then simulated. We conclude that the OSMP scheme coupled with a centred 2nd-order approximation for the diffusive fluxes constitutes a reliable numerical tool for the DNS of compressible turbulent shocked flows, that is completely competitive compared to other approaches since the overall errors are lowered of about one order of magnitude for the same grid resolution.