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.

中文翻译：

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冲击湍流直接数值模拟的高阶一步单调性保持方案的行为

本文的目的是检查高阶 OSMP 方案的能力 [Daru, V., 和 C. Tenaud。2004. “用于非定常可压缩流动计算的高阶一步单调性保持方案。” Journal of Computational Physics 193 (2): 563–594] 准确计算湍流可压缩流，特别关注 MP 约束对壁面有界湍流冲击流解的影响。我们首先在两个典型测试案例上验证数值方法：3D Taylor-Green 涡流和稳定的 2D 冲击波层流边界层相互作用。然后模拟冲击波与湍流边界层相互作用的典型案例。