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Quantifying uncertainties in direct-numerical-simulation statistics due to wall-normal numerics and grids

Peng E. S. Chen1,2, Xiaowei Zhu3, Yipeng Shi1,2, and Xiang I. A. Yang4,*

  • 1College of Engineering, Peking University, Beijing 100871, China
  • 2State Key Laboratory of Turbulence and Complex Systems, Beijing 100871, China
  • 3Department of Mechanical and Materials Engineering, Portland State University, Oregon 97207, USA
  • 4Mechanical Engineering, Pennsylvania State University, Pennsylvania 16802, USA

  • *xzy48@psu.edu
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Phys. Rev. Fluids 8, 074602 – Published 10 July, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.074602

Abstract

This paper takes the perspective of a user of direct-numerical-simulation (DNS) data and quantifies the uncertainties in DNS statistics for plane channel flows. We focus on high-order statistics, such as skewness, kurtosis, and viscous dissipation, and quantify the uncertainties due to wall-normal numerics and grids while minimizing the sampling error and the discretization error in the wall-parallel directions. Two grid distributions and four discretization methods are considered, which are representative of the existing DNSs. Our results show that the available DNS data contain at least a 7% uncertainty in the computed mean viscous dissipation in the buffer layer. Moreover, since turbulence becomes more intermittent at higher Reynolds numbers, the flow will be less well-resolved at the higher Reynolds number if the same grid resolution in terms of the viscous units is employed. Specifically, our estimate shows that a grid that resolves 90% of the dissipation events at Reτ=544 resolves about 87% of the dissipation events at Reτ=10000.

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Phys. Rev. Fluids 8, 074602– Published 10 July, 2023
  • Received 19 January 2023
  • Accepted 12 June 2023
Article part of CHORUS
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