Grid-point and time-step requirements for large-eddy simulation and Reynolds-averaged Navier-Stokes of stratified wakes

Estimates of grid-point and time-step requirements exist for many canonical flows but not for stratified wakes. The purpose of this work is to fill in this gap. We apply the basic meshing principles and estimate the grid-point and time-step requirements for Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulation (LES) of stratified wake flows at high Reynolds numbers, as arise in many geophysical, aircraft, and undersea vehicle systems. Scales representative of a submarine operating in a stably stratified ocean environment are considered, and the quantitative conclusions reached here can be adapted accordingly for particular applications. For a submarine, typical wake conditions are Re0 = 10^8 and Fr0 = 10^2, and wakes extend to Nt = 1000, where Re0 and Fr0 are the initial Reynolds number and the internal Froude number of the wake, respectively, and N is the buoyancy frequency. We consider both spatially developing and temporally evolving wakes. We show that the grid points required for LES and RANS do not depend on the Reynolds number. The ratio of the grid points needed for LES and RANS is proportional to (Nt2,LW)^2/3, where t2,LW marks the end of the late wake and the end of a computational fluid dynamics calculation. According to the present conservative estimates, 0.36 × 10^12 and 0.7 × 10^9 grid points are needed for LES and RANS of a spatially developing wake. The numbers are 8 × 10^9 and 3 × 10^6 for LES and RANS of a temporally evolving wake.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in [Grid-point and time-step requirements for large-eddy simulation and Reynolds-averaged Navier–Stokes of stratified wakes. Physics of Fluids 34, 11 p115125 (2022)] and may be found at https://doi.org/10.1063/5.0127487.

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Work Title Grid-point and time-step requirements for large-eddy simulation and Reynolds-averaged Navier-Stokes of stratified wakes
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Open Access
Creators
  1. Jia Qi J.L. Li
  2. Xiang I.A. Yang
  3. Robert F. Kunz
Keyword
  1. Fluid wakes
  2. Turbulence simulations
  3. Turbulent flows
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Physics of Fluids
Publication Date November 8, 2022
Publisher Identifier (DOI)
  1. https://doi.org/10.1063/5.0127487
Deposited June 05, 2023

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Version 1
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  • Created
  • Added 115125_1_online.pdf
  • Added Creator Jia Qi J.L. Li
  • Added Creator Xiang I.A. Yang
  • Added Creator Robert F. Kunz
  • Published
  • Updated Keyword, Description, Publication Date Show Changes
    Keyword
    • Fluid wakes, Turbulence simulations, Turbulent flows
    Description
    • <p>Estimates of grid-point and time-step requirements exist for many canonical flows but not for stratified wakes. The purpose of this work is to fill in this gap. We apply the basic meshing principles and estimate the grid-point and time-step requirements for Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulation (LES) of stratified wake flows at high Reynolds numbers, as arise in many geophysical, aircraft, and undersea vehicle systems. Scales representative of a submarine operating in a stably stratified ocean environment are considered, and the quantitative conclusions reached here can be adapted accordingly for particular applications. For a submarine, typical wake conditions are R e 0 = 10 8 and F r 0 = 10 2, and wakes extend to Nt = 1000, where Re0 and Fr0 are the initial Reynolds number and the internal Froude number of the wake, respectively, and N is the buoyancy frequency. We consider both spatially developing and temporally evolving wakes. We show that the grid points required for LES and RANS do not depend on the Reynolds number. The ratio of the grid points needed for LES and RANS is proportional to (N t 2, LW) 2 / 3, where t 2, LW marks the end of the late wake and the end of a computational fluid dynamics calculation. According to the present conservative estimates, 0.36 × 10 12 and 0.7 × 10 9 grid points are needed for LES and RANS of a spatially developing wake. The numbers are 8 × 10 9 and 3 × 10 6 for LES and RANS of a temporally evolving wake.</p>
    • <p>Estimates of grid-point and time-step requirements exist for many canonical flows but not for stratified wakes. The purpose of this work is to fill in this gap. We apply the basic meshing principles and estimate the grid-point and time-step requirements for Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulation (LES) of stratified wake flows at high Reynolds numbers, as arise in many geophysical, aircraft, and undersea vehicle systems. Scales representative of a submarine operating in a stably stratified ocean environment are considered, and the quantitative conclusions reached here can be adapted accordingly for particular applications. For a submarine, typical wake conditions are Re0 = 10^8 and Fr0 = 10^2, and wakes extend to Nt = 1000, where Re0 and Fr0 are the initial Reynolds number and the internal Froude number of the wake, respectively, and N is the buoyancy frequency. We consider both spatially developing and temporally evolving wakes. We show that the grid points required for LES and RANS do not depend on the Reynolds number. The ratio of the grid points needed for LES and RANS is proportional to (Nt2,LW)^2/3, where t2,LW marks the end of the late wake and the end of a computational fluid dynamics calculation. According to the present conservative estimates, 0.36 × 10^12 and 0.7 × 10^9 grid points are needed for LES and RANS of a spatially developing wake. The numbers are 8 × 10^9 and 3 × 10^6 for LES and RANS of a temporally evolving wake.</p>
    Publication Date
    • 2022-11-01
    • 2022-11-08
  • Updated