Grid-point and time-step requirements for large-eddy simulation and Reynolds-averaged Navier–Stokes of stratified wakes
Abstract
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=108 and Fr0=102, 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, 0.36×1012 and 0.7×109 grid points are needed for LES and RANS of a spatially developing wake. The numbers are 8×109 and 3×106 for LES and RANS of a temporally evolving wake.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 01, 2022
- Source ID
- 10.1063/5.0127487
Entities
People
- Jiaqi Li
- Robert F. Kunz
- X I A Yang
Organizations
- Office of Naval Research
- Pennsylvania State University