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Large Eddy Simulation of Turbulent Channel Flows by the Rational LES Model

T. Iliescu, P. Fischer

TL;DR

This paper addresses subgrid-scale modeling for large-eddy simulation of wall-bounded turbulence using the Rational LES (RLES) model, derived from a Padé rational approximation to the Gaussian filter. The authors implement RLES in a spectral-element solver and compare it with the gradient and Smagorinsky models against fine DNS for channel flow at $Re_{\tau}=180$ and $395$, showing that $Re_{\tau}=180$ results favor RLES both in accuracy and stability, while at $Re_{\tau}=395$ RLES and gradient are comparable and Smagorinsky often performs best near the channel center. The work demonstrates that the RLES approach can improve SGS stress reconstruction and numerical stability, motivating future development of mixed RLES+Smagorinsky models and investigations of boundary conditions and filter-mesh relationships.

Abstract

The rational large eddy simulation (RLES) model is applied to turbulent channel flows. This approximate deconvolution model is based on a rational (subdiagonal Pade') approximation of the Fourier transform of the Gaussian filter and is proposed as an alternative to the gradient (also known as the nonlinear or tensor-diffusivity) model. We used a spectral element code to perform large eddy simulations of incompressible channel flows at Reynolds numbers based on the friction velocity and the channel half-width Re{sub tau} = 180 and Re{sub tau} = 395. We compared the RLES model with the gradient model. The RLES results showed a clear improvement over those corresponding to the gradient model, comparing well with the fine direct numerical simulation. For comparison, we also present results corresponding to a classical subgrid-scale eddy-viscosity model such as the standard Smagorinsky model.

Large Eddy Simulation of Turbulent Channel Flows by the Rational LES Model

TL;DR

This paper addresses subgrid-scale modeling for large-eddy simulation of wall-bounded turbulence using the Rational LES (RLES) model, derived from a Padé rational approximation to the Gaussian filter. The authors implement RLES in a spectral-element solver and compare it with the gradient and Smagorinsky models against fine DNS for channel flow at and , showing that results favor RLES both in accuracy and stability, while at RLES and gradient are comparable and Smagorinsky often performs best near the channel center. The work demonstrates that the RLES approach can improve SGS stress reconstruction and numerical stability, motivating future development of mixed RLES+Smagorinsky models and investigations of boundary conditions and filter-mesh relationships.

Abstract

The rational large eddy simulation (RLES) model is applied to turbulent channel flows. This approximate deconvolution model is based on a rational (subdiagonal Pade') approximation of the Fourier transform of the Gaussian filter and is proposed as an alternative to the gradient (also known as the nonlinear or tensor-diffusivity) model. We used a spectral element code to perform large eddy simulations of incompressible channel flows at Reynolds numbers based on the friction velocity and the channel half-width Re{sub tau} = 180 and Re{sub tau} = 395. We compared the RLES model with the gradient model. The RLES results showed a clear improvement over those corresponding to the gradient model, comparing well with the fine direct numerical simulation. For comparison, we also present results corresponding to a classical subgrid-scale eddy-viscosity model such as the standard Smagorinsky model.

Paper Structure

This paper contains 6 sections, 12 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The Rational LES Model
  3. Numerical Setting
  4. A Posteriori Tests for $Re_{\tau}=180$
  5. A Posteriori Tests for $Re_{\tau}=395$
  6. Conclusions

Figures (15)

  • Figure 1: Approximations to the Fourier transform of the Gaussian filter: Rational (Padé) vs. Taylor.
  • Figure 2: Problem setup for the channel flow.
  • Figure 3: Spectral element meshes: $Re_\tau=180$ (top), and $Re_\tau=395$ (bottom).
  • Figure 4: $Re_{\tau}=180$, linear total shear stress profile, an indication that the statistically steady state was reached.
  • Figure 5: $Re_{\tau}=395$, linear total shear stress profile, an indication that the statistically steady state was reached.
  • ...and 10 more figures