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The discrete direct deconvolution model in the large eddy simulation of turbulence

Ning Chang, Zelong Yuan, Yunpeng Wang, Jianchun Wang

Abstract

The discrete direct deconvolution model (D3M) is developed for the large-eddy simulation (LES) of turbulence. The D3M is a discrete approximation of previous direct deconvolution model studied by Chang et al. ["The effect of sub-filter scale dynamics in large eddy simulation of turbulence," Phys. Fluids 34, 095104 (2022)]. For the first type model D3M-1, the original Gaussian filter is approximated by local discrete formulation of different orders, and direct inverse of the discrete filter is applied to reconstruct the unfiltered flow field. The inverse of original Gaussian filter can be also approximated by local discrete formulation, leading to a fully local model D3M-2. Compared to traditional models including the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM), the D3M-1 and D3M-2 exhibit much larger correlation coefficients and smaller relative errors in the a priori studies. In the a posteriori validations, both D3M-1 and D3M-2 can accurately predict turbulence statistics, including velocity spectra, probability density functions (PDFs) of sub-filter scale (SFS) stresses and SFS energy flux, as well as time-evolving kinetic energy spectra, momentum thickness, and Reynolds stresses in turbulent mixing layer. Moreover, the proposed model can also well capture spatial structures of the Q-criterion iso surfaces. Thus, the D3M holds potential as an effective SFS modeling approach in turbulence simulations.

The discrete direct deconvolution model in the large eddy simulation of turbulence

Abstract

The discrete direct deconvolution model (D3M) is developed for the large-eddy simulation (LES) of turbulence. The D3M is a discrete approximation of previous direct deconvolution model studied by Chang et al. ["The effect of sub-filter scale dynamics in large eddy simulation of turbulence," Phys. Fluids 34, 095104 (2022)]. For the first type model D3M-1, the original Gaussian filter is approximated by local discrete formulation of different orders, and direct inverse of the discrete filter is applied to reconstruct the unfiltered flow field. The inverse of original Gaussian filter can be also approximated by local discrete formulation, leading to a fully local model D3M-2. Compared to traditional models including the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM), the D3M-1 and D3M-2 exhibit much larger correlation coefficients and smaller relative errors in the a priori studies. In the a posteriori validations, both D3M-1 and D3M-2 can accurately predict turbulence statistics, including velocity spectra, probability density functions (PDFs) of sub-filter scale (SFS) stresses and SFS energy flux, as well as time-evolving kinetic energy spectra, momentum thickness, and Reynolds stresses in turbulent mixing layer. Moreover, the proposed model can also well capture spatial structures of the Q-criterion iso surfaces. Thus, the D3M holds potential as an effective SFS modeling approach in turbulence simulations.
Paper Structure (14 sections, 97 equations, 19 figures, 8 tables)

This paper contains 14 sections, 97 equations, 19 figures, 8 tables.

Table of Contents

  1. INTRODUCTION
  2. GOVERNING EQUATIONS AND NUMERICAL METHODS
  3. A PRIORI STUDY OF DIFFERENT SFS MODELS
  4. A POSTERIORI STUDY of LES
  5. Homogeneous Isotropic Turbulence (HIT)
  6. Temporally evolving turbulent mixing layer (TML)
  7. CONCLUSION
  8. THE DISCRETE GAUSSIAN FILTER
  9. D3M-1
  10. Convolution
  11. Deconvolution
  12. D3M-2
  13. PSEUDO-SPECTRAL METHOD WITH FULLY DEALIASING
  14. THE DYNAMIC SFS MODELS

Figures (19)

  • Figure 1: The comparisons of the discrete filters and the exact Gaussian filter: (a) $\mathrm{FGR}=1$, (b) $\mathrm{FGR}=2$, and (c) $\mathrm{FGR}=4$.
  • Figure 2: The comparison of the inverse of discrete filters and the inverse of exact Gaussian filter: (a) D3M-1 at $\mathrm{FGR}=1$, (b) D3M-2 at $\mathrm{FGR}=1$, (c) D3M-1 at $\mathrm{FGR}=2$, (d) D3M-2 at $\mathrm{FGR}=2$, (e) D3M-1 at $\mathrm{FGR}=4$, and (f) D3M-2 at $\mathrm{FGR}=4$.
  • Figure 3: Correlation coefficients and relative errors of shear components of the SFS stresses $\tau_{12}^A$ for different models with multiple orders of discrete filter at filter width $\bar{\Delta}=32h_{DNS}$ in the a priori study: (a) correlation coefficients C and (b) relative errors $E_r$.
  • Figure 4: Velocity spectra of the a posteriori studies at a grid resolution of $N=128^3$ for different orders of discrete filters: (a) second-order, (b) fourth-order, (c) sixth-order, and (d) eighth-order.
  • Figure 5: PDFs of the SFS stresses at a grid resolution of $N=128^3$ for different orders of discrete filters: (a) second-order, (b) fourth-order, (c) sixth-order, and (d) eighth-order.
  • ...and 14 more figures