Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence

Abstract

Dynamic iterative approximate deconvolution (DIAD) models with Galilean invariance are developed for subgrid-scale (SGS) stress in the large-eddy simulation (LES) of turbulence. The DIAD models recover the unfiltered variables using the filtered variables at neighboring points and iteratively update model coefficients without any a priori knowledge of direct numerical simulation (DNS) data. The a priori analysis indicates that the DIAD models reconstruct the unclosed SGS stress much better than the classical velocity gradient model and approximate deconvolution model with different filter scales ranging from viscous to inertial regions. We also propose a small-scale eddy viscosity (SSEV) model as an artificial dissipation to suppress the numerical instability based on a scale-similarity-based dynamic method without affecting large-scale flow structures. The SSEV model can predict a velocity spectrum very close to that of DNS data, similar to the traditional implicit large-eddy simulation. In the a posteriori testing, the SSEV-enhanced DIAD model is superior to the SSEV model, dynamic Smagorinsky model, and dynamic mixed model, which predicts a variety of statistics and instantaneous spatial structures of turbulence much closer to those of filtered DNS data without significantly increasing the computational cost. The types of explicit filters, local spatial averaging methods, and initial conditions do not significantly affect the accuracy of DIAD models. We further successfully apply DIAD models to the homogeneous shear turbulence. These results illustrate that the current SSEV-enhanced DIAD approach is promising in the development of advanced SGS models in the LES of turbulence.

Dynamic nonlinear algebraic models with scale-similarity dynamic procedure for large-eddy simulation of turbulence

“…Here, the hat stands for the test filtering at scale 4 . Similar to the DSM model, the model coefficients C 1 and C 2 are calculated by the Germano identity dynamic procedure, namely [21,22]…”

“…Large-eddy simulation (LES) is an effective approach which adopts the coarse mesh to only resolve the large flow scales and model the effect of residual subgrid scales (SGS) on the resolved large scales [4][5][6][7]. Extensive SGS models have been proposed to reconstruct the unclosed SGS stress in previous works, including the Smagorinsky model [8][9][10], the velocity-gradient model (VGM) [11], the scale-similarity model [12,13], the implicit LES (ILES) [14][15][16], the Reynolds-stress-constrained LES model [17], the data-driven models [18][19][20][21][22][23][24][25], etc. The Smagorinsky model is one of the commonly-used SGS models whose model coefficient for the original version is statically adjusted by the experimental and DNS data in the early stage.…”

“…A dynamic version of the spatial gradient model (DSGM) [46] was proposed for the parameter determination strategy. Yuan et al developed deconvolutional artificial neural network (DANN) [21] and dynamic iterative approximate deconvolution (DIAD) models [22] to recover the local unfiltered velocity with the neighboring spatial stencils of the filtered velocity. A scale-similarity-based dynamic procedure (SSD) was proposed to adaptively calculate the weights of the spatial stencil [22].…”

“…Yuan et al developed deconvolutional artificial neural network (DANN) [21] and dynamic iterative approximate deconvolution (DIAD) models [22] to recover the local unfiltered velocity with the neighboring spatial stencils of the filtered velocity. A scale-similarity-based dynamic procedure (SSD) was proposed to adaptively calculate the weights of the spatial stencil [22]. The DIAD model with the SSD procedure is superior to the other conventional dynamic SGS models in the reconstruction of the statistics of velocity and transient coherent structures of turbulence [22].…”

“…A scale-similarity-based dynamic procedure (SSD) was proposed to adaptively calculate the weights of the spatial stencil [22]. The DIAD model with the SSD procedure is superior to the other conventional dynamic SGS models in the reconstruction of the statistics of velocity and transient coherent structures of turbulence [22].…”