Abstract
In this work, subgrid-scale (SGS) stress and SGS heat flux of compressible isotropic turbulence are reconstructed by a spatially multi-scale artificial neural network (SMSANN). The input features of the SMSANN model are based on the first order derivatives of the primary and secondary filtered variables at different spatial locations. The SMSANN model performs much better than the gradient model in the a priori test, including the correlation coefficients and relative errors. Specifically, the correlation coefficients of the SGS stress and SGS heat flux can be larger than 0.997 and the relative errors of the SGS stress and SGS heat flux can be smaller than 0.08 for the SMSANN model. In an a posteriori analysis, the performance of the SMSANN model has been evaluated by a detailed comparison of the results of the SMSANN model and the dynamic mixed model (DMM) at a grid resolution of 643 with the Taylor Reynolds number Reλ ranging from 180 to 250. The SMSANN model shows an advantage over the DMM in the prediction of the spectra of velocity and temperature. Besides, the SMSANN model can accurately reconstruct the statistical properties of velocity and temperature and the instantaneous flow structures. An artificial neural network with consideration of spatial multiscale can deepen our understanding of large eddy simulation modeling.
Highlights
Large eddy simulation (LES) offers a good prospect for studying the complex turbulent flows, which solves the large scale structures of turbulence and models the effects of small scale flow structures on the large scale dynamics.1–10 The LES can solve more turbulent fluid dynamics than the Reynolds-averaged Navier Stokes (RANS) method and requires much less computational resources than direct numerical simulation (DNS), with high accuracy on the prediction of the large scale dynamics of turbulence11–16 Compressible turbulence is important in aerospace industry, combustion, astrophysics, and engineering problems
The input features of the spatially multi-scale artificial neural network (SMSANN) model are based on the first order derivatives of the primary and secondary filtered variables at different spatial locations
The input features of the SMSANN model are based on the first order derivatives of the primary and secondary filtered variables at different spatial locations, which depend on the three parameters Rs, Rg, and Rc
Summary
Large eddy simulation (LES) offers a good prospect for studying the complex turbulent flows, which solves the large scale structures of turbulence and models the effects of small scale flow structures on the large scale dynamics. The LES can solve more turbulent fluid dynamics than the Reynolds-averaged Navier Stokes (RANS) method and requires much less computational resources than direct numerical simulation (DNS), with high accuracy on the prediction of the large scale dynamics of turbulence Compressible turbulence is important in aerospace industry, combustion, astrophysics, and engineering problems. The main motivation of this paper is to reconstruct the subgrid-scale (SGS) stress and SGS heat flux of compressible turbulence by a spatially multi-scale artificial neural network (SMSANN) model, which. The approximate deconvolution methods are based on the truncated series expansion of the inverse filter operator, the truncated series expansion of the inverse filter operator has been rarely studied by an artificial neural network approach for the LES of turbulence. Xie et al predicted the SGS stress, SGS heat flux, and SGS force of compressible isotropic turbulence with the ANN model based on the first-order and secondorder derivatives of filtered velocity and temperature on local stencil geometry.. We developed a spatially multi-scale artificial neural network (SMSANN) model to predict the SGS stress and SGS heat flux for the LES based on DNS data of the solenoidally forced stationary compressible isotropic turbulence at a grid resolution of 10243. VI, we summarize and draw a conclusion of our study
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