Volume 27, Issue 3
An Approximate Second-Order Closure Model for Large-Eddy Simulation of Compressible Isotropic Turbulence

Chenyue Xie, Jianchun Wang, Hui Li, Minping Wan & Shiyi Chen

Commun. Comput. Phys., 27 (2020), pp. 775-808.

Published online: 2020-02

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  • Abstract

In this paper, the detailed dynamic characteristics of the subgrid scale (SGS) stress tensor and heat flux are investigated through Taylor series expansion in numericalsimulations ofcompressibleisotropicturbulence. Anewapproximatesecond-order closure (ASOC) model is introduced based on the transport equations of the first-order Taylor series approximation of SGS stress tensor and heat flux. The proposed model is implemented in large eddy simulation (LES) of compressible isotropic turbulence. Detailed comparisons with direct numerical simulation (DNS) dataset using both a priori and a posteriori approaches are carried out. A priori tests show that, SGS stress tensor and heat flux have high correlations with the first-order Taylor series approximation. Their root mean square (rms) values are close to those of the first-order Taylor series approximation. In a posteriori tests, the proposed ASOC model yields good agreement with DNS dataset. Compared with the results of the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM), the ASOC model predicts better energy spectra at high wavenumbers. The probability density function (PDF) and the structure functions of velocity and thermodynamic variables are further studied, demonstrating that the statistical properties of the simulated flows are improved by the ASOC model. The numerical results illustrate the ability of the model to improve the statistical properties of the simulated flows in the context of LES. Finally, a simplified ASOC model can be derived by neglecting the effect of density gradient for low turbulent Mach number turbulence.

  • Keywords

Compressible turbulence, large eddy simulation, Taylor series expansion, approximate second-order closure model.

  • AMS Subject Headings

76F05, 76F50, 76F65, 76N99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xiecy@sustech.edu.cn (Chenyue Xie)

wangjc@sustech.edu.cn (Jianchun Wang)

li hui@whu.edu.cn (Hui Li)

wanmp@sustech.edu.cn (Minping Wan)

chensy@sustech.edu.cn (Shiyi Chen)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-775, author = {Xie , Chenyue and Wang , Jianchun and Li , Hui and Wan , Minping and Chen , Shiyi }, title = {An Approximate Second-Order Closure Model for Large-Eddy Simulation of Compressible Isotropic Turbulence}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {3}, pages = {775--808}, abstract = {

In this paper, the detailed dynamic characteristics of the subgrid scale (SGS) stress tensor and heat flux are investigated through Taylor series expansion in numericalsimulations ofcompressibleisotropicturbulence. Anewapproximatesecond-order closure (ASOC) model is introduced based on the transport equations of the first-order Taylor series approximation of SGS stress tensor and heat flux. The proposed model is implemented in large eddy simulation (LES) of compressible isotropic turbulence. Detailed comparisons with direct numerical simulation (DNS) dataset using both a priori and a posteriori approaches are carried out. A priori tests show that, SGS stress tensor and heat flux have high correlations with the first-order Taylor series approximation. Their root mean square (rms) values are close to those of the first-order Taylor series approximation. In a posteriori tests, the proposed ASOC model yields good agreement with DNS dataset. Compared with the results of the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM), the ASOC model predicts better energy spectra at high wavenumbers. The probability density function (PDF) and the structure functions of velocity and thermodynamic variables are further studied, demonstrating that the statistical properties of the simulated flows are improved by the ASOC model. The numerical results illustrate the ability of the model to improve the statistical properties of the simulated flows in the context of LES. Finally, a simplified ASOC model can be derived by neglecting the effect of density gradient for low turbulent Mach number turbulence.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0306}, url = {http://global-sci.org/intro/article_detail/cicp/13929.html} }
TY - JOUR T1 - An Approximate Second-Order Closure Model for Large-Eddy Simulation of Compressible Isotropic Turbulence AU - Xie , Chenyue AU - Wang , Jianchun AU - Li , Hui AU - Wan , Minping AU - Chen , Shiyi JO - Communications in Computational Physics VL - 3 SP - 775 EP - 808 PY - 2020 DA - 2020/02 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2018-0306 UR - https://global-sci.org/intro/cicp/13929.html KW - Compressible turbulence, large eddy simulation, Taylor series expansion, approximate second-order closure model. AB -

In this paper, the detailed dynamic characteristics of the subgrid scale (SGS) stress tensor and heat flux are investigated through Taylor series expansion in numericalsimulations ofcompressibleisotropicturbulence. Anewapproximatesecond-order closure (ASOC) model is introduced based on the transport equations of the first-order Taylor series approximation of SGS stress tensor and heat flux. The proposed model is implemented in large eddy simulation (LES) of compressible isotropic turbulence. Detailed comparisons with direct numerical simulation (DNS) dataset using both a priori and a posteriori approaches are carried out. A priori tests show that, SGS stress tensor and heat flux have high correlations with the first-order Taylor series approximation. Their root mean square (rms) values are close to those of the first-order Taylor series approximation. In a posteriori tests, the proposed ASOC model yields good agreement with DNS dataset. Compared with the results of the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM), the ASOC model predicts better energy spectra at high wavenumbers. The probability density function (PDF) and the structure functions of velocity and thermodynamic variables are further studied, demonstrating that the statistical properties of the simulated flows are improved by the ASOC model. The numerical results illustrate the ability of the model to improve the statistical properties of the simulated flows in the context of LES. Finally, a simplified ASOC model can be derived by neglecting the effect of density gradient for low turbulent Mach number turbulence.

Chenyue Xie, Jianchun Wang, Hui Li, Minping Wan & Shiyi Chen. (2020). An Approximate Second-Order Closure Model for Large-Eddy Simulation of Compressible Isotropic Turbulence. Communications in Computational Physics. 27 (3). 775-808. doi:10.4208/cicp.OA-2018-0306
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