Evaluating anisotropic minimum dissipation, sigma and modulated gradient subgrid-scale models in large-eddy simulation of compressible mixing layers

Abstract

We evaluate three subgrid-scale (SGS) models in large eddy simulations (LES) of compressible mixing layers up to convective Mach number ($M_c$) 2.0. The initial momentum-thickness based Reynolds number is 1000 to match recent high-resolution simulations of the same configuration. The simulations employ the Localised Artificial Diffusivity (LAD) shock-capturing scheme and evaluate constant-coefficient and dynamic versions of Anisotropic Minimum Dissipation (AMD), Sigma, and Modulated Gradient (MGM) SGS models. The results show that the LAD scheme is crucial for stability at higher convective Mach numbers, for $M_c>1.2$. The SGS models improve the accuracy of the LES predictions, particularly for dissipation and Reynolds stresses. Dynamic versions of all three SGS models give accurate results. The AMD kernel is found to be most sensitive to the flow conditions since the dynamically obtained model coefficient varies the least with $M_c$. Dynamic versions of the SGS models enhance the agreement with reference results compared to the constant-coefficient versions, particularly for the eddy-viscosity AMD and Sigma models, and to a lesser extent for the MGM model. The results also emphasise the importance of retaining a non-zero artificial-shear-viscosity term, even in the presence of explicit SGS models.

Keywords:

• Large eddy simulation
• localised artificial diffusivity
• anisotropic minimum dissipation
• sigma
• modulated gradient model

Acknowledgments

NSG thanks the National Supercomputing Mission Grant No. DST/NSM/R&D_HPC_Applications/2021/28 for providing HPC resources on Param Brahma at IISER Pune and Param Seva at IIT Hyderabad. The authors are grateful to Dr. K. Matsuno and Prof. S. K. Lele for providing access to the high-resolution reference data. The authors thank the three anonymous reviewers for their constructive comments and feedback.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 We refer to these as DNS in view of their reported $\mathrm{\Delta }x/\eta \approx 0.33-0.57$ [52] (η is the Kolmogorov length) which is very close to the resolution requirement of a DNS [60].