Super-resolution-enhanced dynamic mixed model for turbulence closure: a priori and a posteriori assessment

Accurate and efficient modeling of subfilter-scale (SFS) stresses remains a core challenge in large-eddy simulation (LES) of turbulent flows. Traditional approaches typically emphasize either structural fidelity, as in scale-similarity models (SSMs), or SFS energy dissipation, as in functional models like the dynamic Smagorinsky model (DSM), often leading to trade-offs between accuracy and stability. Dynamic mixed models (DMMs) attempt to balance these effects by combining structural and functional components. However, the accuracy of DMMs remains limited by the fidelity of the SSM component and its inherent assumptions.

In this work, we propose a dynamic mixed super-resolution model (DMSRM) that replaces the traditional SSM term with a deep-learning-based super-resolution generative adversarial network (SR-GAN) to explicitly reconstruct SFS motions on an auxiliary grid at twice the resolution of the LES grid. This approach enables a physically consistent reconstruction of the similarity term without relying on test filters or approximate deconvolution. The DSM component is dynamically evaluated using the reconstructed velocity field to ensure sufficient dissipation and numerical stability. Operating across three filter scales, the DMSRM maintains the computational efficiency of traditional DMMs while enhancing structural fidelity through data-driven modeling.

The performance of the proposed DMSRM is evaluated through a priori and a posteriori tests using forced homogeneous isotropic turbulence datasets. A priori results show a significantly stronger correlation between the DMSRM-predicted SFS stress tensor and filtered DNS data compared to the conventional DMM. A posteriori simulations demonstrate improved accuracy in capturing SFS energy dissipation and velocity gradients. These results suggest that the proposed hybrid framework offers a promising direction for integrating machine-learned models into physically consistent turbulence closures, leveraging the complementary strengths of data-driven reconstruction and physics-based modeling.