Dynamic mixed turbulence modeling using a super-resolution generative adversarial approach

TL;DR

This work addresses closure fidelity in large-eddy simulations by introducing the Dynamic Mixed SR-based Model (DMSRM), which uses a super-resolution GAN (SimilarityGAN) to generate high-fidelity, super-resolved velocity fields from LES-scale inputs. The SFS stress is then evaluated on the SR grid, allowing a scale-similarity term and a dynamic Smagorinsky component to be computed in the refined space, with a Germano-based dynamic coefficient. Across a priori HIT tests and a posteriori LES runs spanning resolutions and Reynolds numbers, DMSRM outperforms the traditional Dynamic Mixed Model (DMM) in reproducing SFS stresses, backscatter, energy dissipation, and small-scale intermittency, while maintaining stability. Computationally, the method incurs memory and time overhead primarily from SR inference, which is mitigated by moderate upsampling and GPU acceleration, making DMSRM a practical alternative for LES closures with potential extensions to more complex flows.

Abstract

A dynamic mixed super-resolution model (DMSRM) for large-eddy simulations (LESs) is proposed, which combines the traditional dynamic mixed model (DMM) formulation with the generation of super-resolved velocity fields from which the subfilter-scale (SFS) stress tensor can be computed. A data-driven super-resolution generative adversarial network (SR-GAN) is employed to upsample the grid-filtered velocity fields by a factor of two, enabling the evaluation of both scale-similarity and the dynamic Smagorinsky contributions. A priori analyses of forced homogeneous isotropic turbulence show that the SR-GAN accurately reconstructs fine-scale flow features and generalizes well across different filter sizes and higher Reynolds number flow configurations, even for unseen input fields. The DMSRM reproduces SFS stresses and energy dissipation more accurately than the traditional DMM. A posteriori LES calculations further confirm that DMSRM predicts the energy spectrum and intermittency more accurately than DMM, even for different LES grid-scale resolutions and for higher Reynolds numbers than those used for training. Unlike DMM, DMSRM yields realistic backscatter and physically consistent SFS energy dissipation. These improvements arise from the physically accurate super-resolved fields generated by the SR-GAN, from which SFS stresses are directly computed. The result is a closure that accurately reproduces stress magnitudes and dissipation while reducing reliance on additional dissipation from the dynamic term. The DMSRM formulation achieves a balance of physical fidelity, robustness, and computational efficiency, offering a promising alternative to traditional DMMs for turbulence LES modeling.

Figures (8)

• Figure 1: The generator (above) and discriminator (below) structures of the similarityGAN framework. In these illustrations, $\phi_\mathrm{LR}$ denotes the LR input field, $\phi_\mathrm{{SR}}$ denotes the SR output field, and $\phi_\mathrm{{HR}}$ denotes the corresponding HR target field. Each convolutional block contains kernels of size $k$, $n$ filter maps, and $s$ strides along each spatial dimension of the convolutional layer.
• Figure 2: A priori normalized TKE spectra (left) and PDFs of $\partial u / \partial x$ (right) for "out-of-sample" input $\phi_{\mathrm{LR}}$ fields from the Re200 dataset. The top row shows results for $\mathrm{n}_{\Delta_\mathrm{LR}}=16$, and the bottom row for $\mathrm{n}_{\Delta_\mathrm{LR}}=8$. "SG-Re200 (single)" and "SG-Re200 (multiple)" refer to the similarityGAN framework trained on the Re200 dataset using either a single fixed $\phi_{\mathrm{LR}}$ resolution or multiple varying $\phi_{\mathrm{LR}}$ resolutions, respectively. "SG-Re110 (multiple)" refers to the same framework trained on the Re110 dataset with multiple varying $\phi_{\mathrm{LR}}$ resolutions (see table \ref{['tab:training_configurations']}). For clarity, red and green lines overlap with the target $\mathrm{\phi_{HR}}$ line.
• Figure 3: jPDFs of the F-DNS reference of the SFS stress tensor component $\tau^{\mathrm{F\hbox{-}DNS}}_{12}$ and the SSM component $\tau^{\mathrm{SSM}}_{12}$ (upper left), the SRM component $\tau^{\mathrm{SRM}}_{12}$ (upper right), the DMM component $\tau^{\mathrm{DMM}}_{12}$ (lower left), and the DMSRM component $\tau^{\mathrm{DMSRM}}_{12}$ (lower right), evaluated for a test snapshot of the Re200 dataset at $\mathrm{n}_{\Delta_\mathrm{LR}} = 16$. SRM and DMSRM $\tau_{12}$ components are evaluated using the SR field obtained using the SG-Re200 (multiple) training configuration. "NMSE" indicates the normalized MSE.
• Figure 4: PDFs of $\tau_{12}$ (left) and $\Pi$ (right) obtained from the DMM, DMSRM, and their individual components compared against the F-DNS reference (see Section \ref{['sec:dynamic_mixed_SR_SS_model']}), using the Re200 dataset.
• Figure 5: A posteriori normalized TKE spectra (left) and PDFs of $\partial u/\partial x$ (right) of LES coarsened by $\mathrm{n}_{\Delta_\mathrm{LR}}=16$ (top row) and $\mathrm{n}_{\Delta_\mathrm{LR}}=8$ (bottom row) from the Re200 DNS. F-DNS fields are obtained with a spectral filter kernel operator with consistent ${\Delta_\mathrm{LR}}$. The "DMSRM 200" uses the SG-Re200 (multiple) model, while "DMSRM 110" uses the SG-Re110 (multiple).