  Direct numerical simulation (DNS) of turbulent flows is computationally
expensive and cannot be applied to flows with large Reynolds numbers. Large
eddy simulation (LES) is an alternative that is computationally less demanding,
but is unable to capture all of the scales of turbulent transport accurately.
Our goal in this work is to build a new data-driven methodology based on
super-resolution techniques to reconstruct DNS data from LES predictions. We
leverage the underlying physical relationships to regularize the relationships
amongst different physical variables. We also introduce a hierarchical
generative process and a reverse degradation process to fully explore the
correspondence between DNS and LES data. We demonstrate the effectiveness of
our method through a single-snapshot experiment and a cross-time experiment.
The results confirm that our method can better reconstruct high-resolution DNS
data over space and over time in terms of pixel-wise reconstruction error and
structural similarity. Visual comparisons show that our method performs much
better in capturing fine-level flow dynamics.
